Essec\Faculty\Model\Profile {#2233
  #_id: "B00072305"
  #_source: array:40 [
    "bid" => "B00072305"
    "academId" => "2051"
    "slug" => "kratz-marie"
    "fullName" => "Marie KRATZ"
    "lastName" => "KRATZ"
    "firstName" => "Marie"
    "title" => array:2 [
      "fr" => "Professeur"
      "en" => "Professor"
    ]
    "email" => "kratz@essec.edu"
    "status" => "ACTIF"
    "campus" => "Campus de Cergy"
    "departments" => []
    "phone" => "+33 (0)1 34 43 36 43"
    "sites" => []
    "facNumber" => "2051"
    "externalCvUrl" => "https://faculty.essec.edu/cv/kratz-marie/pdf"
    "googleScholarUrl" => ""
    "facOrcId" => "https://orcid.org/0000-0001-5160-2042"
    "career" => array:15 [
      0 => Essec\Faculty\Model\CareerItem {#2309
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2006-10-01"
          "endDate" => "2011-08-31"
          "isInternalPosition" => true
          "type" => array:2 [
            "fr" => "Positions académiques principales"
            "en" => "Full-time academic appointments"
          ]
          "label" => array:2 [
            "fr" => "Professeur associé"
            "en" => "Associate Professor"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      1 => Essec\Faculty\Model\CareerItem {#2310
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2011-09-01"
          "endDate" => null
          "isInternalPosition" => true
          "type" => array:2 [
            "fr" => "Positions académiques principales"
            "en" => "Full-time academic appointments"
          ]
          "label" => array:2 [
            "fr" => "Professeur"
            "en" => "Full Professor"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      2 => Essec\Faculty\Model\CareerItem {#2311
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "1994-02-01"
          "endDate" => "2006-09-30"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Maître de Conférences"
            "en" => "Assistant, then associate professor"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris Descartes (Paris V)"
            "en" => "Université Paris Descartes (Paris V)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      3 => Essec\Faculty\Model\CareerItem {#2312
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2017-07-01"
          "endDate" => "2020-07-31"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Professeure visitante à temps partiel"
            "en" => "Part-time Visiting Professor"
          ]
          "institution" => array:2 [
            "fr" => "Lund University. School of Economics and Management. Statistics Department"
            "en" => "Lund University. School of Economics and Management. Statistics Department"
          ]
          "country" => array:2 [
            "fr" => "Suède"
            "en" => "Sweden"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      4 => Essec\Faculty\Model\CareerItem {#2313
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2012-07-01"
          "endDate" => "2012-12-31"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Stage à FINMA, Swiss Financial Market Supervisory Authority"
            "en" => "Internship at FINMA, Swiss Financial Market Supervisory Authority"
          ]
          "institution" => array:2 [
            "fr" => "Swiss Financial Market Supervisory Authority FINMA"
            "en" => "Swiss Financial Market Supervisory Authority FINMA"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      5 => Essec\Faculty\Model\CareerItem {#2314
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2013-01-01"
          "endDate" => null
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Directrice du CREAR - Center of Research in Econo-finance and Actuarial Science on Risk"
            "en" => "Director of CREAR - Center of Research in Econo-finance and Actuarial Science on Risk"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      6 => Essec\Faculty\Model\CareerItem {#2315
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2013-09-15"
          "endDate" => null
          "isInternalPosition" => true
          "type" => array:2 [
            "fr" => "Positions académiques principales"
            "en" => "Full-time academic appointments"
          ]
          "label" => array:2 [
            "fr" => "Actuaire agrégée"
            "en" => "Fellow of the French Institute of Actuaries"
          ]
          "institution" => array:2 [
            "fr" => "Institut des Actuaires"
            "en" => "Institut des Actuaires"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      7 => Essec\Faculty\Model\CareerItem {#2316
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "1999-10-01"
          "endDate" => "2000-09-30"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Délégation C.N.R.S.  (SAMOS-MATISSE, UMR 8595)"
            "en" => "Delegation C.N.R.S.  (SAMOS-MATISSE, UMR 8595"
          ]
          "institution" => array:2 [
            "fr" => "CNRS - Centre national de la recherche scientifique"
            "en" => "CNRS - Centre national de la recherche scientifique"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      8 => Essec\Faculty\Model\CareerItem {#2317
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2008-10-01"
          "endDate" => "2012-10-31"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Co-responsable de la filière actuariat ESSEC-ISUP"
            "en" => "Co-responsible of the ESSEC-ISUP actuarial track"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      9 => Essec\Faculty\Model\CareerItem {#2318
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2012-10-01"
          "endDate" => null
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Directrice de la filière actuariat ESSEC-ISUP"
            "en" => "Director of the ESSEC-ISUP actuarial track"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      10 => Essec\Faculty\Model\CareerItem {#2319
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2012-10-01"
          "endDate" => "2016-12-01"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Coordinatrice scientifique du projet européen ‘RARE’ - Risk Analysis, Ruin and Extremes - FP7-PEOPLE-2012-IRSES - Marie Curie Actions, qui vise à renforcer les partenariats de recherche à travers des échanges de professeurs et des activités de networking entre organisations de recherche européennes et organisations de recherche d'autres pays (12 partenaires)"
            "en" => "Scientific Coordinator of the European Project ‘RARE’ - Risk Analysis, Ruin and Extremes - FP7-PEOPLE-2012-IRSES - Marie Curie Actions, which aims to strengthen research partnerships through staff exchanges and networking activities between European research organizations and research organizations from other countries. (12 partners)"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      11 => Essec\Faculty\Model\CareerItem {#2320
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2011-12-01"
          "endDate" => "2014-12-01"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Responsable d'une équipe de recherche"
            "en" => "Director of the Research program with SWISS LIFE on: Consequences of the population ageing on the insurances loss. Impacts on the automobile prevention"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      12 => Essec\Faculty\Model\CareerItem {#2321
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2013-10-01"
          "endDate" => null
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Membre affilié de RiskLab"
            "en" => "Affiliated member to RiskLab"
          ]
          "institution" => array:2 [
            "fr" => "ETH Zurich"
            "en" => "ETH Zurich"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      13 => Essec\Faculty\Model\CareerItem {#2322
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2004-10-01"
          "endDate" => "2009-09-30"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other appointments"
            "fr" => "Autres positions"
          ]
          "label" => array:2 [
            "fr" => "Membre de MAP5 (Mathématiques Appliquées), UMR8145"
            "en" => "Member of MAP5 (Applied Mathematics), UMR8145"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris Descartes (Paris V)"
            "en" => "Université Paris Descartes (Paris V)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      14 => Essec\Faculty\Model\CareerItem {#2323
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2011-12-01"
          "endDate" => "2015-09-01"
          "isInternalPosition" => true
          "type" => array:2 [
            "en" => "Other Academic Appointments"
            "fr" => "Autres positions académiques"
          ]
          "label" => array:2 [
            "fr" => "Directeur du programme de recherche ESSEC - SWISS LIFE "Conséquences de la population le vieillissement sur la perte d'assurance. Impacts sur la prévention automobile""
            "en" => "Director of the research program ESSEC - SWISS LIFE ”Consequences of the population ageing on the insurances loss. Impacts on the automobile prevention”"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
    ]
    "diplomes" => array:3 [
      0 => Essec\Faculty\Model\Diplome {#2235
        #_index: null
        #_id: null
        #_source: array:6 [
          "diplome" => "DIPLOMA"
          "type" => array:2 [
            "fr" => "Diplômes"
            "en" => "Diplomas"
          ]
          "year" => "1993"
          "label" => array:2 [
            "en" => "Doctorate in Applied Mathematics"
            "fr" => "Doctorat en Mathématiques Appliquées"
          ]
          "institution" => array:2 [
            "fr" => "Université Pierre et Marie Curie (UPMC)"
            "en" => "Université Pierre et Marie Curie (UPMC)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      1 => Essec\Faculty\Model\Diplome {#2237
        #_index: null
        #_id: null
        #_source: array:6 [
          "diplome" => "DIPLOMA"
          "type" => array:2 [
            "fr" => "Diplômes"
            "en" => "Diplomas"
          ]
          "year" => "2005"
          "label" => array:2 [
            "en" => "HDR"
            "fr" => "HDR"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris 1 Panthéon-Sorbonne"
            "en" => "Université Paris 1 Panthéon-Sorbonne"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      2 => Essec\Faculty\Model\Diplome {#2234
        #_index: null
        #_id: null
        #_source: array:6 [
          "diplome" => "CERT"
          "type" => array:2 [
            "fr" => "Certificats"
            "en" => "Certificates"
          ]
          "year" => "2010"
          "label" => array:2 [
            "en" => "Global colloquium on participant-centered learning"
            "fr" => "Global colloquium on participant-centered learning"
          ]
          "institution" => array:2 [
            "fr" => "Harvard Business School"
            "en" => "Harvard Business School"
          ]
          "country" => array:2 [
            "fr" => "États-Unis"
            "en" => "United States of America"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
    ]
    "bio" => array:2 [
      "fr" => """
        <p>Professeure, depuis Oct. 2011</p>\n
        \n
        <p>Professeure visitante &agrave; temps partiel (juillet 2017-juillet 2020), Department of Statistics, Lund University, Su&egrave;de</p>\n
        \n
        <p>Directrice de CREAR - <b>C</b>entre de <b>R</b>echerche en <b>E</b>cono-finance et <b>A</b>ctuariat sur le <b>R</b>isk - (<a href="http://crear.essec.edu/research/working-group-on-risk" target="_blank">http://crear.essec.edu</a>), depuis Jan. 2013</p>\n
        \n
        <p>Actuaire Agr&eacute;g&eacute;e de l&#39;Institut des Actuaires (IA 2013; qualification 2015; agr&eacute;gation 2016)</p>\n
        \n
        <p>Professeure Associ&eacute;e, Oct. 2006 - Sept. 2011</p>\n
        \n
        <p>Ma&icirc;tre de Conf&eacute;rences&agrave; l&#39;Universit&eacute; Paris Descartes (UFR Math&eacute;matiques &amp; Informatique) jusqu&#39;en Oct. 2006</p>\n
        \n
        <p>D&eacute;l&eacute;gation C.N.R.S. (SAMOS-MATISSE, UMR 8595, 1999-2000)</p>\n
        \n
        <p>Post-doctorat/d&eacute;l&eacute;gation, avec S. Resnick (Fall sem. 1993, 94, 95), Cornell University (O.R.I.E.), Ithaca, N.Y., USA</p>\n
        \n
        <p>Doctorat de Math&eacute;matiques Appliqu&eacute;es effectu&eacute; en grande partie au Center for Stochastic Processes, UNC Chapel Hill</p>
        """
      "en" => """
        <p>ESSEC Full Professor, from Oct. 2011</p>\n
        \n
        <p>Part time visting professor (July 2017-July 2020), Department of Statistics, Lund University, Sweden</p>\n
        \n
        <p>Director of CREAR - <b>C</b>enter of <b>R</b>esearch in <b>E</b>cono-finance and <b>A</b>ctuarial Science on <b>R</b>isk - (see<b> </b>http://crear.essec.edu), from Jan. 2013</p>\n
        \n
        <p>Fellow of the &quot;Institut des Actuaires&quot; (IA 2013; qualification 2015; certification 2015; fellow 2016)</p>\n
        \n
        <p>ESSEC Associate Professor, Oct. 2006 - Sept. 2011</p>\n
        \n
        <p>Ma&icirc;tre de Conf&eacute;rences at the University Ren&eacute; Descartes Paris V (UFR Math&eacute;matiques &amp; Informatique) until Oct. 2006</p>\n
        \n
        <p>Delegation C.N.R.S. (SAMOS-MATISSE, UMR 8595, 1999-2000)</p>\n
        \n
        <p>Post-doctorat/delegation with S. Resnick (Fall sem. 1993, 94, 95), Cornell University (O.R.I.E.), Ithaca, N.Y., USA</p>\n
        \n
        <p>PhD. in Applied Mathematics, made to a great extent at the Center for Stochastic Processes, UNC Chapel Hill, USA</p>\n
        \n
        <p>&nbsp;</p>\n
        \n
        <p>&nbsp;</p>
        """
    ]
    "department" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "site" => array:2 [
      "fr" => ""
      "en" => ""
    ]
    "industrrySectors" => array:2 [
      "fr" => "Banques - Assurance"
      "en" => "Banks - Insurance"
    ]
    "researchFields" => array:2 [
      "fr" => "Théorie des probabilités et statistiques - Modélisation du risque et Actuariat - Probabilité Appliquée - Analyse des données statistiques - Science actuarielle - Modélisation du risque"
      "en" => "Probability Theory & Mathematical Statistics - Risk Modelling & Actuarial Science - Applied Probability - Statistical Data Analysis - Insurance Mathematics - Risk Analysis and Management"
    ]
    "teachingFields" => array:2 [
      "fr" => "Mathématiques - Théorie des probabilités et statistiques - Modélisation du risque et Actuariat - Analyse des données statistiques - Marchés financiers et institutions financières"
      "en" => "Mathematics - Probability Theory & Mathematical Statistics - Risk Modelling & Actuarial Science - Statistical Data Analysis - Financial Markets & Institutions"
    ]
    "distinctions" => array:10 [
      0 => Essec\Faculty\Model\Distinction {#2324
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2012-12-01"
          "label" => array:2 [
            "fr" => "FP7-PEOPLE-2012-IRSES - Marie Curie Actions"
            "en" => "FP7-PEOPLE-2012-IRSES - Marie Curie Actions"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "Union Européenne"
            "en" => "Union Européenne"
          ]
          "country" => array:2 [
            "fr" => "Belgique"
            "en" => "Belgium"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      1 => Essec\Faculty\Model\Distinction {#2325
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2012-12-01"
          "label" => array:2 [
            "fr" => "European FP7-RARE project"
            "en" => "European FP7-RARE project"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      2 => Essec\Faculty\Model\Distinction {#2326
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2016-01-01"
          "label" => array:2 [
            "fr" => "Visiting scholar and Member of the advisory board of QRFE"
            "en" => "Visiting scholar and Member of the advisory board of QRFE"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "Durham University"
            "en" => "Durham University"
          ]
          "country" => array:2 [
            "fr" => "Royaume-Uni"
            "en" => "United Kingdom"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      3 => Essec\Faculty\Model\Distinction {#2327
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2014-01-01"
          "label" => array:2 [
            "fr" => "Tata Institute for Fundamental Research (TIFR, India), by a grant from the Indo-French Center for Applied Mathematics (IFCAM) for a research project between M. Kratz & S. Vadlamani"
            "en" => "Tata Institute for Fundamental Research (TIFR, India), by a grant from the Indo-French Center for Applied Mathematics (IFCAM) for a research project between M. Kratz & S. Vadlamani"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "Tata Institute for Fundamental Research"
            "en" => "Tata Institute for Fundamental Research"
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      4 => Essec\Faculty\Model\Distinction {#2328
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2016-01-01"
          "label" => array:2 [
            "fr" => "Institute for Mathematical Research (FIM)"
            "en" => "Institute for Mathematical Research (FIM)"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "ETH Zurich"
            "en" => "ETH Zurich"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      5 => Essec\Faculty\Model\Distinction {#2329
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2017-01-01"
          "label" => array:2 [
            "fr" => "ETH Risk Center"
            "en" => "ETH Risk Center"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "ETH Zurich"
            "en" => "ETH Zurich"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      6 => Essec\Faculty\Model\Distinction {#2330
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2010-01-01"
          "label" => array:2 [
            "fr" => "Ceressec Research projects grants"
            "en" => "Ceressec Research projects grants"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      7 => Essec\Faculty\Model\Distinction {#2331
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2014-09-01"
          "label" => array:2 [
            "fr" => "Labex MME-DII"
            "en" => "Labex MME-DII"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "Labex MME-DII"
            "en" => "Labex MME-DII"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      8 => Essec\Faculty\Model\Distinction {#2332
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2018-04-01"
          "label" => array:2 [
            "fr" => "International chair labex MME-DII & ESSEC CREAR on"
            "en" => "International chair labex MME-DII & ESSEC CREAR on Risk Analysis & Management, held by Dr. Michel Dacorogna"
          ]
          "type" => array:2 [
            "fr" => "Bourses"
            "en" => "Grants"
          ]
          "tri" => " 2 "
          "institution" => array:2 [
            "fr" => "ESSEC CREAR"
            "en" => "ESSEC CREAR"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      9 => Essec\Faculty\Model\Distinction {#2333
        #_index: null
        #_id: null
        #_source: array:6 [
          "date" => "2013-09-15"
          "label" => array:2 [
            "fr" => "Actuaire Agrégée IA"
            "en" => "Fellow of the French Institute of Actuaries"
          ]
          "type" => array:2 [
            "fr" => "Prix"
            "en" => "Awards"
          ]
          "tri" => " 1 "
          "institution" => array:2 [
            "fr" => "Institut des Actuaires"
            "en" => "Institut des Actuaires"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
    ]
    "teaching" => array:31 [
      0 => Essec\Faculty\Model\TeachingItem {#2299
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => null
          "program" => null
          "label" => array:2 [
            "fr" => "Impact des risques climatiques extrêmes : la question de l’assurabilité"
            "en" => "Impact des risques climatiques extrêmes : la question de l’assurabilité"
          ]
          "type" => array:2 [
            "fr" => "Co-directeur de thèse"
            "en" => "Thesis co-director"
          ]
          "institution" => array:2 [
            "fr" => "LSCE, CEA-CNRS"
            "en" => "LSCE, CEA-CNRS"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      1 => Essec\Faculty\Model\TeachingItem {#2303
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2024"
          "program" => null
          "label" => array:2 [
            "fr" => "Contributions à l’étude des lois de temps d’atteinte. Applications."
            "en" => "Contributions à l’étude des lois de temps d’atteinte. Applications."
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Claude Bernard Lyon 1"
            "en" => "Université Claude Bernard Lyon 1"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      2 => Essec\Faculty\Model\TeachingItem {#2298
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2024"
          "program" => null
          "label" => array:2 [
            "fr" => "Characterising distributions and their tails using multivariate quantiles and depths"
            "en" => "Characterising distributions and their tails using multivariate quantiles and depths"
          ]
          "type" => array:2 [
            "fr" => "Co-directeur de thèse"
            "en" => "Thesis co-director"
          ]
          "institution" => array:2 [
            "fr" => "TIFR–CAM"
            "en" => "TIFR–CAM"
          ]
          "country" => array:2 [
            "fr" => "Inde"
            "en" => "India"
          ]
        ]
        +lang: "fr"
      }
      3 => Essec\Faculty\Model\TeachingItem {#2302
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2023"
          "program" => null
          "label" => array:2 [
            "fr" => """
              Geometrical characteristics of random fields -\n
              On the perimeter of a binary image: estimation procedures, testing, and numerical implementations.
              """
            "en" => """
              Geometrical characteristics of random fields -\n
              On the perimeter of a binary image: estimation procedures, testing, and numerical implementations.
              """
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris Cité"
            "en" => "Université Paris Cité"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      4 => Essec\Faculty\Model\TeachingItem {#2301
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2023"
          "program" => null
          "label" => array:2 [
            "fr" => "Cyber Risk and Insurance: Risk and Dependence Modelling and Optimal Pricing of Cyber Assistance"
            "en" => "Cyber Risk and Insurance: Risk and Dependence Modelling and Optimal Pricing of Cyber Assistance"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Technische Universität München (TUM)"
            "en" => "Technische Universität München (TUM)"
          ]
          "country" => array:2 [
            "fr" => "Allemagne"
            "en" => "Germany"
          ]
        ]
        +lang: "fr"
      }
      5 => Essec\Faculty\Model\TeachingItem {#2300
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2022"
          "program" => null
          "label" => array:2 [
            "fr" => "Statistical analysis of road accidents in the region Franche-Comté: risk factors for accident injuries and spatial modelling for accident occurrences"
            "en" => "Statistical analysis of road accidents in the region Franche-Comté: risk factors for accident injuries and spatial modelling for accident occurrences"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université de Franche-Comté"
            "en" => "Université de Franche-Comté"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      6 => Essec\Faculty\Model\TeachingItem {#2296
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2022"
          "program" => null
          "label" => array:2 [
            "fr" => "Assessing the time dependence of multivariate extremes"
            "en" => "Assessing the time dependence of multivariate extremes"
          ]
          "type" => array:2 [
            "fr" => "Président de jury"
            "en" => "Thesis jury president"
          ]
          "institution" => array:2 [
            "fr" => "Sorbonne Université"
            "en" => "Sorbonne Université"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      7 => Essec\Faculty\Model\TeachingItem {#2307
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2016"
          "endDate" => "2022"
          "program" => null
          "label" => array:2 [
            "fr" => "Risk analysis (3 grants from Labex MME-DII , from 2020)"
            "en" => "Risk analysis (3 grants from Labex MME-DII , from 2020)"
          ]
          "type" => array:2 [
            "fr" => "Encadrement UV de recherche"
            "en" => "Supervision of Research UV"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      8 => Essec\Faculty\Model\TeachingItem {#2308
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2012"
          "endDate" => "2022"
          "program" => null
          "label" => array:2 [
            "fr" => "Banks, Insurance companies, Consulting companies"
            "en" => "Banks, Insurance companies, Consulting companies"
          ]
          "type" => array:2 [
            "fr" => "Tutorat apprentissage"
            "en" => "Apprenticeship tutoring"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      9 => Essec\Faculty\Model\TeachingItem {#2306
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2012"
          "endDate" => "2022"
          "program" => null
          "label" => array:2 [
            "fr" => ""
            "en" => "Supervision of Master Thesis"
          ]
          "type" => array:2 [
            "fr" => "Encadrement de mémoire"
            "en" => "Supervision of dissertation"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      10 => Essec\Faculty\Model\TeachingItem {#2286
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2019"
          "endDate" => "2021"
          "program" => null
          "label" => array:2 [
            "fr" => "Cyber risk"
            "en" => "Cyber risk"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "ETH Risk Center"
            "en" => "ETH Risk Center"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
      }
      11 => Essec\Faculty\Model\TeachingItem {#2287
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2020"
          "program" => null
          "label" => array:2 [
            "fr" => "Pro-cyclicality of Risk Measurements : Empirical Quantification and Theoretical Confirmation"
            "en" => "Pro-cyclicality of Risk Measurements : Empirical Quantification and Theoretical Confirmation"
          ]
          "type" => array:2 [
            "fr" => "Directeur de thèse"
            "en" => "Thesis director"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      12 => Essec\Faculty\Model\TeachingItem {#2291
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2019"
          "program" => null
          "label" => array:2 [
            "fr" => "Algorithmes de machine learning en assurance : solvabilité, textmining, anonymisation et transparence."
            "en" => "Algorithmes de machine learning en assurance : solvabilité, textmining, anonymisation et transparence."
          ]
          "type" => array:2 [
            "fr" => "Membre de jury"
            "en" => "Thesis jury member"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris-Est Marne-la-Vallée (UPEM)"
            "en" => "Université Paris-Est Marne-la-Vallée (UPEM)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      13 => Essec\Faculty\Model\TeachingItem {#2279
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2017"
          "endDate" => "2017"
          "program" => null
          "label" => array:2 [
            "fr" => "Singapore Actuarial Society Forum sur 'Overview of Copulas for Actuaries in Management'"
            "en" => "Singapore Actuarial Society Forum on 'Overview of Copulas for Actuaries in Management'"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "Singapore Actuarial Society"
            "en" => "Singapore Actuarial Society"
          ]
          "country" => array:2 [
            "fr" => "Singapour"
            "en" => "Singapore"
          ]
        ]
        +lang: "fr"
      }
      14 => Essec\Faculty\Model\TeachingItem {#2278
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2017"
          "endDate" => "2017"
          "program" => null
          "label" => array:2 [
            "fr" => "Atelier de travail de recherche du CFA France, 'A self-Calibrating Method for Heavy Tailed Data Modeling'"
            "en" => "CFA France Research Workshop, 'A self-Calibrating Method for Heavy Tailed Data Modeling'"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "CFA Society France"
            "en" => "CFA Society France"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      15 => Essec\Faculty\Model\TeachingItem {#2290
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2017"
          "program" => null
          "label" => array:2 [
            "fr" => "Credit Valuation Adjustment of Credit Default Swaps by Lévy Structural Models"
            "en" => "Credit Valuation Adjustment of Credit Default Swaps by Lévy Structural Models"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Monash University"
            "en" => "Monash University"
          ]
          "country" => array:2 [
            "fr" => "Australie"
            "en" => "Australia"
          ]
        ]
        +lang: "fr"
      }
      16 => Essec\Faculty\Model\TeachingItem {#2281
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2017"
          "endDate" => "2017"
          "program" => null
          "label" => array:2 [
            "fr" => "Mini workshop sur 'Modeling and Backtesting Heavy Tailed Data'"
            "en" => "Mini-workshop on 'Modeling and Backtesting Heavy Tailed Data'"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "Durham University"
            "en" => "Durham University"
          ]
          "country" => array:2 [
            "fr" => "Royaume-Uni"
            "en" => "United Kingdom"
          ]
        ]
        +lang: "fr"
      }
      17 => Essec\Faculty\Model\TeachingItem {#2280
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2017"
          "endDate" => "2017"
          "program" => null
          "label" => array:2 [
            "fr" => "Atelier de travail d'1/2 journée 'EVT and its Application to finance and insurance',"
            "en" => "1/2 day workshop on 'EVT and its Application to finance and insurance',"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "ETH Risk Center"
            "en" => "ETH Risk Center"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
      }
      18 => Essec\Faculty\Model\TeachingItem {#2288
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2016"
          "program" => null
          "label" => array:2 [
            "fr" => "Contributions actuarielles et statistiques pour l'analyse de risques en assurance liés au vieillissement de la population, notamment en assurance automobile"
            "en" => "Contributions actuarielles et statistiques pour l'analyse de risques en assurance liés au vieillissement de la population, notamment en assurance automobile"
          ]
          "type" => array:2 [
            "fr" => "Directeur de thèse"
            "en" => "Thesis director"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      19 => Essec\Faculty\Model\TeachingItem {#2284
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2016"
          "endDate" => "2016"
          "program" => null
          "label" => array:2 [
            "fr" => "Séminaire exécutif de deux jours sur la Gestion de Risques Quantitative (Quantitative Risk Management)"
            "en" => "Two days executive seminar on Quantitative Risk Management"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "National Institute of Securities Markets (NISM)"
            "en" => "National Institute of Securities Markets (NISM)"
          ]
          "country" => array:2 [
            "fr" => "Inde"
            "en" => "India"
          ]
        ]
        +lang: "fr"
      }
      20 => Essec\Faculty\Model\TeachingItem {#2283
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2016"
          "endDate" => "2016"
          "program" => null
          "label" => array:2 [
            "fr" => "'A self-Calibrating Method for Heavy Tailed Data Modeling'"
            "en" => "'A self-Calibrating Method for Heavy Tailed Data Modeling'"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "Swiss Re"
            "en" => "Swiss Re"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
      }
      21 => Essec\Faculty\Model\TeachingItem {#2282
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2016"
          "endDate" => "2016"
          "program" => null
          "label" => array:2 [
            "fr" => "'An implicit backtest for Expected Shortfall via a simple multinomial approach'"
            "en" => "'An implicit backtest for Expected Shortfall via a simple multinomial approach'"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "Bank of International Settlements"
            "en" => "Bank of International Settlements"
          ]
          "country" => array:2 [
            "fr" => "Suisse"
            "en" => "Switzerland"
          ]
        ]
        +lang: "fr"
      }
      22 => Essec\Faculty\Model\TeachingItem {#2292
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2015"
          "program" => null
          "label" => array:2 [
            "fr" => "Modélisation de la dépendance et estimation du risque agrégé"
            "en" => "Modélisation de la dépendance et estimation du risque agrégé"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Claude Bernard Lyon 1"
            "en" => "Université Claude Bernard Lyon 1"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      23 => Essec\Faculty\Model\TeachingItem {#2289
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2015"
          "program" => null
          "label" => array:2 [
            "fr" => "Approche algébrique et théorie des valeurs extrêmes pour la détection de ruptures: application aux signaux biomédicaux"
            "en" => "Approche algébrique et théorie des valeurs extrêmes pour la détection de ruptures: application aux signaux biomédicaux"
          ]
          "type" => array:2 [
            "fr" => "Co-directeur de thèse"
            "en" => "Thesis co-director"
          ]
          "institution" => array:2 [
            "fr" => "URCA"
            "en" => "URCA"
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      24 => Essec\Faculty\Model\TeachingItem {#2293
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2014"
          "program" => null
          "label" => array:2 [
            "fr" => "Modelado matemático de sistemas dinámicos en epidemiología"
            "en" => "Modelado matemático de sistemas dinámicos en epidemiología"
          ]
          "type" => array:2 [
            "fr" => "Membre de jury"
            "en" => "Thesis jury member"
          ]
          "institution" => array:2 [
            "fr" => "Universidad de Malaga"
            "en" => "Universidad de Malaga"
          ]
          "country" => array:2 [
            "fr" => "Espagne"
            "en" => "Spain"
          ]
        ]
        +lang: "fr"
      }
      25 => Essec\Faculty\Model\TeachingItem {#2294
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2013"
          "program" => null
          "label" => array:2 [
            "fr" => "Valeurs extrêmes de mosaïques aléatoires"
            "en" => "Valeurs extrêmes de mosaïques aléatoires"
          ]
          "type" => array:2 [
            "fr" => "Président de jury"
            "en" => "Thesis jury president"
          ]
          "institution" => array:2 [
            "fr" => "Université de Rouen"
            "en" => "Université de Rouen"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      26 => Essec\Faculty\Model\TeachingItem {#2285
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2013"
          "endDate" => "2013"
          "program" => null
          "label" => array:2 [
            "fr" => "'An Introduction to Quantitative Risk Management' - cours enseigné durant l'Ecole d'été sur la Gestion des risques en Finance et en Assurance (Summer School on Risk Management in Finance and Insurance)"
            "en" => "'An Introduction to Quantitative Risk Management' - course given at the Summer School on Risk Management in Finance and Insurance"
          ]
          "type" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "institution" => array:2 [
            "fr" => "National Economics University"
            "en" => "National Economics University"
          ]
          "country" => array:2 [
            "fr" => "Viêt Nam"
            "en" => "Vietnam"
          ]
        ]
        +lang: "fr"
      }
      27 => Essec\Faculty\Model\TeachingItem {#2295
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2008"
          "program" => null
          "label" => array:2 [
            "fr" => "Estimation et tests en théorie des valeurs extrêmes"
            "en" => "Estimation et tests en théorie des valeurs extrêmes"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Pierre et Marie Curie (UPMC)"
            "en" => "Université Pierre et Marie Curie (UPMC)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
      }
      28 => Essec\Faculty\Model\TeachingItem {#2305
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "2008"
          "endDate" => "2008"
          "program" => null
          "label" => array:2 [
            "fr" => "Research training at ESSEC: "Extreme Value Theory for discrete random variables, with applications in Epidemiology and in Finance""
            "en" => "Research training at ESSEC: "Extreme Value Theory for discrete random variables, with applications in Epidemiology and in Finance""
          ]
          "type" => array:2 [
            "fr" => "Coaching de groupe"
            "en" => "Coaching"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      29 => Essec\Faculty\Model\TeachingItem {#2304
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => "1997"
          "endDate" => "2006"
          "program" => null
          "label" => array:2 [
            "fr" => "Paris Descartes Master students final professional trainings (MST2-ISASH, DESS MSB, Master 2 IMSV)"
            "en" => "Paris Descartes Master students final professional trainings (MST2-ISASH, DESS MSB, Master 2 IMSV)"
          ]
          "type" => array:2 [
            "fr" => "Coaching de groupe"
            "en" => "Coaching"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
      }
      30 => Essec\Faculty\Model\TeachingItem {#2297
        #_index: null
        #_id: null
        #_source: array:7 [
          "startDate" => null
          "endDate" => "2004"
          "program" => null
          "label" => array:2 [
            "fr" => "Estabilidad en Sistemas Neuronales Realimentados. Aplicación al Control"
            "en" => "Estabilidad en Sistemas Neuronales Realimentados. Aplicación al Control"
          ]
          "type" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Universidad de Malaga"
            "en" => "Universidad de Malaga"
          ]
          "country" => array:2 [
            "fr" => "Espagne"
            "en" => "Spain"
          ]
        ]
        +lang: "fr"
      }
    ]
    "otherActivities" => array:42 [
      0 => Essec\Faculty\Model\ExtraActivity {#2238
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2009-10-01"
          "endDate" => null
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Organisatrice du Working-Group-on-Risk ( séries de séminaires bimensuels du CREAR)"
            "en" => "Organizer of the  Working-Group-on-Risk (CREAR series of fortnightly seminars)"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      1 => Essec\Faculty\Model\ExtraActivity {#2232
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2018-07-26"
          "endDate" => "2018-07-27"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "'Cyber risks – Threats and Opportunities for the Asia Pacific Insurance Industry', 4th SAS ERM - ESSEC CREAR Conference"
            "en" => "'Cyber risks – Threats and Opportunities for the Asia Pacific Insurance Industry', 4th SAS ERM - ESSEC CREAR Conference"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => "Singapour"
            "en" => "Singapore"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      2 => Essec\Faculty\Model\ExtraActivity {#2236
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2016-12-01"
          "endDate" => "2016-12-01"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "'Lois Scientifiques et Modèles Mathématiques: de la physique à l'actuariat', Colloque SCOR-IA, Paris"
            "en" => "'Lois Scientifiques et Modèles Mathématiques: de la physique à l'actuariat', Colloquium SCOR-IA, Paris"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      3 => Essec\Faculty\Model\ExtraActivity {#2239
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2016-10-20"
          "endDate" => "2016-10-20"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "'Financial risk: Black Swan or Opportunities?'"
            "en" => "'Financial risk: Black Swan or Opportunities?'"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      4 => Essec\Faculty\Model\ExtraActivity {#2240
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2016-07-03"
          "endDate" => "2016-07-08"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Conclusion de la Conférence Internationale 'RARE' sur le sujet Risk Analysis, Ruin theory, Extremes, La Baule (CREAR, avec le soutien de Swiss Re, Institut des Actuaires, SCOR science foundation, Bank of England, AMIES-IA, IFoA, BFA-SFdS)"
            "en" => "Concluding International 'RARE' Conference on Risk Analysis, Ruin theory, Extremes, La Baule (CREAR, with the support of Swiss Re, Institut des Actuaires, SCOR science foundation, Bank of England, AMIES-IA, IFoA, BFA-SFdS)"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      5 => Essec\Faculty\Model\ExtraActivity {#2241
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2015-06-10"
          "endDate" => "2015-06-10"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Table Ronde Internationale sur les nouvelles règles IFRS : Actuaries meet Accountants,  Paris La Défense (CREAR, avec le soutien de Labex MME-DII, Institut des Actuaires & BFA-SFdS)"
            "en" => "International Round Table on New IFRS rules : Actuaries meet Accountants, Paris La Défense (CREAR, with the support of Labex MME-DII, Institut des Actuaires & BFA-SFdS)"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      6 => Essec\Faculty\Model\ExtraActivity {#2242
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2014-06-20"
          "endDate" => "2014-06-20"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Mini workshop "Small data " (CREAR & BFA-SFdS), 13ème Congrès des Actuaires, Paris"
            "en" => "Mini-workshop "Small data " (CREAR & BFA-SFdS), 13ème Congrès des Actuaires, Paris"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      7 => Essec\Faculty\Model\ExtraActivity {#2243
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2012-11-19"
          "endDate" => "2012-11-19"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Conférence ESSEC CREAR - SWISS LIFE: 'Risk, Insurance and Longevity', ESSEC La Défense"
            "en" => "ESSEC CREAR - SWISS LIFE conference: 'Risk, Insurance and Longevity', ESSEC La Défense"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      8 => Essec\Faculty\Model\ExtraActivity {#2244
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2010-04-09"
          "endDate" => "2010-04-09"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
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          "label" => array:2 [
            "fr" => "Groupe BFA - SFdS & ESSEC WG Risk:  'Régulation financière' , Paris"
            "en" => "BFA - SFdS & ESSEC WG Risk: 'Financial Regulation' , Paris"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      9 => Essec\Faculty\Model\ExtraActivity {#2245
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2009-01-26"
          "endDate" => "2009-01-26"
          "year" => null
          "uuid" => "201"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Organisation d'une conférence ou d'un séminaire"
            "en" => "Organization of a conference or a seminar"
          ]
          "label" => array:2 [
            "fr" => "Workshop européen EVT & Finance - Paris La défense"
            "en" => "European workshop on EVT & Finance - Paris La défense"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      10 => Essec\Faculty\Model\ExtraActivity {#2246
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "1994-09-30"
          "endDate" => null
          "year" => null
          "uuid" => "501"
          "type" => array:2 [
            "fr" => "Activités professionnelles"
            "en" => "Professional activities"
          ]
          "subType" => array:2 [
            "fr" => "Membre d'une association professionnelle, d'un groupe d'experts ou d'un conseil d'administration"
            "en" => "Member of a professional association, of an expert group or of a board of directors"
          ]
          "label" => array:2 [
            "fr" => "BERNOULLI SOCIETY (pour les statistiques mathématiques et les probabilités- section ISI)"
            "en" => "BERNOULLI SOCIETY (for Mathematical Statistics and Probability- ISI section)"
          ]
          "institution" => array:2 [
            "fr" => "International Statistical Institute"
            "en" => "International Statistical Institute"
          ]
          "country" => array:2 [
            "fr" => "Pays-Bas"
            "en" => "Netherlands"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      11 => Essec\Faculty\Model\ExtraActivity {#2247
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2007-09-01"
          "endDate" => null
          "year" => null
          "uuid" => "501"
          "type" => array:2 [
            "fr" => "Activités professionnelles"
            "en" => "Professional activities"
          ]
          "subType" => array:2 [
            "fr" => "Membre d'une association professionnelle, d'un groupe d'experts ou d'un conseil d'administration"
            "en" => "Member of a professional association, of an expert group or of a board of directors"
          ]
          "label" => array:2 [
            "fr" => "SFdS - Société Française de Statistique"
            "en" => "SFdS - Société Française de Statistique"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      12 => Essec\Faculty\Model\ExtraActivity {#2248
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2014-01-01"
          "endDate" => null
          "year" => null
          "uuid" => "R1_101"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Participation au comité scientifique d'une conférence ou reviewer pour une conférence"
            "en" => "Participation in scientific commissions or reviewer for a conference"
          ]
          "label" => array:2 [
            "fr" => "Membre du Comité Scientifique de la IRFRC Conference, NTU Singapore"
            "en" => "Member of the Scientific Committee of the IRFRC Conference, NTU Singapore"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      13 => Essec\Faculty\Model\ExtraActivity {#2249
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2015-01-01"
          "endDate" => null
          "year" => null
          "uuid" => "R1_101"
          "type" => array:2 [
            "fr" => "Activités de recherche"
            "en" => "Research activities"
          ]
          "subType" => array:2 [
            "fr" => "Participation au comité scientifique d'une conférence ou reviewer pour une conférence"
            "en" => "Participation in scientific commissions or reviewer for a conference"
          ]
          "label" => array:2 [
            "fr" => "Membre du Comité Consultatif de QRFE, Durham Business School"
            "en" => "Member of the Advisory Board of QRFE, Durham Business School"
          ]
          "institution" => array:2 [
            "fr" => null
            "en" => null
          ]
          "country" => array:2 [
            "fr" => "Royaume-Uni"
            "en" => "United Kingdom"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      14 => Essec\Faculty\Model\ExtraActivity {#2250
        #_index: null
        #_id: null
        #_source: array:9 [
          "startDate" => "2010-10-01"
          "endDate" => null
          "year" => null
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            "en" => "Member of a professional association, of an expert group or of a board of directors"
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          ]
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            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      15 => Essec\Faculty\Model\ExtraActivity {#2251
        #_index: null
        #_id: null
        #_source: array:9 [
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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      16 => Essec\Faculty\Model\ExtraActivity {#2252
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        #_id: null
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          "country" => array:2 [
            "fr" => "Malaisie"
            "en" => "Malaysia"
          ]
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      17 => Essec\Faculty\Model\ExtraActivity {#2253
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        #_id: null
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          ]
          "country" => array:2 [
            "fr" => "Royaume-Uni"
            "en" => "United Kingdom"
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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      18 => Essec\Faculty\Model\ExtraActivity {#2254
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        #_id: null
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            "fr" => "Forum d'Experts sur les Mesures et la Régulation du Risque en Assurance, Swiss Re Learning Center (sur invitation), Zurich"
            "en" => "Experts Forum on Risk Measures and Regulation in Insurance, Swiss Re Learning Center (by invitation), Zurich"
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            "en" => null
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        #_id: null
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      21 => Essec\Faculty\Model\ExtraActivity {#2257
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        #_id: null
        #_source: array:9 [
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            "en" => "Research activities"
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          "subType" => array:2 [
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            "en" => "Participation in scientific commissions or reviewer for a conference"
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          "label" => array:2 [
            "fr" => "Membre du Comité scientifique de l'ISUP-UPMC"
            "en" => "Member of the Scientific Committee of ISUP-UPMC"
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            "en" => null
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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      22 => Essec\Faculty\Model\ExtraActivity {#2258
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        #_id: null
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            "en" => "Member of the ANR Ameriska on the Analysis of Multivariate Extremes and RISKs Assessment"
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      23 => Essec\Faculty\Model\ExtraActivity {#2259
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      24 => Essec\Faculty\Model\ExtraActivity {#2260
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        #_id: null
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          "subType" => array:2 [
            "fr" => "Membre d'une association académique"
            "en" => "Member of an academic association"
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          "label" => array:2 [
            "fr" => "Responsable à Paris Descartes du GREFI-MEFI (Groupe de Recherche Européen Franco Italien - Matematica Fisica)"
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      25 => Essec\Faculty\Model\ExtraActivity {#2261
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        #_id: null
        #_source: array:9 [
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            "fr" => null
            "en" => null
          ]
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      26 => Essec\Faculty\Model\ExtraActivity {#2262
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        #_id: null
        #_source: array:9 [
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      27 => Essec\Faculty\Model\ExtraActivity {#2263
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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      28 => Essec\Faculty\Model\ExtraActivity {#2264
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      30 => Essec\Faculty\Model\ExtraActivity {#2266
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            "en" => "Institut des Actuaires"
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      32 => Essec\Faculty\Model\ExtraActivity {#2268
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            "fr" => "ELected member of the Board of Overseers"
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      35 => Essec\Faculty\Model\ExtraActivity {#2271
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      36 => Essec\Faculty\Model\ExtraActivity {#2272
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      38 => Essec\Faculty\Model\ExtraActivity {#2274
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        #_id: null
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            "en" => "IMS - Bernoulli Society"
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        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      39 => Essec\Faculty\Model\ExtraActivity {#2275
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            "en" => "Fondation "La Science Statistique""
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        +"parent": Essec\Faculty\Model\Profile {#2233}
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      40 => Essec\Faculty\Model\ExtraActivity {#2276
        #_index: null
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        #_source: array:9 [
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      41 => Essec\Faculty\Model\ExtraActivity {#2277
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    "theses" => array:17 [
      0 => Essec\Faculty\Model\These {#2334
        #_index: null
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        #_source: array:9 [
          "year" => "2023"
          "startDate" => null
          "endDate" => "2023"
          "student" => "ABAACH M."
          "firstJob" => ""
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            "fr" => """
              Geometrical characteristics of random fields -\n
              On the perimeter of a binary image: estimation procedures, testing, and numerical implementations.
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            "en" => """
              Geometrical characteristics of random fields -\n
              On the perimeter of a binary image: estimation procedures, testing, and numerical implementations.
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            "en" => "Thesis referee"
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          "institution" => array:2 [
            "fr" => "Université Paris Cité"
            "en" => "Université Paris Cité"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      1 => Essec\Faculty\Model\These {#2335
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => null
          "startDate" => null
          "endDate" => null
          "student" => "AKA S."
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          "label" => array:2 [
            "fr" => "Impact des risques climatiques extrêmes : la question de l’assurabilité"
            "en" => "Impact of extreme climate risks: the question of insurability"
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          "role" => array:2 [
            "fr" => "Co-directeur de thèse"
            "en" => "Thesis co-director"
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          "institution" => array:2 [
            "fr" => "LSCE, CEA-CNRS"
            "en" => "LSCE, CEA-CNRS"
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          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      2 => Essec\Faculty\Model\These {#2336
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2004"
          "startDate" => null
          "endDate" => "2004"
          "student" => "ATENCIA M."
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          "label" => array:2 [
            "fr" => "Estabilidad en Sistemas Neuronales Realimentados. Aplicación al Control"
            "en" => "Estabilidad en Sistemas Neuronales Realimentados. Aplicación al Control"
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          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
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          "institution" => array:2 [
            "fr" => "Universidad de Malaga"
            "en" => "Universidad de Malaga"
          ]
          "country" => array:2 [
            "fr" => "Espagne"
            "en" => "Spain"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      3 => Essec\Faculty\Model\These {#2337
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2017"
          "startDate" => null
          "endDate" => "2017"
          "student" => "BENTLEY M."
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          "label" => array:2 [
            "fr" => "Credit Valuation Adjustment of Credit Default Swaps by Lévy Structural Models"
            "en" => """
              Credit Valuation Adjustment of Credit Default Swaps \n
              by Lévy Structural Models Credit Valuation Adjustment of Credit Default Swaps by Lévy Structural Models
              """
          ]
          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
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          "institution" => array:2 [
            "fr" => "Monash University"
            "en" => "Monash University"
          ]
          "country" => array:2 [
            "fr" => "Australie"
            "en" => "Australia"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      4 => Essec\Faculty\Model\These {#2338
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2020"
          "startDate" => null
          "endDate" => "2020"
          "student" => "Bräutigam M."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Pro-cyclicality of Risk Measurements : Empirical Quantification and Theoretical Confirmation"
            "en" => "Pro-cyclicality of Risk Measurements : Empirical Quantification and Theoretical Confirmation"
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          "role" => array:2 [
            "fr" => "Directeur de thèse"
            "en" => "Thesis director"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      5 => Essec\Faculty\Model\These {#2339
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2022"
          "startDate" => null
          "endDate" => "2022"
          "student" => "BURITICA G."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Assessing the time dependence of multivariate extremes"
            "en" => "Assessing the time dependence of multivariate extremes"
          ]
          "role" => array:2 [
            "fr" => "Président de jury"
            "en" => "Thesis jury president"
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          "institution" => array:2 [
            "fr" => "Sorbonne Université"
            "en" => "Sorbonne Université"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      6 => Essec\Faculty\Model\These {#2340
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2016"
          "startDate" => null
          "endDate" => "2016"
          "student" => "Cadena M."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Contributions actuarielles et statistiques pour l'analyse de risques en assurance liés au vieillissement de la population, notamment en assurance automobile"
            "en" => "Contributions actuarielles et statistiques pour l'analyse de risques en assurance liés au vieillissement de la population, notamment en assurance automobile"
          ]
          "role" => array:2 [
            "fr" => "Directeur de thèse"
            "en" => "Thesis director"
          ]
          "institution" => array:2 [
            "fr" => "ESSEC Business School"
            "en" => "ESSEC Business School"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      7 => Essec\Faculty\Model\These {#2341
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2013"
          "startDate" => null
          "endDate" => "2013"
          "student" => "CHEVANIER N."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Valeurs extrêmes de mosaïques aléatoires"
            "en" => "Valeurs extrêmes de mosaïques aléatoires"
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          "role" => array:2 [
            "fr" => "Président de jury"
            "en" => "Thesis jury president"
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          "institution" => array:2 [
            "fr" => "Université de Rouen"
            "en" => "Université de Rouen"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      8 => Essec\Faculty\Model\These {#2342
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2015"
          "startDate" => null
          "endDate" => "2015"
          "student" => "CUBEROS A."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Modélisation de la dépendance et estimation du risque agrégé"
            "en" => "Modélisation de la dépendance et estimation du risque agrégé"
          ]
          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Claude Bernard Lyon 1"
            "en" => "Université Claude Bernard Lyon 1"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      9 => Essec\Faculty\Model\These {#2343
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2015"
          "startDate" => null
          "endDate" => "2015"
          "student" => "Debbabi N."
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          "label" => array:2 [
            "fr" => "Approche algébrique et théorie des valeurs extrêmes pour la détection de ruptures: application aux signaux biomédicaux"
            "en" => "Approche algébrique et théorie des valeurs extrêmes pour la détection de ruptures: application aux signaux biomédicaux"
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          "role" => array:2 [
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            "en" => "Thesis co-director"
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          "institution" => array:2 [
            "fr" => "URCA"
            "en" => "URCA"
          ]
          "country" => array:2 [
            "fr" => null
            "en" => null
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      10 => Essec\Faculty\Model\These {#2344
        #_index: null
        #_id: null
        #_source: array:9 [
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          "startDate" => null
          "endDate" => "2024"
          "student" => "DOROBANTU D."
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            "en" => "Contributions à l’étude des lois de temps d’atteinte. Applications."
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          "institution" => array:2 [
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            "en" => "Université Claude Bernard Lyon 1"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      11 => Essec\Faculty\Model\These {#2345
        #_index: null
        #_id: null
        #_source: array:9 [
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          "startDate" => null
          "endDate" => "2014"
          "student" => "GARCÍA GARALUZ M. E."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Modelado matemático de sistemas dinámicos en epidemiología"
            "en" => "Modelado matemático de sistemas dinámicos en epidemiología"
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          "role" => array:2 [
            "fr" => "Membre de jury"
            "en" => "Thesis jury member"
          ]
          "institution" => array:2 [
            "fr" => "Universidad de Malaga"
            "en" => "Universidad de Malaga"
          ]
          "country" => array:2 [
            "fr" => "Espagne"
            "en" => "Spain"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      12 => Essec\Faculty\Model\These {#2346
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2019"
          "startDate" => null
          "endDate" => "2019"
          "student" => "LY A."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Algorithmes de machine learning en assurance : solvabilité, textmining, anonymisation et transparence."
            "en" => "Algorithmes de machine learning en assurance : solvabilité, textmining, anonymisation et transparence."
          ]
          "role" => array:2 [
            "fr" => "Membre de jury"
            "en" => "Thesis jury member"
          ]
          "institution" => array:2 [
            "fr" => "Université Paris-Est Marne-la-Vallée (UPEM)"
            "en" => "Université Paris-Est Marne-la-Vallée (UPEM)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      13 => Essec\Faculty\Model\These {#2347
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2024"
          "startDate" => null
          "endDate" => "2024"
          "student" => "SINGHA S."
          "firstJob" => "Postdoc at Telecom Paris, IP Paris"
          "label" => array:2 [
            "fr" => "Characterising distributions and their tails using multivariate quantiles and depths"
            "en" => "Characterising distributions and their tails using multivariate quantiles and depthsCharacterising distributions and their tails using multivariate quantiles and depths"
          ]
          "role" => array:2 [
            "fr" => "Co-directeur de thèse"
            "en" => "Thesis co-director"
          ]
          "institution" => array:2 [
            "fr" => "TIFR–CAM"
            "en" => "TIFR–CAM"
          ]
          "country" => array:2 [
            "fr" => "Inde"
            "en" => "India"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      14 => Essec\Faculty\Model\These {#2348
        #_index: null
        #_id: null
        #_source: array:9 [
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          "startDate" => null
          "endDate" => "2022"
          "student" => "SPYCHALA C."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Statistical analysis of road accidents in the region Franche-Comté: risk factors for accident injuries and spatial modelling for accident occurrences"
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          ]
          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université de Franche-Comté"
            "en" => "Université de Franche-Comté"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      15 => Essec\Faculty\Model\These {#2349
        #_index: null
        #_id: null
        #_source: array:9 [
          "year" => "2008"
          "startDate" => null
          "endDate" => "2008"
          "student" => "TOULEMONDE G."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Estimation et tests en théorie des valeurs extrêmes"
            "en" => "Estimation et tests en théorie des valeurs extrêmes"
          ]
          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Université Pierre et Marie Curie (UPMC)"
            "en" => "Université Pierre et Marie Curie (UPMC)"
          ]
          "country" => array:2 [
            "fr" => "France"
            "en" => "France"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
      16 => Essec\Faculty\Model\These {#2350
        #_index: null
        #_id: null
        #_source: array:9 [
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          "startDate" => null
          "endDate" => "2023"
          "student" => "ZELLER G."
          "firstJob" => ""
          "label" => array:2 [
            "fr" => "Cyber Risk and Insurance: Risk and Dependence Modelling and Optimal Pricing of Cyber Assistance"
            "en" => "Cyber Risk and Insurance: Risk and Dependence Modelling and Optimal Pricing of Cyber Assistance"
          ]
          "role" => array:2 [
            "fr" => "Rapporteur"
            "en" => "Thesis referee"
          ]
          "institution" => array:2 [
            "fr" => "Technische Universität München (TUM)"
            "en" => "Technische Universität München (TUM)"
          ]
          "country" => array:2 [
            "fr" => "Allemagne"
            "en" => "Germany"
          ]
        ]
        +lang: "fr"
        +"parent": Essec\Faculty\Model\Profile {#2233}
      }
    ]
    "indexedAt" => "2024-12-21T17:21:22.000Z"
    "contributions" => array:173 [
      0 => Essec\Faculty\Model\Contribution {#2352
        #_index: "academ_contributions"
        #_id: "769"
        #_source: array:18 [
          "id" => "769"
          "slug" => "central-limit-theorem-for-lipschitz-killing-curvatures-of-excursion-sets-of-gaussian-random-fields"
          "yearMonth" => "2017-04"
          "year" => "2017"
          "title" => "Central Limit Theorem for Lipschitz–Killing Curvatures of Excursion Sets of Gaussian Random Fields"
          "description" => "KRATZ, M. et VADLAMANI, S. (2017). Central Limit Theorem for Lipschitz–Killing Curvatures of Excursion Sets of Gaussian Random Fields. <i>Journal of Theoretical Probability</i>, 31(3), pp. 1729-1758."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI Sreekar"
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          "ouvrage" => ""
          "keywords" => array:5 [
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            1 => "CLT"
            2 => "Excursion sets"
            3 => "Gaussian fields"
            4 => "Lipschitz-Killing curvatures"
          ]
          "updatedAt" => "2024-07-09 09:52:53"
          "publicationUrl" => "https://link.springer.com/article/10.1007%2Fs10959-017-0760-6"
          "publicationInfo" => array:3 [
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            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear functionals of Gaussian random fields have been studied [see Berman (Sojourns and extremes of stochastic processes, Wadsworth & Brooks, Monterey, 1991), Kratz and León (Extremes 3(1):57–86, 2000), Kratz and León (J Theor Probab 14(3):639–672, 2001), Meshenmoser and Shashkin (Stat Probab Lett 81(6):642–646, 2011), Pham (Stoch Proc Appl 123(6):2158–2174, 2013), Spodarev (Chapter in modern stochastics and applications, volume 90 of the series Springer optimization and its applications, pp 221–241, 2013) for a sample of works in such settings], the most recent addition being (Adler and Naitzat in Stoch Proc Appl 2016; Estrade and León in Ann Probab 2016) where a central limit theorem (CLT) for Euler integral and Euler–Poincaré characteristic, respectively, of the excursions set of a Gaussian random field is proven under some conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz–Killing curvatures of excursion sets of Gaussian random fields, in an appropriate setting."
            "en" => "Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, asymptotics of nonlinear functionals of Gaussian random fields have been studied [see Berman (Sojourns and extremes of stochastic processes, Wadsworth & Brooks, Monterey, 1991), Kratz and León (Extremes 3(1):57–86, 2000), Kratz and León (J Theor Probab 14(3):639–672, 2001), Meshenmoser and Shashkin (Stat Probab Lett 81(6):642–646, 2011), Pham (Stoch Proc Appl 123(6):2158–2174, 2013), Spodarev (Chapter in modern stochastics and applications, volume 90 of the series Springer optimization and its applications, pp 221–241, 2013) for a sample of works in such settings], the most recent addition being (Adler and Naitzat in Stoch Proc Appl 2016; Estrade and León in Ann Probab 2016) where a central limit theorem (CLT) for Euler integral and Euler–Poincaré characteristic, respectively, of the excursions set of a Gaussian random field is proven under some conditions. In this paper, we obtain a CLT for some global geometric functionals, called the Lipschitz–Killing curvatures of excursion sets of Gaussian random fields, in an appropriate setting."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      1 => Essec\Faculty\Model\Contribution {#2354
        #_index: "academ_contributions"
        #_id: "777"
        #_source: array:18 [
          "id" => "777"
          "slug" => "characterization-of-a-general-class-of-tail-probability-distributions"
          "yearMonth" => "2019-11"
          "year" => "2019"
          "title" => "Characterization of a general class of tail probability distributions"
          "description" => "CADENA, M., KRATZ, M. et OMEY, E. (2019). Characterization of a general class of tail probability distributions. <i>Statistics & Probability Letters</i>, 154, pp. 108553."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
            2 => array:1 [
              "name" => "OMEY E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:5 [
            0 => "Karamata functions"
            1 => "Laplace transform"
            2 => "Probability distribution"
            3 => "Regularly varying function"
            4 => "Semi-exponential tail distribution"
          ]
          "updatedAt" => "2022-03-04 16:20:32"
          "publicationUrl" => "https://www.sciencedirect.com/science/article/abs/pii/S0167715219301907?via%3Dihub"
          "publicationInfo" => array:3 [
            "pages" => "108553"
            "volume" => "154"
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behavior at infinity, when normalized by a logarithm (Cadena et al., 2016–17). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is addressed here, studying general classes of distribution functions of the type limx→∞logU(x)H(x)=ρ≤0 for normalizing functions H such that limx→∞H(x)=∞."
            "en" => "Recently, new classes of positive and measurable functions, M(ρ) and M(±∞), have been defined in terms of their asymptotic behavior at infinity, when normalized by a logarithm (Cadena et al., 2016–17). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is addressed here, studying general classes of distribution functions of the type limx→∞logU(x)H(x)=ρ≤0 for normalizing functions H such that limx→∞H(x)=∞."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      2 => Essec\Faculty\Model\Contribution {#2356
        #_index: "academ_contributions"
        #_id: "781"
        #_source: array:18 [
          "id" => "781"
          "slug" => "chord-length-distribution-functions-and-rice-formulae-application-to-random-media"
          "yearMonth" => "2012-09"
          "year" => "2012"
          "title" => "Chord-Length Distribution Functions and Rice Formulae. Application to Random Media"
          "description" => "ESTRADE, A., IRIBARREN, I. et KRATZ, M. (2012). Chord-Length Distribution Functions and Rice Formulae. Application to Random Media. <i>Extremes</i>, 15(3), pp. 333-352."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ESTRADE A."
            ]
            2 => array:1 [
              "name" => "IRIBARREN I."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:7 [
            0 => "Chord"
            1 => "(Up/down) crossing"
            2 => "Gaussian process"
            3 => "Level-cut process"
            4 => "Palm probability"
            5 => "Porous medium"
            6 => "Rice formula"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-011-0141-y"
          "publicationInfo" => array:3 [
            "pages" => "333-352"
            "volume" => "15"
            "number" => "3"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it, and see each line as a one-dimensional level-cut process with value 0 or 1 according to whether a regular stationary process X is less or greater than a given level. The intervals corresponding to the points at which X is in a given phase are named chords. We are interested in obtaining information on the chord-length distribution functions. Working with the Palm probability measure and using level crossings techniques, in particular, Rice methods, we can obtain not only the exact analytical formula of the chord-length distribution function but also the joint distribution function of the lengths of two successive chords. Finally, we indicate some concrete applications for the computation of usual stereological parameters."
            "en" => "We consider a stationary and isotropic bi-phasic (pore and solid) medium, draw many lines through it, and see each line as a one-dimensional level-cut process with value 0 or 1 according to whether a regular stationary process X is less or greater than a given level. The intervals corresponding to the points at which X is in a given phase are named chords. We are interested in obtaining information on the chord-length distribution functions. Working with the Palm probability measure and using level crossings techniques, in particular, Rice methods, we can obtain not only the exact analytical formula of the chord-length distribution function but also the joint distribution function of the lengths of two successive chords. Finally, we indicate some concrete applications for the computation of usual stereological parameters."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      3 => Essec\Faculty\Model\Contribution {#2353
        #_index: "academ_contributions"
        #_id: "997"
        #_source: array:18 [
          "id" => "997"
          "slug" => "discussion-on-the-paper-elicitability-and-backtesting-perspectives-for-banking-regulation"
          "yearMonth" => "2017-12"
          "year" => "2017"
          "title" => "Discussion on the Paper: Elicitability and Backtesting: Perspectives for Banking Regulation"
          "description" => "KRATZ, M. (2017). Discussion on the Paper: Elicitability and Backtesting: Perspectives for Banking Regulation. <i>Annals of Applied Statistics</i>, 11(4), pp. 1894-1900."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:4 [
            0 => "Backtesting"
            1 => "Forecasting"
            2 => "Risk management"
            3 => "Scoring rule"
          ]
          "updatedAt" => "2024-05-27 16:50:26"
          "publicationUrl" => "https://projecteuclid.org/journals/annals-of-applied-statistics/volume-11/issue-4/Discussion-of-Elicitability-and-backtesting-Perspectives-for-banking-regulation/10.1214/17-AOAS1041A.full"
          "publicationInfo" => array:3 [
            "pages" => "1894-1900"
            "volume" => "11"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The discussion focuses on four points in the context of Basel 3. The first concerns the choice of test functions in the calibration tests. Then we discuss the interpretation of the “internal model,” as well as the choice of risk measures. Last, we consider the score difference stationarity, an important issue in practice."
            "en" => "The discussion focuses on four points in the context of Basel 3. The first concerns the choice of test functions in the calibration tests. Then we discuss the interpretation of the “internal model,” as well as the choice of risk measures. Last, we consider the score difference stationarity, an important issue in practice."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      4 => Essec\Faculty\Model\Contribution {#2357
        #_index: "academ_contributions"
        #_id: "4331"
        #_source: array:18 [
          "id" => "4331"
          "slug" => "a-multinomial-test-to-discriminate-between-models"
          "yearMonth" => "2016-06"
          "year" => "2016"
          "title" => "A Multinomial Test to Discriminate Between Models"
          "description" => "KRATZ, M., LOK, Y. et NCNEIL, A. (2016). A Multinomial Test to Discriminate Between Models. Dans: <i>2016 ASTIN Colloquium</i>. Lisbon School of Economics and Management."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LOK Y."
            ]
            2 => array:1 [
              "name" => "NCNEIL A."
            ]
          ]
          "ouvrage" => "2016 ASTIN Colloquium"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      5 => Essec\Faculty\Model\Contribution {#2351
        #_index: "academ_contributions"
        #_id: "1177"
        #_source: array:18 [
          "id" => "1177"
          "slug" => "explicit-diversification-benefit-for-dependent-risks"
          "yearMonth" => "2016-04"
          "year" => "2016"
          "title" => "Explicit Diversification Benefit for Dependent Risks"
          "description" => "DACOROGNA, M., ELBAHTOURI, L. et KRATZ, M. (2016). Explicit Diversification Benefit for Dependent Risks. <i>SCOR</i>."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
            2 => array:1 [
              "name" => "ELBAHTOURI L."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:13 [
            0 => "Aggregation of risks"
            1 => "Archimedean copula"
            2 => "Clayton"
            3 => "Diversification (benefit)"
            4 => "Gaussian"
            5 => "Gumbel"
            6 => "Heavy tail"
            7 => "Mixing technique"
            8 => "Pareto"
            9 => "Risk measure"
            10 => "TVaR"
            11 => "VaR"
            12 => "Weibull"
          ]
          "updatedAt" => "2021-07-13 14:30:15"
          "publicationUrl" => "https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2716093"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue professionnelle"
            "en" => "Professional journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence."
            "en" => "We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      6 => Essec\Faculty\Model\Contribution {#2355
        #_index: "academ_contributions"
        #_id: "5335"
        #_source: array:18 [
          "id" => "5335"
          "slug" => "a-shifted-clt-an-alternative-solution-to-correctly-estimate-in-a-gaussian-realm-the-var-in-presence-of-heavy-tails"
          "yearMonth" => "2013-09"
          "year" => "2013"
          "title" => "A Shifted CLT: An Alternative Solution to Correctly Estimate in a Gaussian Realm the Var In Presence Of Heavy Tails"
          "description" => "KRATZ, M. (2013). A Shifted CLT: An Alternative Solution to Correctly Estimate in a Gaussian Realm the Var In Presence Of Heavy Tails. Dans: Workshop EVT - Extremes in Vimeiro 2013."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Workshop EVT - Extremes in Vimeiro 2013"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      7 => Essec\Faculty\Model\Contribution {#2358
        #_index: "academ_contributions"
        #_id: "5405"
        #_source: array:18 [
          "id" => "5405"
          "slug" => "an-implicit-backtest-for-es-via-a-simple-multinomial-approach"
          "yearMonth" => "2016-06"
          "year" => "2016"
          "title" => "An Implicit Backtest for ES via a Simple Multinomial Approach"
          "description" => "KRATZ, M. (2016). An Implicit Backtest for ES via a Simple Multinomial Approach. Dans: 5th Iberian Congress of Actuaries."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "5th Iberian Congress of Actuaries"
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:07"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      8 => Essec\Faculty\Model\Contribution {#2359
        #_index: "academ_contributions"
        #_id: "1321"
        #_source: array:18 [
          "id" => "1321"
          "slug" => "how-fast-can-the-chord-length-distribution-decay"
          "yearMonth" => "2011-07"
          "year" => "2011"
          "title" => "How Fast Can the Chord-Length Distribution Decay?"
          "description" => "DEMICHEL, Y., ESTRADE, A., KRATZ, M. et SAMARODNITSKY, S. (2011). How Fast Can the Chord-Length Distribution Decay? <i>Advances in Applied Probability</i>, 43(2), pp. 504-523."
          "authors" => array:4 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEMICHEL Y."
            ]
            2 => array:1 [
              "name" => "ESTRADE A."
            ]
            3 => array:1 [
              "name" => "SAMARODNITSKY S."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:5 [
            0 => "Chord length"
            1 => "Crossing"
            2 => "Gaussian field"
            3 => "Bi-phasic medium"
            4 => "Tail of distribution"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://hal.archives-ouvertes.fr/hal-00419202v1/document"
          "publicationInfo" => array:3 [
            "pages" => "504-523"
            "volume" => "43"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The modeling of random bi-phasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this paper we consider a thresholded random process X as a source of the two phases. The intervals when X is in a given phase, named chords, are the subject of interest. We focus on the study of the tails of the chord-length distribution functions. In the literature, different types of the tail behavior have been reported, among them exponential-like or power-like decay. We look for the link between the dependence structure of the underlying thresholded process X and the rate of decay of the chord-length distribution. When the process X is a stationary Gaussian process, we relate the latter to the rate at which the covariance function of X decays at large lags. We show that exponential, or nearly exponential, decay of the tail of the distribution of the chord-lengths is very common, perhaps surprisingly so."
            "en" => "The modeling of random bi-phasic, or porous, media has been, and still is, under active investigation by mathematicians, physicists or physicians. In this paper we consider a thresholded random process X as a source of the two phases. The intervals when X is in a given phase, named chords, are the subject of interest. We focus on the study of the tails of the chord-length distribution functions. In the literature, different types of the tail behavior have been reported, among them exponential-like or power-like decay. We look for the link between the dependence structure of the underlying thresholded process X and the rate of decay of the chord-length distribution. When the process X is a stationary Gaussian process, we relate the latter to the rate at which the covariance function of X decays at large lags. We show that exponential, or nearly exponential, decay of the tail of the distribution of the chord-lengths is very common, perhaps surprisingly so."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      9 => Essec\Faculty\Model\Contribution {#2360
        #_index: "academ_contributions"
        #_id: "5562"
        #_source: array:18 [
          "id" => "5562"
          "slug" => "clt-for-lipschitz-killing-curvatures"
          "yearMonth" => "2016-11"
          "year" => "2016"
          "title" => "CLT for Lipschitz-Killing Curvatures"
          "description" => "KRATZ, M. et VADLAMANI, S. (2016). CLT for Lipschitz-Killing Curvatures. Dans: 6th Ritsumeikan-Monash Symposium on Probability and Relative Fields."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI S."
            ]
          ]
          "ouvrage" => "6th Ritsumeikan-Monash Symposium on Probability and Relative Fields"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      10 => Essec\Faculty\Model\Contribution {#2361
        #_index: "academ_contributions"
        #_id: "5639"
        #_source: array:18 [
          "id" => "5639"
          "slug" => "contributions-to-risk-theory"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "Contributions to Risk Theory"
          "description" => "KRATZ, M. (2014). Contributions to Risk Theory. Dans: 2014 Actuarial Teachers and Researchers Conference."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "2014 Actuarial Teachers and Researchers Conference"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      11 => Essec\Faculty\Model\Contribution {#2362
        #_index: "academ_contributions"
        #_id: "614"
        #_source: array:18 [
          "id" => "614"
          "slug" => "alarm-system-for-insurance-companies-a-strategy-for-capital-allocation"
          "yearMonth" => "2012-07"
          "year" => "2012"
          "title" => "Alarm System for Insurance Companies: A Strategy for Capital Allocation"
          "description" => "DAS, S. et KRATZ, M. (2012). Alarm System for Insurance Companies: A Strategy for Capital Allocation. <i>Insurance: Mathematics and Economics</i>, 51(1), pp. 53-65."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DAS S."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Alarm system"
            1 => "Capital accumulation function"
            2 => "Capital allocation"
            3 => "Quantitative risk management"
            4 => "Risk process"
            5 => "Ruin probability"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://www.sciencedirect.com/science/article/abs/pii/S016766871200025X"
          "publicationInfo" => array:3 [
            "pages" => "53-65"
            "volume" => "51"
            "number" => "1"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement outgo for the insurance company. The main purpose of this work is to design an effective alarm system, i.e. to define alarm times and to recommend augmentation of capital of suitable magnitude at those points to reduce the chance of ruin.\n
              To draw a fair measure of effectiveness of alarm system, comparison is drawn between an alarm system, with capital being added at the sound of every alarm, and the corresponding system without any alarm, but an equivalently higher initial capital. Analytical results are obtained in general setup and this is backed up by simulated performances with various types of loss severity distributions. This provides a strategy for suitably spreading out the capital and yet addressing survivability concerns at satisfactory level.
              """
            "en" => """
              One possible way of risk management for an insurance company is to develop an early and appropriate alarm system before the possible ruin. The ruin is defined through the status of the aggregate risk process, which in turn is determined by premium accumulation as well as claim settlement outgo for the insurance company. The main purpose of this work is to design an effective alarm system, i.e. to define alarm times and to recommend augmentation of capital of suitable magnitude at those points to reduce the chance of ruin.\n
              To draw a fair measure of effectiveness of alarm system, comparison is drawn between an alarm system, with capital being added at the sound of every alarm, and the corresponding system without any alarm, but an equivalently higher initial capital. Analytical results are obtained in general setup and this is backed up by simulated performances with various types of loss severity distributions. This provides a strategy for suitably spreading out the capital and yet addressing survivability concerns at satisfactory level.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      12 => Essec\Faculty\Model\Contribution {#2363
        #_index: "academ_contributions"
        #_id: "633"
        #_source: array:18 [
          "id" => "633"
          "slug" => "an-extreme-value-theory-approach-for-the-early-detection-of-time-clusters-a-simulation-based-assessment-and-an-illustration-to-the-surveillance-of-salmonella"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "An Extreme Value Theory Approach for the Early Detection of Time Clusters. A Simulation-Based Assessment and an Illustration to the Surveillance of Salmonella"
          "description" => "GUILLOU, A., KRATZ, M. et LE STRAT, Y. (2014). An Extreme Value Theory Approach for the Early Detection of Time Clusters. A Simulation-Based Assessment and an Illustration to the Surveillance of Salmonella. <i>Statistics in Medicine</i>, 33(28), pp. 5015-5027."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "GUILLOU A."
            ]
            2 => array:1 [
              "name" => "LE STRAT Y."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Extreme value theory"
            1 => "Return level"
            2 => "Return period"
            3 => "Outbreak detection"
            4 => "Salmonella"
            5 => "Surveillance"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.6275"
          "publicationInfo" => array:3 [
            "pages" => "5015-5027"
            "volume" => "33"
            "number" => "28"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We propose a new method which could be part of a warning system for the early detection of time clusters applied to public health surveillance data. This method is based on the extreme value theory (EVT). To any new count of a particular infection reported to a surveillance system, we associate a return period which corresponds to the time that we expect to be able to see again such a level. If such a level is reached, an alarm is generated. Although standard EVT is only defined in the context of continuous observations, our approach allows to handle the case of discrete observations occurring in the public health surveillance framework. Moreover it applies without any assumption on the underlying unknown distribution function. The performance of our method is assessed on an extensive simulation study and is illustrated on real data from Salmonella surveillance in France."
            "en" => "We propose a new method which could be part of a warning system for the early detection of time clusters applied to public health surveillance data. This method is based on the extreme value theory (EVT). To any new count of a particular infection reported to a surveillance system, we associate a return period which corresponds to the time that we expect to be able to see again such a level. If such a level is reached, an alarm is generated. Although standard EVT is only defined in the context of continuous observations, our approach allows to handle the case of discrete observations occurring in the public health surveillance framework. Moreover it applies without any assumption on the underlying unknown distribution function. The performance of our method is assessed on an extensive simulation study and is illustrated on real data from Salmonella surveillance in France."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      13 => Essec\Faculty\Model\Contribution {#2364
        #_index: "academ_contributions"
        #_id: "10741"
        #_source: array:18 [
          "id" => "10741"
          "slug" => "data-analytics-on-cyber-crimes-complaints-registered-at-c3n-of-gendarmerie-nationale"
          "yearMonth" => "2019-10"
          "year" => "2019"
          "title" => "Data Analytics on Cyber Crimes Complaints Registered at C3N of Gendarmerie Nationale"
          "description" => "KRATZ, M., DEBBABI, N. et DACOROGNA, M. (2019). Data Analytics on Cyber Crimes Complaints Registered at C3N of Gendarmerie Nationale. Dans: 2019 Joint AFIR-ERM / ASTIN Symposium."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "2019 Joint AFIR-ERM / ASTIN Symposium"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      14 => Essec\Faculty\Model\Contribution {#2365
        #_index: "academ_contributions"
        #_id: "4456"
        #_source: array:18 [
          "id" => "4456"
          "slug" => "combining-algebraic-approach-with-extreme-value-theory-for-spike-detection"
          "yearMonth" => "2012-08"
          "year" => "2012"
          "title" => "Combining Algebraic Approach with Extreme Value Theory for Spike Detection"
          "description" => "DEBBABI, N., KRATZ, M., MBOUP, M. et EL ASMI, S. (2012). Combining Algebraic Approach with Extreme Value Theory for Spike Detection. Dans: <i>Proceedings of EUSIPCO 2012</i>. "
          "authors" => array:4 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
            3 => array:1 [
              "name" => "EL ASMI S."
            ]
          ]
          "ouvrage" => "Proceedings of EUSIPCO 2012"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This paper uses the Extreme Value Theory (EVT) for threshold selection in a previously proposed algebraic spike detection method. The algebraic method characterizes the occurrence of a spike by an irregularity in the neural signal and devises a nonlinear (Volterra) filter which enhances the presence of such irregularities. These appear as (positive) high amplitude pulses in the output signal. The pulses are isolated. We then interpret the occurrence of a spike as a rare and extreme event that we model in the framework of EVT. With this model, we derive an explicit expression of the decision threshold corresponding to a given probability of false-alarm. Simulation results show that the empirical probability of false alarm is close to the predicted one by applying the derived theoretical threshold."
            "en" => "This paper uses the Extreme Value Theory (EVT) for threshold selection in a previously proposed algebraic spike detection method. The algebraic method characterizes the occurrence of a spike by an irregularity in the neural signal and devises a nonlinear (Volterra) filter which enhances the presence of such irregularities. These appear as (positive) high amplitude pulses in the output signal. The pulses are isolated. We then interpret the occurrence of a spike as a rare and extreme event that we model in the framework of EVT. With this model, we derive an explicit expression of the decision threshold corresponding to a given probability of false-alarm. Simulation results show that the empirical probability of false alarm is close to the predicted one by applying the derived theoretical threshold."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      15 => Essec\Faculty\Model\Contribution {#2366
        #_index: "academ_contributions"
        #_id: "4529"
        #_source: array:18 [
          "id" => "4529"
          "slug" => "distribution-hybride-pour-la-modelisation-de-donnees-a-deux-queues-lourdes-application-sur-les-donnees-neuronales"
          "yearMonth" => "2015-09"
          "year" => "2015"
          "title" => "Distribution hybride pour la modélisation de données à deux queues lourdes: Application sur les données neuronales"
          "description" => "DEBBABI, N., KRATZ, M., MBOUP, M. et EL ASMI, S. (2015). Distribution hybride pour la modélisation de données à deux queues lourdes: Application sur les données neuronales. Dans: <i>25ème Édition du Colloque GRETSI</i>. École Normale Supérieure de Lyon."
          "authors" => array:4 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
            3 => array:1 [
              "name" => "EL ASMI S."
            ]
          ]
          "ouvrage" => "25ème Édition du Colloque GRETSI"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Ce travail propose un modèle hybride pour modéliser des données à deux queues lourdes. Le modèle proposé est une distribution à trois composantes pondérées : une distribution Gaussienne, pour modéliser le comportement moyen des données, liée à deux distributions de Pareto généralisées pour modéliser les comportements extrêmes. Un algorithme itératif et non supervisé est ensuite proposé pour une estimation fiable des points de jonctions entre les trois distributions, les paramètres de ces dernières ainsi que les poids affectés à chaque composante du modèle hybride. Une application sur des données neuronales réelles issues d’un enregistrement extracellulaire, est développée pour évaluer les performances du modèle proposé, comparé à la distribution normale."
            "en" => "A new hybrid model for two heavy tailed data modelling is proposed in this study. The proposed model is a weighted three-components distribution: a Gaussian distribution, to model the mean behavior of the data, linked to two generalized Pareto distributions, modelling the extreme ones. An unsupervised iterative algorithm is then developed to estimate accurately the junction points between the three distributions, the parameters of these latter as well as the weights of the hybrid model. An application on real extracellular neural recordings isdeveloped to evaluate the performance of the proposed hybrid model, compared to the normal distribution."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      16 => Essec\Faculty\Model\Contribution {#2367
        #_index: "academ_contributions"
        #_id: "4620"
        #_source: array:18 [
          "id" => "4620"
          "slug" => "fixed-points-of-the-abe-formulation-of-stochastic-hopfield-networks"
          "yearMonth" => "2007-09"
          "year" => "2007"
          "title" => "Fixed Points of the Abe Formulation of Stochastic Hopfield Networks"
          "description" => "KRATZ, M., ATENCIA, M. et JOYA, G. (2007). Fixed Points of the Abe Formulation of Stochastic Hopfield Networks. Dans: <i>ICANN - LNCS 4668</i>. Springer."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ATENCIA M."
            ]
            2 => array:1 [
              "name" => "JOYA G."
            ]
          ]
          "ouvrage" => "ICANN - LNCS 4668"
          "keywords" => array:1 [
            0 => "Stochastic Hopfield Neural Networks"
          ]
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization."
            "en" => "The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      17 => Essec\Faculty\Model\Contribution {#2368
        #_index: "academ_contributions"
        #_id: "4917"
        #_source: array:18 [
          "id" => "4917"
          "slug" => "on-functions-bounded-by-karamata-functions"
          "yearMonth" => "2017-08"
          "year" => "2017"
          "title" => "On Functions Bounded by Karamata Functions"
          "description" => "CADENA, M., KRATZ, M. et OMEY, E. (2017). On Functions Bounded by Karamata Functions. Dans: <i>Proceedings of XXXIV International Seminar on Stability Problems for Stochastic Models</i>. Journal of Mathematical Analysis and Applications."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
            2 => array:1 [
              "name" => "OMEY E."
            ]
          ]
          "ouvrage" => "Proceedings of XXXIV International Seminar on Stability Problems for Stochastic Models"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity. This new class extends the class of regularly varying functions, for broader applications. We provide different characterizations of the new class and consider integrals, convolutions and Laplace transforms. We give some applications in probability theory. Some natural extensions of the new class are also derived."
            "en" => "We define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity. This new class extends the class of regularly varying functions, for broader applications. We provide different characterizations of the new class and consider integrals, convolutions and Laplace transforms. We give some applications in probability theory. Some natural extensions of the new class are also derived."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      18 => Essec\Faculty\Model\Contribution {#2369
        #_index: "academ_contributions"
        #_id: "11614"
        #_source: array:18 [
          "id" => "11614"
          "slug" => "adapting-to-the-new-risk-landscape-is-cyber-insurable"
          "yearMonth" => "2019-04"
          "year" => "2019"
          "title" => "Adapting to the new risk landscape: is cyber insurable?"
          "description" => "KRATZ, M. (2019). Adapting to the new risk landscape: is cyber insurable? <i>ESSEC Knowledge</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "http://knowledge.essec.edu/en/economy-finance/adapting-to-new-risk-landscape-is-cyber-insurable.html"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      19 => Essec\Faculty\Model\Contribution {#2370
        #_index: "academ_contributions"
        #_id: "11615"
        #_source: array:18 [
          "id" => "11615"
          "slug" => "sadapter-au-nouvel-environnement-des-risques-peut-on-assurer-le-risque-cyber"
          "yearMonth" => "2019-04"
          "year" => "2019"
          "title" => "S’adapter au nouvel environnement des risques : peut-on assurer le risque cyber ?"
          "description" => "KRATZ, M. (2019). S’adapter au nouvel environnement des risques : peut-on assurer le risque cyber ? <i>Reflets ESSEC Magazine</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      20 => Essec\Faculty\Model\Contribution {#2371
        #_index: "academ_contributions"
        #_id: "11966"
        #_source: array:18 [
          "id" => "11966"
          "slug" => "understanding-procyclicality"
          "yearMonth" => "2020-11"
          "year" => "2020"
          "title" => "Understanding Procyclicality"
          "description" => "KRATZ, M. (2020). Understanding Procyclicality. <i>ESSEC Knowledge</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "http://knowledge.essec.edu/en/economy-finance/understanding-procyclicality.html"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => "Nov. 2020"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      21 => Essec\Faculty\Model\Contribution {#2372
        #_index: "academ_contributions"
        #_id: "12215"
        #_source: array:18 [
          "id" => "12215"
          "slug" => "bivariate-fclt-for-the-sample-quantile-and-measures-of-dispersion-for-augmented-garchp-q-processes"
          "yearMonth" => "2019-06"
          "year" => "2019"
          "title" => "Bivariate FCLT For The Sample Quantile And Measures Of Dispersion For Augmented Garch(p, q) Processes"
          "description" => "BRÄUTIGAM, M. et KRATZ, M. (2019). <i>Bivariate FCLT For The Sample Quantile And Measures Of Dispersion For Augmented Garch(p, q) Processes</i>. WP1909, ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      22 => Essec\Faculty\Model\Contribution {#2373
        #_index: "academ_contributions"
        #_id: "12238"
        #_source: array:18 [
          "id" => "12238"
          "slug" => "data-analytics-on-cyber-crimes-complaints-registered-at-c3n-of-pjgn"
          "yearMonth" => "2019-05"
          "year" => "2019"
          "title" => "Data Analytics on  Cyber Crimes Complaints  Registered at C3N of PJGN"
          "description" => "KRATZ, M. (2019). Data Analytics on  Cyber Crimes Complaints  Registered at C3N of PJGN. Dans: Annual SCOR Group Actuarial Conference."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Annual SCOR Group Actuarial Conference"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      23 => Essec\Faculty\Model\Contribution {#2374
        #_index: "academ_contributions"
        #_id: "12239"
        #_source: array:18 [
          "id" => "12239"
          "slug" => "evaluating-the-cyber-risk-the-researcher-point-of-view"
          "yearMonth" => "2019-06"
          "year" => "2019"
          "title" => "Evaluating the cyber risk: the researcher point of view"
          "description" => "KRATZ, M. (2019). Evaluating the cyber risk: the researcher point of view. Dans: Pôle Analyse : Peut-on évaluer les risques Cyber?, PJGN."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Pôle Analyse : Peut-on évaluer les risques Cyber?, PJGN"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      24 => Essec\Faculty\Model\Contribution {#2375
        #_index: "academ_contributions"
        #_id: "12241"
        #_source: array:18 [
          "id" => "12241"
          "slug" => "data-analytics-on-cyber-crimes-complaints-registered-at-c3n-of-pjgn"
          "yearMonth" => "2019-10"
          "year" => "2019"
          "title" => "Data Analytics on  Cyber Crimes Complaints  Registered at C3N of PJGN"
          "description" => "KRATZ, M. (2019). Data Analytics on  Cyber Crimes Complaints  Registered at C3N of PJGN. Dans: ASTIN-AFIR conference. Warsaw."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "ASTIN-AFIR conference"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      25 => Essec\Faculty\Model\Contribution {#2376
        #_index: "academ_contributions"
        #_id: "12243"
        #_source: array:18 [
          "id" => "12243"
          "slug" => "the-impact-of-traditional-risk-measurement-on-the-pro-cyclicality"
          "yearMonth" => "2019-06"
          "year" => "2019"
          "title" => "The impact of traditional risk measurement on the pro-cyclicality"
          "description" => "KRATZ, M. (2019). The impact of traditional risk measurement on the pro-cyclicality. Dans: Paris Seine Initiative Scientific Day. Neuville."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Paris Seine Initiative Scientific Day"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      26 => Essec\Faculty\Model\Contribution {#2377
        #_index: "academ_contributions"
        #_id: "5264"
        #_source: array:18 [
          "id" => "5264"
          "slug" => "invited-a-self-calibrating-method-for-heavy-tailed-data-modeling-applications-in-finance-and-insurance"
          "yearMonth" => "2017-09"
          "year" => "2017"
          "title" => "[Invited] A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2017). [Invited] A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance. Dans: CFA France Research Workshop."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => "CFA France Research Workshop"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
            "en" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      27 => Essec\Faculty\Model\Contribution {#2378
        #_index: "academ_contributions"
        #_id: "5267"
        #_source: array:18 [
          "id" => "5267"
          "slug" => "keynote-a-self-calibrating-method-for-heavy-tailed-data-modeling-applications-in-finance-and-insurance"
          "yearMonth" => "2017-06"
          "year" => "2017"
          "title" => "[Keynote] A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2017). [Keynote] A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance. Dans: 2017 IRFRC Annual Conference."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => "2017 IRFRC Annual Conference"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
            "en" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      28 => Essec\Faculty\Model\Contribution {#2379
        #_index: "academ_contributions"
        #_id: "5281"
        #_source: array:18 [
          "id" => "5281"
          "slug" => "a-brief-review-on-evt-basics-and-operational-risk-measures"
          "yearMonth" => "2009-01"
          "year" => "2009"
          "title" => "A Brief Review on EVT Basics and Operational Risk Measures"
          "description" => "KRATZ, M. (2009). A Brief Review on EVT Basics and Operational Risk Measures. Dans: European Workshop on Risk Analysis and EVT."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "European Workshop on Risk Analysis and EVT"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We shall introduce the univariate as well as the multivariate extreme value theory, with the different methods involved. Applications to Finance will be considered, in particular to define the notion of operational risk measures, such as VaR and stress-testing."
            "en" => "We shall introduce the univariate as well as the multivariate extreme value theory, with the different methods involved. Applications to Finance will be considered, in particular to define the notion of operational risk measures, such as VaR and stress-testing."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      29 => Essec\Faculty\Model\Contribution {#2380
        #_index: "academ_contributions"
        #_id: "5319"
        #_source: array:18 [
          "id" => "5319"
          "slug" => "a-new-unsupervised-threshold-determination-for-hybrid-models"
          "yearMonth" => "2014-05"
          "year" => "2014"
          "title" => "A New Unsupervised Threshold Determination for Hybrid Models"
          "description" => "DEBBABI, N. et KRATZ, M. (2014). A New Unsupervised Threshold Determination for Hybrid Models. Dans: 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
          ]
          "ouvrage" => "2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      30 => Essec\Faculty\Model\Contribution {#2381
        #_index: "academ_contributions"
        #_id: "5332"
        #_source: array:18 [
          "id" => "5332"
          "slug" => "a-self-calibrating-method-for-heavy-tailed-data-modeling-applications-in-finance-and-insurance"
          "yearMonth" => "2017-12"
          "year" => "2017"
          "title" => "A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2017). A Self-Calibrating Method for Heavy Tailed Data Modeling. Applications in Finance and Insurance. Dans: CMAstat 2017."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => "CMAstat 2017"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
            "en" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      31 => Essec\Faculty\Model\Contribution {#2382
        #_index: "academ_contributions"
        #_id: "5333"
        #_source: array:18 [
          "id" => "5333"
          "slug" => "a-self-calibrating-method-for-heavy-tailed-data-modelling-application-in-neuroscience-and-finance"
          "yearMonth" => "2018-06"
          "year" => "2018"
          "title" => "A Self-Calibrating Method for Heavy Tailed Data Modelling. Application in Neuroscience and Finance"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2018). A Self-Calibrating Method for Heavy Tailed Data Modelling. Application in Neuroscience and Finance. Dans: 6th European Seminar on Computing (ESCO 2018)."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => "6th European Seminar on Computing (ESCO 2018)"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      32 => Essec\Faculty\Model\Contribution {#2383
        #_index: "academ_contributions"
        #_id: "5334"
        #_source: array:18 [
          "id" => "5334"
          "slug" => "a-self-calibrating-method-for-heavy-tailed-modeling"
          "yearMonth" => "2017-12"
          "year" => "2017"
          "title" => "A self-calibrating method for heavy-tailed modeling"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2017). A self-calibrating method for heavy-tailed modeling. Dans: 2017 ERCIM Working Group on Computational and Methodological Statistics (CMStatistics), Birkbeck University of London and King's College London."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => "2017 ERCIM Working Group on Computational and Methodological Statistics (CMStatistics), Birkbeck University of London and King's College London."
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      33 => Essec\Faculty\Model\Contribution {#2384
        #_index: "academ_contributions"
        #_id: "5402"
        #_source: array:18 [
          "id" => "5402"
          "slug" => "an-evt-approach-for-the-early-detection-of-time-clusters-application-in-health-surveillance"
          "yearMonth" => "2017-07"
          "year" => "2017"
          "title" => "An EVT Approach for the Early Detection of Time Clusters. Application in Health Surveillance"
          "description" => "GUILLOU, A., KRATZ, M. et LE STRAT, Y. (2017). An EVT Approach for the Early Detection of Time Clusters. Application in Health Surveillance. Dans: Probability: from East to West (PEW 2017)."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "GUILLOU A."
            ]
            2 => array:1 [
              "name" => "LE STRAT Y."
            ]
          ]
          "ouvrage" => "Probability: from East to West (PEW 2017)"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      34 => Essec\Faculty\Model\Contribution {#2385
        #_index: "academ_contributions"
        #_id: "5406"
        #_source: array:18 [
          "id" => "5406"
          "slug" => "an-implicit-backtest-for-expected-shortfall-via-a-simple-multinomial-approach"
          "yearMonth" => "2017-12"
          "year" => "2017"
          "title" => "An Implicit Backtest for Expected Shortfall via a Simple Multinomial Approach"
          "description" => "KRATZ, M., LOK, Y. et MCNEIL, A. (2017). An Implicit Backtest for Expected Shortfall via a Simple Multinomial Approach. Dans: 2017 IASSL 3rd International Conference - Statistics for Good Governance."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LOK Y."
            ]
            2 => array:1 [
              "name" => "MCNEIL A."
            ]
          ]
          "ouvrage" => "2017 IASSL 3rd International Conference - Statistics for Good Governance"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      35 => Essec\Faculty\Model\Contribution {#2386
        #_index: "academ_contributions"
        #_id: "5560"
        #_source: array:18 [
          "id" => "5560"
          "slug" => "chord-distribution-functions-and-rice-formulae-application-to-random-media"
          "yearMonth" => "2007-07"
          "year" => "2007"
          "title" => "Chord-distribution Functions and Rice Formulae. Application to Random Media."
          "description" => "KRATZ, M., ESTRADE, A. et IRIBARREN, I. (2007). Chord-distribution Functions and Rice Formulae. Application to Random Media."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ESTRADE A."
            ]
            2 => array:1 [
              "name" => "IRIBARREN I."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:1 [
            0 => "Chords"
          ]
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We consider a two-phases model to describe a porous medium, an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase. Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato)."
            "en" => "We consider a two-phases model to describe a porous medium, an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase. Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato)."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      36 => Essec\Faculty\Model\Contribution {#2387
        #_index: "academ_contributions"
        #_id: "5563"
        #_source: array:18 [
          "id" => "5563"
          "slug" => "clt-for-lipschitz-killing-curvatures-of-excursion-sets-of-gaussian-fields"
          "yearMonth" => "2016-04"
          "year" => "2016"
          "title" => "CLT for Lipschitz-Killing Curvatures of Excursion Sets of Gaussian Fields"
          "description" => "KRATZ, M. et VADLAMANI, S. (2016). CLT for Lipschitz-Killing Curvatures of Excursion Sets of Gaussian Fields. Dans: Monash Probability Conference in Honor of Robert Liptser’s 80th Birthday."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI S."
            ]
          ]
          "ouvrage" => "Monash Probability Conference in Honor of Robert Liptser’s 80th Birthday"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      37 => Essec\Faculty\Model\Contribution {#2388
        #_index: "academ_contributions"
        #_id: "5724"
        #_source: array:18 [
          "id" => "5724"
          "slug" => "detecting-and-forecasting-large-deviations-and-bubbles-in-a-near-explosive-random-coefficient-model"
          "yearMonth" => "2014-08"
          "year" => "2014"
          "title" => "Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model"
          "description" => "CHEVILLON, G., BANERJEE, A. et KRATZ, M. (2014). Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model. Dans: 68th European Meeting of the Econometric Society."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => "68th European Meeting of the Econometric Society"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      38 => Essec\Faculty\Model\Contribution {#2389
        #_index: "academ_contributions"
        #_id: "5725"
        #_source: array:18 [
          "id" => "5725"
          "slug" => "detecting-and-forecasting-large-deviations-and-bubbles-in-a-near-explosive-random-co-efficient-model"
          "yearMonth" => "2014-07"
          "year" => "2014"
          "title" => "Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Co-efficient Model"
          "description" => "BANERJEE, A., CHEVILLON, G. et KRATZ, M. (2014). Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Co-efficient Model. Dans: Summer Institute 2014 of the National Bureau of Economic Research."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A"
            ]
          ]
          "ouvrage" => "Summer Institute 2014 of the National Bureau of Economic Research"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      39 => Essec\Faculty\Model\Contribution {#2390
        #_index: "academ_contributions"
        #_id: "5726"
        #_source: array:18 [
          "id" => "5726"
          "slug" => "detecting-and-predicting-rational-asset-price-bubbles-in-a-near-explosive-random-coefficient-autoregressive-model"
          "yearMonth" => "2012-06"
          "year" => "2012"
          "title" => "Detecting and Predicting Rational Asset Price Bubbles in a Near Explosive Random Coefficient Autoregressive Model"
          "description" => "BANERJEE, A., CHEVILLON, G. et KRATZ, M. (2012). Detecting and Predicting Rational Asset Price Bubbles in a Near Explosive Random Coefficient Autoregressive Model. Dans: SMU-ESSEC Symposium on Empirical Finance and Financial Econometrics 2012."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => "SMU-ESSEC Symposium on Empirical Finance and Financial Econometrics 2012"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      40 => Essec\Faculty\Model\Contribution {#2391
        #_index: "academ_contributions"
        #_id: "5790"
        #_source: array:18 [
          "id" => "5790"
          "slug" => "does-risk-diversification-always-work-the-answer-through-simple-modelling"
          "yearMonth" => "2013-09"
          "year" => "2013"
          "title" => "Does Risk Diversification Always Work? The Answer Through Simple Modelling"
          "description" => "KRATZ, M., BUSSE, M. et DACOROGNA, M. (2013). Does Risk Diversification Always Work? The Answer Through Simple Modelling. Dans: 13th Annual Conference of the European Network for Business and Industrial Statistics (ENBIS-13)."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BUSSE M."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => "13th Annual Conference of the European Network for Business and Industrial Statistics (ENBIS-13)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      41 => Essec\Faculty\Model\Contribution {#2392
        #_index: "academ_contributions"
        #_id: "5947"
        #_source: array:18 [
          "id" => "5947"
          "slug" => "exploration-statistique-de-donnees-dattaques-cyber-et-approche-methodologique"
          "yearMonth" => "2018-10"
          "year" => "2018"
          "title" => "Exploration statistique de données d'attaques cyber et approche méthodologique"
          "description" => "KRATZ, M. (2018). Exploration statistique de données d'attaques cyber et approche méthodologique. Dans: Colloque international 'Méthodes de recherche en sciences humaines et sociales sur la cybersécurité."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Colloque international 'Méthodes de recherche en sciences humaines et sociales sur la cybersécurité"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      42 => Essec\Faculty\Model\Contribution {#2393
        #_index: "academ_contributions"
        #_id: "6014"
        #_source: array:18 [
          "id" => "6014"
          "slug" => "franchissement-de-courbe-de-niveau-formules-de-rice-et-extremum"
          "yearMonth" => "2009-08"
          "year" => "2009"
          "title" => "Franchissement de courbe de niveau, formules de Rice et extremum"
          "description" => "KRATZ, M. (2009). Franchissement de courbe de niveau, formules de Rice et extremum. Dans: MAS."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "MAS"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "L'étude des extrema est fortement liée à celle des ensembles de niveau, l'approche par les ensembles de niveau permettant d'obtenir des résultats sur les comportements d'extrema de processus ou champs aléatoires. Le domaine des valeurs extrêmes constitue l'une des applications possibles parmi de nombreuses autres (géométrie stochastique, physique, optique, océanographie) et la littérature sur les ensembles de niveau s¿est sensiblement  développée depuis le milieu du siècle dernier, en témoignent, suite au travaux pionniers de Rice, les livres de Cramér & Leadbetter (67), Adler (81), Wschebor (85) et plus récemment  Adler et Taylor (07) et  Azaïs et Wschebor (à venir), pour ne citer que les ouvrages parus (ou à paraître) sur le sujet.  C'est dans ce cadre d¿ensembles de niveau que nous nous placerons, et plus spécifiquement en dimension 1, en s'intéressant au nombre de franchissements d'une courbe de niveau par un processus Gaussien stationnaire. Nous étudierons son comportement asymptotique selon la nature de la courbe de niveau (Kratz & Leon, submitted preprint). Il s¿agit de la généralisation d'un résultat que nous avions obtenu pour un niveau fixé, rendue possible grâce à l'utilisation des formules généralisées de Rice, de notre méthode générale donnant la représentation dans le chaos de Itô-Wiener et des TLCs pour des fonctionnelles de niveau de processus Gaussiens (K&L, 01), ainsi que d'outils techniques développés récemment  (K & L, 06). Nous terminerons la discussion avec des applications, en particulier en référence aux extrema."
            "en" => "L'étude des extrema est fortement liée à celle des ensembles de niveau, l'approche par les ensembles de niveau permettant d'obtenir des résultats sur les comportements d'extrema de processus ou champs aléatoires. Le domaine des valeurs extrêmes constitue l'une des applications possibles parmi de nombreuses autres (géométrie stochastique, physique, optique, océanographie) et la littérature sur les ensembles de niveau s¿est sensiblement  développée depuis le milieu du siècle dernier, en témoignent, suite au travaux pionniers de Rice, les livres de Cramér & Leadbetter (67), Adler (81), Wschebor (85) et plus récemment  Adler et Taylor (07) et  Azaïs et Wschebor (à venir), pour ne citer que les ouvrages parus (ou à paraître) sur le sujet.  C'est dans ce cadre d¿ensembles de niveau que nous nous placerons, et plus spécifiquement en dimension 1, en s'intéressant au nombre de franchissements d'une courbe de niveau par un processus Gaussien stationnaire. Nous étudierons son comportement asymptotique selon la nature de la courbe de niveau (Kratz & Leon, submitted preprint). Il s¿agit de la généralisation d'un résultat que nous avions obtenu pour un niveau fixé, rendue possible grâce à l'utilisation des formules généralisées de Rice, de notre méthode générale donnant la représentation dans le chaos de Itô-Wiener et des TLCs pour des fonctionnelles de niveau de processus Gaussiens (K&L, 01), ainsi que d'outils techniques développés récemment  (K & L, 06). Nous terminerons la discussion avec des applications, en particulier en référence aux extrema."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      43 => Essec\Faculty\Model\Contribution {#2394
        #_index: "academ_contributions"
        #_id: "12976"
        #_source: array:18 [
          "id" => "12976"
          "slug" => "pro-cyclicality-of-traditional-risk-measurement"
          "yearMonth" => "2021-06"
          "year" => "2021"
          "title" => "Pro-­Cyclicality of traditional risk measurement"
          "description" => "BRÄUTIGAM, M., KRATZ, M. et DACOROGNA, M. (2021). Pro-­Cyclicality of traditional risk measurement. Dans: 8th European Congress of Mathematics."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
            2 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "8th European Congress of Mathematics"
          "keywords" => []
          "updatedAt" => "2023-01-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
            "en" => "Information Systems, Decision Sciences and Statistics"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      44 => Essec\Faculty\Model\Contribution {#2395
        #_index: "academ_contributions"
        #_id: "13086"
        #_source: array:18 [
          "id" => "13086"
          "slug" => "special-issue-cyber-risk-and-security"
          "yearMonth" => "2022-05"
          "year" => "2022"
          "title" => "Special Issue “Cyber Risk and Security”"
          "description" => "DACOROGNA, M. et KRATZ, M. (2022). Special Issue “Cyber Risk and Security”. <i>Risks</i>, 10."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2024-10-31 13:51:19"
          "publicationUrl" => "https://doi.org/10.3390/risks10060112"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => "10"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Editeur invité d'un numéro spécial"
            "en" => "Guest editor of a journal special issue"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      45 => Essec\Faculty\Model\Contribution {#2396
        #_index: "academ_contributions"
        #_id: "13088"
        #_source: array:18 [
          "id" => "13088"
          "slug" => "assurabilite-des-risques-cyber"
          "yearMonth" => "2021-10"
          "year" => "2021"
          "title" => "Assurabilité des Risques Cyber"
          "description" => "KRATZ, M. (2021). Assurabilité des Risques Cyber. Dans: 1er Colloque International  de l’Actuariat Francophone. Virtuel."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "1er Colloque International  de l’Actuariat Francophone"
          "keywords" => []
          "updatedAt" => "2023-01-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      46 => Essec\Faculty\Model\Contribution {#2397
        #_index: "academ_contributions"
        #_id: "13144"
        #_source: array:18 [
          "id" => "13144"
          "slug" => "building-up-cyber-resilience-by-better-grasping-cyber-risk-via-a-new-algorithm-for-modelling-heavy-tailed-data"
          "yearMonth" => "2022-09"
          "year" => "2022"
          "title" => "Building up Cyber Resilience by Better Grasping Cyber Risk Via a New Algorithm for Modelling Heavy-Tailed Data"
          "description" => "KRATZ, M. (2022). <i>Building up Cyber Resilience by Better Grasping Cyber Risk Via a New Algorithm for Modelling Heavy-Tailed Data</i>. WP 2210, ESSEC Business School."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2023-01-27 01:00:44"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Cahier de Recherche"
            "en" => "Working Papers"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      47 => Essec\Faculty\Model\Contribution {#2398
        #_index: "academ_contributions"
        #_id: "6763"
        #_source: array:18 [
          "id" => "6763"
          "slug" => "on-efficiency-and-alarm-system-in-reinsurance-contracts"
          "yearMonth" => "2008-07"
          "year" => "2008"
          "title" => "On efficiency and Alarm System in Reinsurance Contracts"
          "description" => "KRATZ, M. et SHUBHABRATA, D. (2008). On efficiency and Alarm System in Reinsurance Contracts. Dans: 7th World Congress in Probability and Statistics."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "SHUBHABRATA D."
            ]
          ]
          "ouvrage" => "7th World Congress in Probability and Statistics"
          "keywords" => array:1 [
            0 => "Excess of Loss"
          ]
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Insurance companies protect themselves from large claims by entering into reinsurance contracts in exchange for sharing part of the premiums. One popular criterion for selecting appropriate form of reinsurance contract is the benefit in the survival probability of the primary insurer (cedent) through entering such contracts. Recent literature (Ignatov et al. (2004), Kaishev et al. (2006)) has studied the problem by looking at the cedent and reinsurers perspective simultaneously, however such research is limited to one to one relationship between cedent and reinsurer. In practice, a reinsurer has reinsurance contract with multiple cedent companies. Thus the reinsurer may survive a lean period from a particular contract thanks to the financial status in the other reinsurance contracts. One goal of the current work is to exhibit this phenomenon through a model involving single reinsurer and multiple cedents. While we focus on Excess of Loss contracts, we plan to cover other reinsurance schemes and compare their efficiencies. We consider two alternative formulations of the efficiency measures of the reinsurance system, depending on whether the contracts are identical across all the cedents or not. A second motivation of the study is to explore the effectiveness of having multiple layers of reinsurance contracts in the system. Towards this we propose a modified version of the efficiency measure(s) and study its behaviour.  The efficiency measures help in selecting one among the possible reinsurance schemes as well as specific choice of optimal parameter, like retention level in Excess of Loss contract, or number of reinsurance layers.  An additional way of risk management for the (re-) insurance company is to develop an early and appropriate alarm system before the possible ruin. In that case, the problem boils down to the determination of a suitable level for the risk process which corresponds to a minimum pre-specified high probability of ruin within a given timeframe after the alarm. The formulation may be generalized from covering a single risk process to multiple ones, extending the concept of alarm system to reinsurance contracts."
            "en" => "Insurance companies protect themselves from large claims by entering into reinsurance contracts in exchange for sharing part of the premiums. One popular criterion for selecting appropriate form of reinsurance contract is the benefit in the survival probability of the primary insurer (cedent) through entering such contracts. Recent literature (Ignatov et al. (2004), Kaishev et al. (2006)) has studied the problem by looking at the cedent and reinsurers perspective simultaneously, however such research is limited to one to one relationship between cedent and reinsurer. In practice, a reinsurer has reinsurance contract with multiple cedent companies. Thus the reinsurer may survive a lean period from a particular contract thanks to the financial status in the other reinsurance contracts. One goal of the current work is to exhibit this phenomenon through a model involving single reinsurer and multiple cedents. While we focus on Excess of Loss contracts, we plan to cover other reinsurance schemes and compare their efficiencies. We consider two alternative formulations of the efficiency measures of the reinsurance system, depending on whether the contracts are identical across all the cedents or not. A second motivation of the study is to explore the effectiveness of having multiple layers of reinsurance contracts in the system. Towards this we propose a modified version of the efficiency measure(s) and study its behaviour.  The efficiency measures help in selecting one among the possible reinsurance schemes as well as specific choice of optimal parameter, like retention level in Excess of Loss contract, or number of reinsurance layers.  An additional way of risk management for the (re-) insurance company is to develop an early and appropriate alarm system before the possible ruin. In that case, the problem boils down to the determination of a suitable level for the risk process which corresponds to a minimum pre-specified high probability of ruin within a given timeframe after the alarm. The formulation may be generalized from covering a single risk process to multiple ones, extending the concept of alarm system to reinsurance contracts."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      48 => Essec\Faculty\Model\Contribution {#2399
        #_index: "academ_contributions"
        #_id: "6776"
        #_source: array:18 [
          "id" => "6776"
          "slug" => "on-the-decay-of-chord-lengths"
          "yearMonth" => "2009-07"
          "year" => "2009"
          "title" => "On the decay of Chord-lengths"
          "description" => "KRATZ, M. (2009). On the decay of Chord-lengths. Dans: Stochastic Processes and their Applications."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Stochastic Processes and their Applications"
          "keywords" => array:1 [
            0 => "Chord-length"
          ]
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The modelling of  random bi-phasic or porous media (bones, stones, ...) has been, and still is, subject to investigation by mathematicians, physicists or physicians.  Here, we consider a thresholded random process X as a model, and look for information through the intervals when X is in a given phase, named chords.  We focus on the study of the chord-length tail distribution function. In the literature, different types of tail's behavior have been observed, among which exponential or power like decay. In this work, we look for the link between those two possible types of decay for the chord-length tail distribution function and the covariance function of X. First we perform with no  a priori on the chord-length tail's behavior, a statistical analysis on simulated data, using the Mean Excess Plot method as a graphical method to discriminate between  light or heavy tails, and estimating the shape parameter of the associated GPD of the tail. Then we provide theoretical results proving on one hand the exponential decay of the chord-length tail distribution function when considering exponentially decreasing covariance function of a stationary Gaussian process , on the other hand, a decay faster than any negative power function  when considering a r-mixing process X. Joint work with Y. Demichel, A. Estrade and G. Samorodnitsky"
            "en" => "The modelling of  random bi-phasic or porous media (bones, stones, ...) has been, and still is, subject to investigation by mathematicians, physicists or physicians.  Here, we consider a thresholded random process X as a model, and look for information through the intervals when X is in a given phase, named chords.  We focus on the study of the chord-length tail distribution function. In the literature, different types of tail's behavior have been observed, among which exponential or power like decay. In this work, we look for the link between those two possible types of decay for the chord-length tail distribution function and the covariance function of X. First we perform with no  a priori on the chord-length tail's behavior, a statistical analysis on simulated data, using the Mean Excess Plot method as a graphical method to discriminate between  light or heavy tails, and estimating the shape parameter of the associated GPD of the tail. Then we provide theoretical results proving on one hand the exponential decay of the chord-length tail distribution function when considering exponentially decreasing covariance function of a stationary Gaussian process , on the other hand, a decay faster than any negative power function  when considering a r-mixing process X. Joint work with Y. Demichel, A. Estrade and G. Samorodnitsky"
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      49 => Essec\Faculty\Model\Contribution {#2400
        #_index: "academ_contributions"
        #_id: "6777"
        #_source: array:18 [
          "id" => "6777"
          "slug" => "on-the-dependence-between-quantile-and-dispersion-estimators-application-to-quantitative-financial-risk-management"
          "yearMonth" => "2018-12"
          "year" => "2018"
          "title" => "On the Dependence between Quantile and Dispersion Estimators. Application to Quantitative Financial Risk Management"
          "description" => "BRÄUTIGAM, M. et KRATZ, M. (2018). On the Dependence between Quantile and Dispersion Estimators. Application to Quantitative Financial Risk Management. Dans: 7th Monash-Ritsumeikan Symposium on Probability and Related Fields 2018."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
          ]
          "ouvrage" => "7th Monash-Ritsumeikan Symposium on Probability and Related Fields 2018"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      50 => Essec\Faculty\Model\Contribution {#2401
        #_index: "academ_contributions"
        #_id: "6785"
        #_source: array:18 [
          "id" => "6785"
          "slug" => "on-the-regularity-of-time-occupation-functionals-for-gaussian-processes"
          "yearMonth" => "2018-06"
          "year" => "2018"
          "title" => "On the Regularity of Time Occupation Functionals for Gaussian Processes"
          "description" => "KRATZ, M. (2018). On the Regularity of Time Occupation Functionals for Gaussian Processes. Dans: Conference on ’Rough Paths Theory and Malliavin Calculus’, Rencontres Mathématiques de Rouen."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Conference on ’Rough Paths Theory and Malliavin Calculus’, Rencontres Mathématiques de Rouen"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      51 => Essec\Faculty\Model\Contribution {#2402
        #_index: "academ_contributions"
        #_id: "7077"
        #_source: array:18 [
          "id" => "7077"
          "slug" => "risk-measure-estimates-in-quiet-and-turbulent-times-an-empirical-study"
          "yearMonth" => "2016-12"
          "year" => "2016"
          "title" => "Risk Measure Estimates in Quiet and Turbulent Times: an Empirical Study"
          "description" => "KRATZ, M. et CHOTARD, R. (2016). Risk Measure Estimates in Quiet and Turbulent Times: an Empirical Study. Dans: 10th International Conference on Computational and Financial Econometrics (CFE 2016)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CHOTARD R."
            ]
          ]
          "ouvrage" => "10th International Conference on Computational and Financial Econometrics (CFE 2016)"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      52 => Essec\Faculty\Model\Contribution {#2403
        #_index: "academ_contributions"
        #_id: "7453"
        #_source: array:18 [
          "id" => "7453"
          "slug" => "the-tail-distributions-of-functionals-of-random-excursion-sets"
          "yearMonth" => "2012-06"
          "year" => "2012"
          "title" => "The Tail Distributions of Functionals of Random Excursion Sets"
          "description" => "KRATZ, M. et NAGEL, W. (2012). The Tail Distributions of Functionals of Random Excursion Sets. Dans: Sixth International Workshop on Applied Probability (IWAP 2012)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "NAGEL W."
            ]
          ]
          "ouvrage" => "Sixth International Workshop on Applied Probability (IWAP 2012)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "When a random field $(X_t, \ t\in {\mathbb R}^D)$ is thresholded on a given level $\gamma$ the excursion set is given by its indicator ${\bf 1}_{(\gamma , \infty )}(X_t)$.The purpose of this work is to study several functionals (as established in Stochastic Geometry) of these random excursion sets, as e.g. the capacity functional, as well as the tails of their distributions. It extends results obtained for the one-dimensional case by M. Kratz and coauthors (Demichel et al. (2011), Estrade et al (2001)) to the multidimensional case, mainly when D=2, with tools borrowed to EVT and to stochastic geometry. Various approaches are considered, among which approaches based on Rice type formulas (e.g. Azais and Wschebor (2009)) or on Morse formulas (Adler and Taylor (2007))."
            "en" => "When a random field $(X_t, \ t\in {\mathbb R}^D)$ is thresholded on a given level $\gamma$ the excursion set is given by its indicator ${\bf 1}_{(\gamma , \infty )}(X_t)$.The purpose of this work is to study several functionals (as established in Stochastic Geometry) of these random excursion sets, as e.g. the capacity functional, as well as the tails of their distributions. It extends results obtained for the one-dimensional case by M. Kratz and coauthors (Demichel et al. (2011), Estrade et al (2001)) to the multidimensional case, mainly when D=2, with tools borrowed to EVT and to stochastic geometry. Various approaches are considered, among which approaches based on Rice type formulas (e.g. Azais and Wschebor (2009)) or on Morse formulas (Adler and Taylor (2007))."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      53 => Essec\Faculty\Model\Contribution {#2404
        #_index: "academ_contributions"
        #_id: "7454"
        #_source: array:18 [
          "id" => "7454"
          "slug" => "the-tail-distributions-of-functionals-of-random-excursion-sets-co-author-nagel-w"
          "yearMonth" => "2012-06"
          "year" => "2012"
          "title" => "The Tail Distributions of Functionals of Random Excursion Sets (co-author NAGEL W.)"
          "description" => "KRATZ, M. et NAGEL, W. (2012). The Tail Distributions of Functionals of Random Excursion Sets (co-author NAGEL W.). Dans: Stereology, Spatial Statistics and Stochastic Geometry 7th International Conference (S4G 2012)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "NAGEL W."
            ]
          ]
          "ouvrage" => "Stereology, Spatial Statistics and Stochastic Geometry 7th International Conference (S4G 2012)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "When a random field $(X_t, \ t\in {\mathbb R}^D)$ is thresholded on a given level $\gamma$ the excursion set is given by its indicator ${\bf 1}_{(\gamma , \infty )}(X_t)$.The purpose of this work is to study several functionals (as established in Stochastic Geometry) of these random excursion sets, as e.g. the capacity functional, as well as the tails of their distributions. It extends results obtained for the one-dimensional case by M. Kratz and coauthors (Demichel et al. (2011), Estrade et al (2001)) to the multidimensional case, mainly when D=2, with tools borrowed to EVT and to stochastic geometry. Various approaches are considered, among which approaches based on Rice type formulas (e.g. Azais and Wschebor (2009)) or on Morse formulas (Adler and Taylor (2007))."
            "en" => "When a random field $(X_t, \ t\in {\mathbb R}^D)$ is thresholded on a given level $\gamma$ the excursion set is given by its indicator ${\bf 1}_{(\gamma , \infty )}(X_t)$.The purpose of this work is to study several functionals (as established in Stochastic Geometry) of these random excursion sets, as e.g. the capacity functional, as well as the tails of their distributions. It extends results obtained for the one-dimensional case by M. Kratz and coauthors (Demichel et al. (2011), Estrade et al (2001)) to the multidimensional case, mainly when D=2, with tools borrowed to EVT and to stochastic geometry. Various approaches are considered, among which approaches based on Rice type formulas (e.g. Azais and Wschebor (2009)) or on Morse formulas (Adler and Taylor (2007))."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      54 => Essec\Faculty\Model\Contribution {#2405
        #_index: "academ_contributions"
        #_id: "7624"
        #_source: array:18 [
          "id" => "7624"
          "slug" => "what-is-the-best-risk-measure-in-pratice-a-comparison-of-standard-measures"
          "yearMonth" => "2015-07"
          "year" => "2015"
          "title" => "What is the Best Risk Measure in Pratice? A Comparison of Standard Measures"
          "description" => "EMMER, S., KRATZ, M. et TASCHE, D. (2015). What is the Best Risk Measure in Pratice? A Comparison of Standard Measures. Dans: 2nd International Conference of the Society for Economic Measurement."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "EMMER S."
            ]
            2 => array:1 [
              "name" => "TASCHE D."
            ]
          ]
          "ouvrage" => "2nd International Conference of the Society for Economic Measurement"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      55 => Essec\Faculty\Model\Contribution {#2406
        #_index: "academ_contributions"
        #_id: "14394"
        #_source: array:18 [
          "id" => "14394"
          "slug" => "cyber-risk-analysis-overview-and-focus-on-extremes"
          "yearMonth" => "2023-07"
          "year" => "2023"
          "title" => "Cyber Risk Analysis: Overview and Focus on Extremes"
          "description" => "KRATZ, M. et DACOROGNA, M. (2023). Cyber Risk Analysis: Overview and Focus on Extremes. Dans: 54èmes Journées de Statistique de la SFdS (JdS2023). Brussels."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "54èmes Journées de Statistique de la SFdS (JdS2023)"
          "keywords" => []
          "updatedAt" => "2023-09-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      56 => Essec\Faculty\Model\Contribution {#2407
        #_index: "academ_contributions"
        #_id: "7880"
        #_source: array:18 [
          "id" => "7880"
          "slug" => "a-self-calibrating-method-for-heavy-tailed-data-modeling-application-in-neuroscience-and-nance"
          "yearMonth" => "2016-12"
          "year" => "2016"
          "title" => "A Self-Calibrating Method for Heavy Tailed Data Modeling. Application in Neuroscience and  Nance"
          "description" => "DEBBABI, N., KRATZ, M. et MBOUP, M. (2016). <i>A Self-Calibrating Method for Heavy Tailed Data Modeling. Application in Neuroscience and  Nance</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DEBBABI N."
            ]
            2 => array:1 [
              "name" => "MBOUP M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
            "en" => "One of the main issues in the statistical literature of extremes concerns the tail index estimation, closely linked to the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other suggesting self-calibrating methods, where the threshold is algorithmically determined. Our approach belongs to this second class proposing a hybrid distribution for heavy tailed data modeling, which links a normal (or lognormal) distribution to a GPD via an exponential distribution that bridges the gap between mean and asymptotic behaviors. A new unsupervised algorithm is then developed for estimating the parameters of this model. The effectiveness of our self-calibrating method is studied in terms of goodness-of-fit on simulated data. Then, it is applied to real data from neuroscience and finance, respectively. A comparison with other more standard extreme approaches follows."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      57 => Essec\Faculty\Model\Contribution {#2408
        #_index: "academ_contributions"
        #_id: "7898"
        #_source: array:18 [
          "id" => "7898"
          "slug" => "an-extension-of-the-class-of-regularly-varying-functions"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "An Extension of the Class of Regularly Varying Functions"
          "description" => "KRATZ, M. et CADENA, M. (2014). <i>An Extension of the Class of Regularly Varying Functions</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              We define a new class of positive and Lebesgue measurable functions in terms\n
              of their asymptotic behavior, which includes the class of regularly varying functions.\n
              We also characterize it by transformations, corresponding to generalized moments\n
              when these functions are random variables. We study the properties of this new class\n
              and discuss their applications to Extreme Value Theory.
              """
            "en" => """
              We define a new class of positive and Lebesgue measurable functions in terms\n
              of their asymptotic behavior, which includes the class of regularly varying functions.\n
              We also characterize it by transformations, corresponding to generalized moments\n
              when these functions are random variables. We study the properties of this new class\n
              and discuss their applications to Extreme Value Theory.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      58 => Essec\Faculty\Model\Contribution {#2409
        #_index: "academ_contributions"
        #_id: "7945"
        #_source: array:18 [
          "id" => "7945"
          "slug" => "clt-for-lipschitz-killing-curvatures-of-excursion-sets-of-gaussian-random-fields"
          "yearMonth" => "2016-08"
          "year" => "2016"
          "title" => "CLT for Lipschitz-Killing Curvatures of Excursion Sets of Gaussian Random Fields"
          "description" => "KRATZ, M. et VADLAMANI, S. (2016). <i>CLT for Lipschitz-Killing Curvatures of Excursion Sets of Gaussian Random Fields</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI S."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:14"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times ( see Berman, Kratz and Leon, Meshenmoser and Shashkin, Pham, Spodarev, for a sample of works in such settings). The most recent addition Estrade and Leon where a CLT for Euler-Poincaré characteristic of the excursions set of a Gaussian random field is proven under appropriate conditions. In this paper, we shall obtain a central limit theorem for some global geometric functionals, called the Lipschitz-Killing curvatures of excursion sets of Gaussian random fields in an appropriate setting."
            "en" => "Our interest in this paper is to explore limit theorems for various geometric functionals of excursion sets of isotropic Gaussian random fields. In the past, limit theorems have been proven for various geometric functionals of excursion sets/sojourn times ( see Berman, Kratz and Leon, Meshenmoser and Shashkin, Pham, Spodarev, for a sample of works in such settings). The most recent addition Estrade and Leon where a CLT for Euler-Poincaré characteristic of the excursions set of a Gaussian random field is proven under appropriate conditions. In this paper, we shall obtain a central limit theorem for some global geometric functionals, called the Lipschitz-Killing curvatures of excursion sets of Gaussian random fields in an appropriate setting."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      59 => Essec\Faculty\Model\Contribution {#2410
        #_index: "academ_contributions"
        #_id: "7992"
        #_source: array:18 [
          "id" => "7992"
          "slug" => "diversification-benefits-under-multivariate-second-order-regular-variation"
          "yearMonth" => "2017-04"
          "year" => "2017"
          "title" => "Diversification Benefits Under Multivariate Second Order Regular Variation"
          "description" => "DAS, S. et KRATZ, M. (2017). <i>Diversification Benefits Under Multivariate Second Order Regular Variation</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DAS S."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk. The asymptotic limits are computed in a few examples exhibiting a variety of different assumptions made on marginal or joint distributions. This study ties up existing related results available in the literature under a broader umbrella."
            "en" => "We analyze risk diversification in a portfolio of heavy-tailed risk factors under the assumption of second order multivariate regular variation. Asymptotic limits for a measure of diversification benefit are obtained when considering, for instance, the value-at-risk. The asymptotic limits are computed in a few examples exhibiting a variety of different assumptions made on marginal or joint distributions. This study ties up existing related results available in the literature under a broader umbrella."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      60 => Essec\Faculty\Model\Contribution {#2411
        #_index: "academ_contributions"
        #_id: "9160"
        #_source: array:18 [
          "id" => "9160"
          "slug" => "managing-risk-is-about-raising-societys-resilience"
          "yearMonth" => "2015-12"
          "year" => "2015"
          "title" => "Managing Risk Is about Raising Society’s Resilience"
          "description" => "KRATZ, M. (2015). Managing Risk Is about Raising Society’s Resilience. <i>Business Times Singapore</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 18:37:46"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      61 => Essec\Faculty\Model\Contribution {#2412
        #_index: "academ_contributions"
        #_id: "9305"
        #_source: array:18 [
          "id" => "9305"
          "slug" => "the-future-of-insurance-with-the-advent-of-artificial-intelligence"
          "yearMonth" => "2017-03"
          "year" => "2017"
          "title" => "The Future of Insurance with the Advent of Artificial Intelligence"
          "description" => "KRATZ, M. (2017). The Future of Insurance with the Advent of Artificial Intelligence. <i>ESSEC Knowledge</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      62 => Essec\Faculty\Model\Contribution {#2413
        #_index: "academ_contributions"
        #_id: "9384"
        #_source: array:18 [
          "id" => "9384"
          "slug" => "editorial-foreword-by-the-guest-editors-of-the-rare-special-issue"
          "yearMonth" => "2018-09"
          "year" => "2018"
          "title" => "Editorial: Foreword by the Guest Editors of the RARE special issue"
          "description" => "CONSTANTINESCU, C., HASHORVA, E. et KRATZ, M. (2018). Editorial: Foreword by the Guest Editors of the RARE special issue. <i>Annals of Actuarial Science</i>, 12, pp. 209-210."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CONSTANTINESCU C."
            ]
            2 => array:1 [
              "name" => "HASHORVA E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "209-210"
            "volume" => "12"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Préfaces / Introductions de revue"
            "en" => "Prefaces of a journal"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      63 => Essec\Faculty\Model\Contribution {#2414
        #_index: "academ_contributions"
        #_id: "9408"
        #_source: array:18 [
          "id" => "9408"
          "slug" => "hdr"
          "yearMonth" => "2005-06"
          "year" => "2005"
          "title" => "HDR"
          "description" => "KRATZ, M. (2005). HDR. France."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 18:37:46"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "HDR"
            "en" => "HDR"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      64 => Essec\Faculty\Model\Contribution {#2415
        #_index: "academ_contributions"
        #_id: "9696"
        #_source: array:18 [
          "id" => "9696"
          "slug" => "approximation-poissonnienne-relative-du-processus-empirique"
          "yearMonth" => "1993-05"
          "year" => "1993"
          "title" => "Approximation Poissonnienne relative du processus empirique"
          "description" => "KRATZ, M. (1993). Approximation Poissonnienne relative du processus empirique., 316, série I, pp. 1221-1224."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:3 [
            0 => "AMS classification "
            1 => "Poisson approximation"
            2 => "uniform empirical process"
          ]
          "updatedAt" => "2020-12-17 18:37:46"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "1221-1224"
            "volume" => "316, série I"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We use a direct method to study the relative Poisson approximation of the uniform empirical process."
            "en" => "We use a direct method to study the relative Poisson approximation of the uniform empirical process."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      65 => Essec\Faculty\Model\Contribution {#2416
        #_index: "academ_contributions"
        #_id: "9717"
        #_source: array:18 [
          "id" => "9717"
          "slug" => "statistics-of-tails-of-distributions-and-poisson-approximation"
          "yearMonth" => "1993-03"
          "year" => "1993"
          "title" => "Statistics of tails of distributions and Poisson approximation"
          "description" => "KRATZ, M. (1993). <i>Statistics of tails of distributions and Poisson approximation</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:19"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      66 => Essec\Faculty\Model\Contribution {#2417
        #_index: "academ_contributions"
        #_id: "4008"
        #_source: array:18 [
          "id" => "4008"
          "slug" => "mathematics-of-risk-introduction-to-extreme-value-theory-applications-to-risk-analysis-management"
          "yearMonth" => "2019-04"
          "year" => "2019"
          "title" => "Mathematics of Risk - Introduction to Extreme Value Theory. Applications to Risk Analysis & Management"
          "description" => "KRATZ, M. (2019). Mathematics of Risk - Introduction to Extreme Value Theory. Applications to Risk Analysis & Management. Dans: <i>2017 MATRIX Annals - Mathematics of Risk</i>. 1st ed. Springer, pp. 591-637."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "2017 MATRIX Annals - Mathematics of Risk"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "591-637"
            "volume" => "2"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Chapitres"
            "en" => "Book chapters"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              We present an overview of Univariate Extreme Value Theory (EVT) providing standard and new tools to model the tails of distributions. One of the main issues in the statistical literature of extremes concerns the tail index estimation, which governs the probability of extreme occurrences. This estimation relies heavily on the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one qualified as ’supervised’, using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other class collects unsupervised methods, where the threshold is algorithmically determined. We introduce here a new and practically relevant method belonging to this second class. It is a self-calibrating method for modeling heavy tailed data, which we developed with N. Debbabi and M. Mboup. Effectiveness of the method is addressed on simulated data, followed by applications in neuro-science and finance. Results are compared with those obtained by more standard EVT approaches. Then we turn to the notion of dependence and the various ways to measure it, in particular in the tails. Through examples, we show that dependence is also a crucial topic in risk analysis and management. Underestimating the dependence among extreme risks can lead to serious consequences, as for instance those we experienced during the last financial crisis. We introduce the notion of copula, which splits the dependence structure from the marginal distribution, and show how to use it in practice. Taking into account the dependence between random variables (risks) allows us to extend univariate EVT to multivariate EVT. We only give the first steps of the latter, to motivate the reader to follow or to participate in the increasing research development on this topic.\n
              \n
              EVT; stochastic dependence
              """
            "en" => """
              We present an overview of Univariate Extreme Value Theory (EVT) providing standard and new tools to model the tails of distributions. One of the main issues in the statistical literature of extremes concerns the tail index estimation, which governs the probability of extreme occurrences. This estimation relies heavily on the determination of a threshold above which a Generalized Pareto Distribution (GPD) can be fitted. Approaches to this estimation may be classified into two classes, one qualified as ’supervised’, using standard Peak Over Threshold (POT) methods, in which the threshold to estimate the tail is chosen graphically according to the problem, the other class collects unsupervised methods, where the threshold is algorithmically determined. We introduce here a new and practically relevant method belonging to this second class. It is a self-calibrating method for modeling heavy tailed data, which we developed with N. Debbabi and M. Mboup. Effectiveness of the method is addressed on simulated data, followed by applications in neuro-science and finance. Results are compared with those obtained by more standard EVT approaches. Then we turn to the notion of dependence and the various ways to measure it, in particular in the tails. Through examples, we show that dependence is also a crucial topic in risk analysis and management. Underestimating the dependence among extreme risks can lead to serious consequences, as for instance those we experienced during the last financial crisis. We introduce the notion of copula, which splits the dependence structure from the marginal distribution, and show how to use it in practice. Taking into account the dependence between random variables (risks) allows us to extend univariate EVT to multivariate EVT. We only give the first steps of the latter, to motivate the reader to follow or to participate in the increasing research development on this topic.\n
              \n
              EVT; stochastic dependence
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      67 => Essec\Faculty\Model\Contribution {#2418
        #_index: "academ_contributions"
        #_id: "10002"
        #_source: array:18 [
          "id" => "10002"
          "slug" => "estadisticas-de-valores-extremos"
          "yearMonth" => "2004-07"
          "year" => "2004"
          "title" => "Estadisticas de valores extremos"
          "description" => "KRATZ, M. (2004). Estadisticas de valores extremos. Dans: IX Encuentro de Matem\'atica y sus Aplicaciones y IV Seminario de Estad\'istica Aplicada. Quito."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "IX Encuentro de Matem\'atica y sus Aplicaciones y IV Seminario de Estad\'istica Aplicada"
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:24"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      68 => Essec\Faculty\Model\Contribution {#2419
        #_index: "academ_contributions"
        #_id: "4048"
        #_source: array:18 [
          "id" => "4048"
          "slug" => "on-the-estimation-of-the-distribution-of-aggregated-heavy-tailed-risks-application-to-risk-measures"
          "yearMonth" => "2016-11"
          "year" => "2016"
          "title" => "On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures"
          "description" => "KRATZ, M. (2016). On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures. Dans: <i>Extreme Events in Finance: Handbook of Extreme Value Theory and Its Applications</i>. 1st ed. Wiley, pp. 239-282."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Extreme Events in Finance: Handbook of Extreme Value Theory and Its Applications"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "239-282"
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Chapitres"
            "en" => "Book chapters"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The presence of heavy tails has been long recognized for financial and insurance data, which makes the gaussian distribution a poor approximation of the extreme risks distribution. The main objective of this study is to tackle this problem by, on one hand, obtaining the most accurate evaluations of the aggregated risks distribution and thus the risk measures used in solvency regulations, and, on the other hand, by providing practical solutions for estimating high quantiles of aggregated risks. In this chapter, we explore theoretically as well as numerically new approaches to handle this question, based on properties of upper order statistics and on trimmed sums. We show that these approaches compare very favorably to existing methods, for instance with the one based on the Generalized Central Limit Theorem."
            "en" => "The presence of heavy tails has been long recognized for financial and insurance data, which makes the gaussian distribution a poor approximation of the extreme risks distribution. The main objective of this study is to tackle this problem by, on one hand, obtaining the most accurate evaluations of the aggregated risks distribution and thus the risk measures used in solvency regulations, and, on the other hand, by providing practical solutions for estimating high quantiles of aggregated risks. In this chapter, we explore theoretically as well as numerically new approaches to handle this question, based on properties of upper order statistics and on trimmed sums. We show that these approaches compare very favorably to existing methods, for instance with the one based on the Generalized Central Limit Theorem."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      69 => Essec\Faculty\Model\Contribution {#2420
        #_index: "academ_contributions"
        #_id: "10074"
        #_source: array:18 [
          "id" => "10074"
          "slug" => "on-level-functionals-of-gaussian-fields"
          "yearMonth" => "2005-08"
          "year" => "2005"
          "title" => "On level functionals of Gaussian fields"
          "description" => "KRATZ, M. (2005). On level functionals of Gaussian fields. Dans: 2nd Intern. Conf. of Applied Mathematics. Plovdiv."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "2nd Intern. Conf. of Applied Mathematics"
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:26"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      70 => Essec\Faculty\Model\Contribution {#2421
        #_index: "academ_contributions"
        #_id: "2677"
        #_source: array:18 [
          "id" => "2677"
          "slug" => "the-impact-of-systemic-risk-on-the-diversification-benefits-of-a-risk-portfolio"
          "yearMonth" => "2014-07"
          "year" => "2014"
          "title" => "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio"
          "description" => "BUSSE, M., DACAOROGNA, M. et KRATZ, M. (2014). The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio. <i>Risks</i>, 2, pp. 260-276."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BUSSE M."
            ]
            2 => array:1 [
              "name" => "DACAOROGNA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://www.researchgate.net/publication/259044786_The_Impact_of_Systemic_Risk_on_the_Diversification_Benefits_of_a_Risk_Portfolio"
          "publicationInfo" => array:3 [
            "pages" => "260-276"
            "volume" => "2"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low."
            "en" => "Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      71 => Essec\Faculty\Model\Contribution {#2422
        #_index: "academ_contributions"
        #_id: "7473"
        #_source: array:18 [
          "id" => "7473"
          "slug" => "there-is-a-var-beyond-usual-approximations"
          "yearMonth" => "2013-01"
          "year" => "2013"
          "title" => "There is a VaR Beyond Usual Approximations"
          "description" => "KRATZ, M. (2013). There is a VaR Beyond Usual Approximations. Dans: Workshop on  Heavy-tailed Distributions and Extreme Value Theory."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Workshop on  Heavy-tailed Distributions and Extreme Value Theory"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      72 => Essec\Faculty\Model\Contribution {#2423
        #_index: "academ_contributions"
        #_id: "7575"
        #_source: array:18 [
          "id" => "7575"
          "slug" => "validation-of-risk-models"
          "yearMonth" => "2016-03"
          "year" => "2016"
          "title" => "Validation of Risk Models"
          "description" => "KRATZ, M. (2016). Validation of Risk Models. Dans: IFoA Asia conference."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "IFoA Asia conference"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      73 => Essec\Faculty\Model\Contribution {#2424
        #_index: "academ_contributions"
        #_id: "2835"
        #_source: array:18 [
          "id" => "2835"
          "slug" => "validation-of-aggregated-risks-models"
          "yearMonth" => "2018-09"
          "year" => "2018"
          "title" => "Validation of Aggregated Risks Models"
          "description" => "DACOROGNA, M., ELBAHTOURI, L. et KRATZ, M. (2018). Validation of Aggregated Risks Models. <i>Annals of Actuarial Science</i>, 12(2), pp. 1-22."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
            2 => array:1 [
              "name" => "ELBAHTOURI L."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.researchgate.net/publication/321495926_Validation_of_aggregated_risks_models"
          "publicationInfo" => array:3 [
            "pages" => "1-22"
            "volume" => "12"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Validation of risk models is required by regulators and demanded by management and shareholders. Those models rely in practice heavily on Monte Carlo (MC) simulations. Given their complexity, the convergence of the MC algorithm is difficult to prove mathematically. To circumvent this problem and nevertheless explore the conditions of convergence, we suggest an analytical approach. Considering standard models, we compute, via mixing techniques, closed form formulas for risk measures as Value-at-Risk (VaR) VaR or Tail Value-at-Risk (TVaR) TVaR on a portfolio of risks, and consequently for the associated diversification benefit. The numerical convergence of MC simulations of those various quantities is then tested against their analytical evaluations. The speed of convergence appears to depend on the fatness of the tail of the marginal distributions; the higher the tail index, the faster the convergence. We also explore the behaviour of the diversification benefit with various dependence structures and marginals (heavy and light tails). As expected, it varies heavily with the type of dependence between aggregated risks. The diversification benefit is also studied as a function of the risk measure, VaR or TVaR."
            "en" => "Validation of risk models is required by regulators and demanded by management and shareholders. Those models rely in practice heavily on Monte Carlo (MC) simulations. Given their complexity, the convergence of the MC algorithm is difficult to prove mathematically. To circumvent this problem and nevertheless explore the conditions of convergence, we suggest an analytical approach. Considering standard models, we compute, via mixing techniques, closed form formulas for risk measures as Value-at-Risk (VaR) VaR or Tail Value-at-Risk (TVaR) TVaR on a portfolio of risks, and consequently for the associated diversification benefit. The numerical convergence of MC simulations of those various quantities is then tested against their analytical evaluations. The speed of convergence appears to depend on the fatness of the tail of the marginal distributions; the higher the tail index, the faster the convergence. We also explore the behaviour of the diversification benefit with various dependence structures and marginals (heavy and light tails). As expected, it varies heavily with the type of dependence between aggregated risks. The diversification benefit is also studied as a function of the risk measure, VaR or TVaR."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      74 => Essec\Faculty\Model\Contribution {#2425
        #_index: "academ_contributions"
        #_id: "7623"
        #_source: array:18 [
          "id" => "7623"
          "slug" => "what-is-the-best-risk-measure-in-practice"
          "yearMonth" => "2015-07"
          "year" => "2015"
          "title" => "What is the Best Risk Measure in Practice ?"
          "description" => "EMMER, S., KRATZ, M. et TASCHE, D. (2015). What is the Best Risk Measure in Practice ? Dans: 2015 IMS-China International Conference on Statistics and Probability."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "EMMER S."
            ]
            2 => array:1 [
              "name" => "TASCHE D."
            ]
          ]
          "ouvrage" => "2015 IMS-China International Conference on Statistics and Probability"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      75 => Essec\Faculty\Model\Contribution {#2426
        #_index: "academ_contributions"
        #_id: "2876"
        #_source: array:18 [
          "id" => "2876"
          "slug" => "what-is-the-best-risk-measure-in-practice-a-comparison-of-standard-measures"
          "yearMonth" => "2015-12"
          "year" => "2015"
          "title" => "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures"
          "description" => "EMMER, S., KRATZ, M. et TASCHE, D. (2015). What Is the Best Risk Measure in Practice? A Comparison of Standard Measures. <i>Journal of Risk</i>, 18(2), pp. 31-60."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "EMMER S."
            ]
            2 => array:1 [
              "name" => "TASCHE D."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://www.researchgate.net/publication/290797597_What_is_the_best_risk_measure_in_practice_A_comparison_of_standard_measures"
          "publicationInfo" => array:3 [
            "pages" => "31-60"
            "volume" => "18"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straight-forward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES."
            "en" => "Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straight-forward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      76 => Essec\Faculty\Model\Contribution {#2427
        #_index: "academ_contributions"
        #_id: "8535"
        #_source: array:18 [
          "id" => "8535"
          "slug" => "annals-of-actuarial-science"
          "yearMonth" => "2018-09"
          "year" => "2018"
          "title" => "Annals of Actuarial Science"
          "description" => "CONSTANTINESCU, C., HASHORVA, E. et KRATZ, M. (2018). Annals of Actuarial Science. <i>Annals of Actuarial Science</i>, 12."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CONSTANTINESCU C."
            ]
            2 => array:1 [
              "name" => "HASHORVA E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => "12"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Editeur invité d'un numéro spécial"
            "en" => "Guest editor of a journal special issue"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      77 => Essec\Faculty\Model\Contribution {#2428
        #_index: "academ_contributions"
        #_id: "8727"
        #_source: array:18 [
          "id" => "8727"
          "slug" => "changing-times-require-new-tools-for-risk-management"
          "yearMonth" => "2016-12"
          "year" => "2016"
          "title" => "Changing Times Require New Tools for Risk Management"
          "description" => "DACOROGNA, M., KRATZ, M. et LECOMTE, P. (2016). Changing Times Require New Tools for Risk Management. <i>Asia Insurance Review</i>, pp. 98-99."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
            2 => array:1 [
              "name" => "LECOMTE P."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "98-99"
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      78 => Essec\Faculty\Model\Contribution {#2429
        #_index: "academ_contributions"
        #_id: "8962"
        #_source: array:18 [
          "id" => "8962"
          "slug" => "lactuariat-des-activites-et-competences-en-pleine-evolution"
          "yearMonth" => "2016-11"
          "year" => "2016"
          "title" => "L'actuariat, des activités et compétences en pleine évolution"
          "description" => "KRATZ, M. (2016). L'actuariat, des activités et compétences en pleine évolution. <i>Grandes Ecoles Magazine</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles ou vidéos de vulgarisation"
            "en" => "Press article, video or other popular media"
          ]
          "support_type" => array:2 [
            "fr" => "Presse"
            "en" => "Press"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      79 => Essec\Faculty\Model\Contribution {#2430
        #_index: "academ_contributions"
        #_id: "2132"
        #_source: array:18 [
          "id" => "2132"
          "slug" => "on-the-order-of-functions-at-infinity"
          "yearMonth" => "2017-08"
          "year" => "2017"
          "title" => "On the Order of Functions at Infinity"
          "description" => "CADENA, M., KRATZ, M. et OMEY, E. (2017). On the Order of Functions at Infinity. <i>Journal of Mathematical Analysis and Applications</i>, 452(1), pp. 109-125."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
            2 => array:1 [
              "name" => "OMEY E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:4 [
            0 => "Karamata's theorem"
            1 => "Karamata's Tauberian theorem"
            2 => "Regular variation"
            3 => "Representation theorems"
          ]
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.sciencedirect.com/science/article/abs/pii/S0022247X17301920"
          "publicationInfo" => array:3 [
            "pages" => "109-125"
            "volume" => "452"
            "number" => "1"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity. This new class extends the class of regularly varying functions, for broader applications. We provide different characterizations of the new class and consider integrals, convolutions and Laplace transforms. We give some applications in probability theory. Some natural extensions of the new class are also derived."
            "en" => "We define a new class of positive and measurable functions in terms of their asymptotic behavior at infinity. This new class extends the class of regularly varying functions, for broader applications. We provide different characterizations of the new class and consider integrals, convolutions and Laplace transforms. We give some applications in probability theory. Some natural extensions of the new class are also derived."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      80 => Essec\Faculty\Model\Contribution {#2431
        #_index: "academ_contributions"
        #_id: "6530"
        #_source: array:18 [
          "id" => "6530"
          "slug" => "level-crossings-and-applications"
          "yearMonth" => "2018-04"
          "year" => "2018"
          "title" => "Level Crossings and Applications"
          "description" => "KRATZ, M. (2018). Level Crossings and Applications. Dans: Workshop on 'Can Stochastic Geometry handle Dynamics of Risk Management?'."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Workshop on 'Can Stochastic Geometry handle Dynamics of Risk Management?'"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      81 => Essec\Faculty\Model\Contribution {#2432
        #_index: "academ_contributions"
        #_id: "6531"
        #_source: array:18 [
          "id" => "6531"
          "slug" => "level-functionals-for-gaussian-fields-and-applications-to-oceanography"
          "yearMonth" => "2018-06"
          "year" => "2018"
          "title" => "Level Functionals for Gaussian Fields and Applications to Oceanography"
          "description" => "KRATZ, M. (2018). Level Functionals for Gaussian Fields and Applications to Oceanography. Dans: 2018 Random Waves in Oxford."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "2018 Random Waves in Oxford"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      82 => Essec\Faculty\Model\Contribution {#2433
        #_index: "academ_contributions"
        #_id: "6545"
        #_source: array:18 [
          "id" => "6545"
          "slug" => "limit-theorems-for-functionals-of-excursion-sets-of-gaussian-random-fields"
          "yearMonth" => "2017-07"
          "year" => "2017"
          "title" => "Limit Theorems for Functionals of Excursion Sets of Gaussian Random Fields"
          "description" => "KRATZ, M. (2017). Limit Theorems for Functionals of Excursion Sets of Gaussian Random Fields. Dans: 39th Conference on Stochastic Processes and their Applications."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "39th Conference on Stochastic Processes and their Applications"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      83 => Essec\Faculty\Model\Contribution {#2434
        #_index: "academ_contributions"
        #_id: "6701"
        #_source: array:18 [
          "id" => "6701"
          "slug" => "modeling-and-backtesting-heavy-tailed-data"
          "yearMonth" => "2017-01"
          "year" => "2017"
          "title" => "Modeling and Backtesting Heavy Tailed Data"
          "description" => "KRATZ, M. (2017). Modeling and Backtesting Heavy Tailed Data. Dans: Durham Business School Workshop."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Durham Business School Workshop"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      84 => Essec\Faculty\Model\Contribution {#2435
        #_index: "academ_contributions"
        #_id: "6760"
        #_source: array:18 [
          "id" => "6760"
          "slug" => "on-a-generalization-of-some-karamata-results-and-standard-evt-characterizations"
          "yearMonth" => "2014-08"
          "year" => "2014"
          "title" => "On a Generalization of Some Karamata Results and Standard EVT Characterizations"
          "description" => "KRATZ, M. et CADENA, M. (2014). On a Generalization of Some Karamata Results and Standard EVT Characterizations. Dans: 37th Conference on Stochastic Processes and their Applications."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
          ]
          "ouvrage" => "37th Conference on Stochastic Processes and their Applications"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      85 => Essec\Faculty\Model\Contribution {#2436
        #_index: "academ_contributions"
        #_id: "6764"
        #_source: array:18 [
          "id" => "6764"
          "slug" => "on-functionals-of-excursion-sets-of-gaussian-random-fields-on-r2"
          "yearMonth" => "2015-03"
          "year" => "2015"
          "title" => "On Functionals of Excursion Sets of Gaussian Random Fields on R2"
          "description" => "KRATZ, M. et VADLAMANI, S. (2015). On Functionals of Excursion Sets of Gaussian Random Fields on R2. Dans: 5th Monash-Ritsumeikan Symposium."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI S."
            ]
          ]
          "ouvrage" => "5th Monash-Ritsumeikan Symposium"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      86 => Essec\Faculty\Model\Contribution {#2437
        #_index: "academ_contributions"
        #_id: "6765"
        #_source: array:18 [
          "id" => "6765"
          "slug" => "on-functionals-of-excursion-sets-of-gaussian-random-fields-on-r2"
          "yearMonth" => "2015-06"
          "year" => "2015"
          "title" => "On Functionals of Excursion Sets of Gaussian Random Fields on R2"
          "description" => "KRATZ, M. et VADLAMANI, S. (2015). On Functionals of Excursion Sets of Gaussian Random Fields on R2. Dans: 9th international conference on Extreme Value Analysis (EVA 2015)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "VADLAMANI S."
            ]
          ]
          "ouvrage" => "9th international conference on Extreme Value Analysis (EVA 2015)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      87 => Essec\Faculty\Model\Contribution {#2438
        #_index: "academ_contributions"
        #_id: "6767"
        #_source: array:18 [
          "id" => "6767"
          "slug" => "on-new-ifrs-rules-when-actuaires-meet-accountants"
          "yearMonth" => "2016-06"
          "year" => "2016"
          "title" => "On New IFRS Rules: When Actuaires Meet Accountants"
          "description" => "KRATZ, M. (2016). On New IFRS Rules: When Actuaires Meet Accountants. Dans: International Round Table."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "International Round Table"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      88 => Essec\Faculty\Model\Contribution {#2439
        #_index: "academ_contributions"
        #_id: "6768"
        #_source: array:18 [
          "id" => "6768"
          "slug" => "on-risk-aggregation"
          "yearMonth" => "2017-12"
          "year" => "2017"
          "title" => "On Risk Aggregation"
          "description" => "KRATZ, M. (2017). On Risk Aggregation. Dans: MATRIX workshop: "Mathematics of Risk"."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "MATRIX workshop: "Mathematics of Risk""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      89 => Essec\Faculty\Model\Contribution {#2440
        #_index: "academ_contributions"
        #_id: "6769"
        #_source: array:18 [
          "id" => "6769"
          "slug" => "on-risk-aggregation-and-diversification-benefits"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "On risk aggregation and diversification benefits"
          "description" => "KRATZ, M. (2014). On risk aggregation and diversification benefits. Dans: Conference on Extreme Events in Finance."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Conference on Extreme Events in Finance"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      90 => Essec\Faculty\Model\Contribution {#2441
        #_index: "academ_contributions"
        #_id: "6770"
        #_source: array:18 [
          "id" => "6770"
          "slug" => "on-risk-concentration"
          "yearMonth" => "2016-06"
          "year" => "2016"
          "title" => "On Risk Concentration"
          "description" => "KRATZ, M. et DAS, S. (2016). On Risk Concentration. Dans: 3rd ISNPS (International Society for Non-Parametric Statistics) Conference."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DAS S."
            ]
          ]
          "ouvrage" => "3rd ISNPS (International Society for Non-Parametric Statistics) Conference"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      91 => Essec\Faculty\Model\Contribution {#2442
        #_index: "academ_contributions"
        #_id: "6774"
        #_source: array:18 [
          "id" => "6774"
          "slug" => "on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-r2"
          "yearMonth" => "2013-07"
          "year" => "2013"
          "title" => "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R^2"
          "description" => "KRATZ, M. et NAGEL, W. (2013). On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R^2. Dans: EVA 2013."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "NAGEL W."
            ]
          ]
          "ouvrage" => "EVA 2013"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      92 => Essec\Faculty\Model\Contribution {#2443
        #_index: "academ_contributions"
        #_id: "6781"
        #_source: array:18 [
          "id" => "6781"
          "slug" => "on-the-generalization-of-karamata-and-standard-evt-characterizations"
          "yearMonth" => "2014-06"
          "year" => "2014"
          "title" => "On the Generalization of Karamata and Standard EVT Characterizations"
          "description" => "KRATZ, M. (2014). On the Generalization of Karamata and Standard EVT Characterizations. Dans: 7th International Workshop on Applied Probability."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "7th International Workshop on Applied Probability"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      93 => Essec\Faculty\Model\Contribution {#2444
        #_index: "academ_contributions"
        #_id: "6783"
        #_source: array:18 [
          "id" => "6783"
          "slug" => "on-the-local-behavior-of-the-extreme-quantiles-of-the-sum-of-heavy-tailed-distributed-random-variables"
          "yearMonth" => "2015-07"
          "year" => "2015"
          "title" => "On the Local Behavior of the Extreme Quantiles of the Sum of Heavy Tailed Distributed Random Variables"
          "description" => "KRATZ, M. et DAS, S. (2015). On the Local Behavior of the Extreme Quantiles of the Sum of Heavy Tailed Distributed Random Variables. Dans: 60th ISI World Statistics Congress (WSC)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DAS S."
            ]
          ]
          "ouvrage" => "60th ISI World Statistics Congress (WSC)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      94 => Essec\Faculty\Model\Contribution {#2445
        #_index: "academ_contributions"
        #_id: "6784"
        #_source: array:18 [
          "id" => "6784"
          "slug" => "on-the-regularity-of-functionals-for-stationary-gaussian-processes"
          "yearMonth" => "2019-07"
          "year" => "2019"
          "title" => "On the Regularity of Functionals for Stationary Gaussian Processes"
          "description" => "KRATZ, M. et AMABA, T. (2019). On the Regularity of Functionals for Stationary Gaussian Processes. Dans: 41st conference on Stochastic Processes and their Applications (SPA) 2019."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "AMABA T."
            ]
          ]
          "ouvrage" => "41st conference on Stochastic Processes and their Applications (SPA) 2019"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      95 => Essec\Faculty\Model\Contribution {#2446
        #_index: "academ_contributions"
        #_id: "6848"
        #_source: array:18 [
          "id" => "6848"
          "slug" => "overview-of-copulas-for-actuaries-in-management"
          "yearMonth" => "2017-02"
          "year" => "2017"
          "title" => "Overview of Copulas for Actuaries in Management"
          "description" => "KRATZ, M. (2017). Overview of Copulas for Actuaries in Management. Dans: SAS Forum Singapore 2017."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "SAS Forum Singapore 2017"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      96 => Essec\Faculty\Model\Contribution {#2447
        #_index: "academ_contributions"
        #_id: "6940"
        #_source: array:18 [
          "id" => "6940"
          "slug" => "probabilistic-forecasting-of-bubbles-and-flash-crashes"
          "yearMonth" => "2018-06"
          "year" => "2018"
          "title" => "Probabilistic Forecasting of Bubbles and Flash Crashes"
          "description" => "BANERJEE, A., CHEVILLON, G. et KRATZ, M. (2018). Probabilistic Forecasting of Bubbles and Flash Crashes. Dans: 2018 Asian Meeting of the Econometric Society."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => "2018 Asian Meeting of the Econometric Society"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      97 => Essec\Faculty\Model\Contribution {#2448
        #_index: "academ_contributions"
        #_id: "6948"
        #_source: array:18 [
          "id" => "6948"
          "slug" => "procyclicality-of-empirical-measurements-of-risk-in-financial-markets"
          "yearMonth" => "2017-09"
          "year" => "2017"
          "title" => "Procyclicality of Empirical Measurements of Risk in Financial Markets"
          "description" => "BRAÜTIGAM, M., DACOROGNA, M. et KRATZ, M. (2017). Procyclicality of Empirical Measurements of Risk in Financial Markets. Dans: 2017 Risk Measurement and Regulatory Issues in Business."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRAÜTIGAM M."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => "2017 Risk Measurement and Regulatory Issues in Business"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      98 => Essec\Faculty\Model\Contribution {#2449
        #_index: "academ_contributions"
        #_id: "6949"
        #_source: array:18 [
          "id" => "6949"
          "slug" => "procyclicality-of-empirical-measurements-of-risk-in-financial-markets"
          "yearMonth" => "2017-06"
          "year" => "2017"
          "title" => "Procyclicality of Empirical Measurements of Risk in Financial Markets"
          "description" => "BRAÜTIGAM, M., DACOROGNA, M. et KRATZ, M. (2017). Procyclicality of Empirical Measurements of Risk in Financial Markets. Dans: 10th International Conference on Extreme Value Analysis."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRAÜTIGAM M."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => "10th International Conference on Extreme Value Analysis"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      99 => Essec\Faculty\Model\Contribution {#2450
        #_index: "academ_contributions"
        #_id: "7078"
        #_source: array:18 [
          "id" => "7078"
          "slug" => "risk-models-validation-keynote-speaker"
          "yearMonth" => "2016-09"
          "year" => "2016"
          "title" => "Risk Models Validation [Keynote speaker]"
          "description" => "KRATZ, M. (2016). Risk Models Validation [Keynote speaker]. Dans: 3rd ERM Conference-Singapore Actuarial Society (SAS)."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "3rd ERM Conference-Singapore Actuarial Society (SAS)"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      100 => Essec\Faculty\Model\Contribution {#2451
        #_index: "academ_contributions"
        #_id: "7125"
        #_source: array:18 [
          "id" => "7125"
          "slug" => "sentiment-driven-buoyancy"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "Sentiment Driven Buoyancy"
          "description" => "CHEVILLON, G., BANERJEE, A. et KRATZ, M. (2014). Sentiment Driven Buoyancy. Dans: 8th International Conference on Computational and Financial Econometrics (CFE 2014)."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => "8th International Conference on Computational and Financial Econometrics (CFE 2014)"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      101 => Essec\Faculty\Model\Contribution {#2452
        #_index: "academ_contributions"
        #_id: "7130"
        #_source: array:18 [
          "id" => "7130"
          "slug" => "setting-the-risk-appetite-in-the-presence-of-systemic-risk"
          "yearMonth" => "2014-11"
          "year" => "2014"
          "title" => "Setting the risk appetite in the presence of systemic risk"
          "description" => "KRATZ, M. (2014). Setting the risk appetite in the presence of systemic risk. Dans: Enterprise Risk Management (ERM) conference."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Enterprise Risk Management (ERM) conference"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      102 => Essec\Faculty\Model\Contribution {#2453
        #_index: "academ_contributions"
        #_id: "7162"
        #_source: array:18 [
          "id" => "7162"
          "slug" => "standard-risk-measures-a-statistical-debate"
          "yearMonth" => "2016-07"
          "year" => "2016"
          "title" => "Standard Risk Measures: A Statistical Debate"
          "description" => "KRATZ, M. (2016). Standard Risk Measures: A Statistical Debate. Dans: 2015 IMS-China International Conference on Statistics and Probability."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "2015 IMS-China International Conference on Statistics and Probability"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      103 => Essec\Faculty\Model\Contribution {#2454
        #_index: "academ_contributions"
        #_id: "5928"
        #_source: array:18 [
          "id" => "5928"
          "slug" => "evt-and-its-application-to-finance-and-insurance"
          "yearMonth" => "2017-03"
          "year" => "2017"
          "title" => "EVT and its Application to finance and insurance"
          "description" => "KRATZ, M. (2017). EVT and its Application to finance and insurance. Dans: ETH Risk Center March 2017 Workshop."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "ETH Risk Center March 2017 Workshop"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      104 => Essec\Faculty\Model\Contribution {#2455
        #_index: "academ_contributions"
        #_id: "5946"
        #_source: array:18 [
          "id" => "5946"
          "slug" => "explicit-diversification-benefit-formulas-for-dependent-risks"
          "yearMonth" => "2012-09"
          "year" => "2012"
          "title" => "Explicit Diversification Benefit Formulas for Dependent Risks"
          "description" => "ELBAHTOURI, L., DACOROGNA, M. et KRATZ, M. (2012). Explicit Diversification Benefit Formulas for Dependent Risks. Dans: 1st European Actuarial Journal Conference."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ELBAHTOURI L."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => "1st European Actuarial Journal Conference"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      105 => Essec\Faculty\Model\Contribution {#2456
        #_index: "academ_contributions"
        #_id: "5997"
        #_source: array:18 [
          "id" => "5997"
          "slug" => "forecasting-bubbles-in-a-near-explosive-random-coefficient-model"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "Forecasting Bubbles in a Near Explosive Random Coefficient Model"
          "description" => "CHEVILLON, G., BANERJEE, A. et KRATZ, M. (2014). Forecasting Bubbles in a Near Explosive Random Coefficient Model. Dans: 25th EC2 Conference on "Advances in Forecasting"."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => "25th EC2 Conference on "Advances in Forecasting""
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      106 => Essec\Faculty\Model\Contribution {#2457
        #_index: "academ_contributions"
        #_id: "1905"
        #_source: array:18 [
          "id" => "1905"
          "slug" => "level-crossings-and-other-level-functionals-of-stationary-gaussian-processes"
          "yearMonth" => "2006-01"
          "year" => "2006"
          "title" => "Level Crossings and Other Level Functionals of Stationary Gaussian Processes"
          "description" => "KRATZ, M. (2006). Level Crossings and Other Level Functionals of Stationary Gaussian Processes. <i>Probability Surveys</i>, pp. 230-288."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:2 [
            0 => "Gaussian processes"
            1 => "Hermite polynomials"
          ]
          "updatedAt" => "2020-12-17 17:55:06"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "230-288"
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal   comparison method, Rice method, Stein-Chen method, a general m-dependent method] used to obtain them, these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation   functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey."
            "en" => "This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal   comparison method, Rice method, Stein-Chen method, a general m-dependent method] used to obtain them, these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation   functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      107 => Essec\Faculty\Model\Contribution {#2458
        #_index: "academ_contributions"
        #_id: "1906"
        #_source: array:18 [
          "id" => "1906"
          "slug" => "level-curves-crossings-and-applications-for-gaussian-models"
          "yearMonth" => "2010-09"
          "year" => "2010"
          "title" => "Level Curves Crossings and Applications for Gaussian Models"
          "description" => "KRATZ, M. et LEON, J.R. (2010). Level Curves Crossings and Applications for Gaussian Models. <i>Extremes</i>, 13(3), pp. 315-351."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON J.R."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:9 [
            0 => "Co-area formula"
            1 => "Crossings"
            2 => "CLT"
            3 => "Gaussian fields"
            4 => "Harmonic oscillator"
            5 => "Hermite polynomials"
            6 => "Level curve"
            7 => "(Generalized) Rice formula"
            8 => "Specular point"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-009-0090-x"
          "publicationInfo" => array:3 [
            "pages" => "315-351"
            "volume" => "13"
            "number" => "3"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Representations into the Itô-Wiener Chaos and asymptotic results such as CLTs are obtained for the curve-crossings number of a stationary Gaussian process according to the form of the curve. Applications in physics and sea modelling follow, with the study of the estimator of the natural frequency of a harmonic oscillator and the study of specular points."
            "en" => "Representations into the Itô-Wiener Chaos and asymptotic results such as CLTs are obtained for the curve-crossings number of a stationary Gaussian process according to the form of the curve. Applications in physics and sea modelling follow, with the study of the estimator of the natural frequency of a harmonic oscillator and the study of specular points."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      108 => Essec\Faculty\Model\Contribution {#2459
        #_index: "academ_contributions"
        #_id: "6265"
        #_source: array:18 [
          "id" => "6265"
          "slug" => "key-issues-and-challenges-that-researchers-of-risk-and-practitioners-from-industries-perceive-as-significant-over-the-next-few-years"
          "yearMonth" => "2015-04"
          "year" => "2015"
          "title" => "Key Issues and Challenges that Researchers of Risk And Practitioners from Industries, Perceive as Significant over the Next Few Years"
          "description" => "KRATZ, M. (2015). Key Issues and Challenges that Researchers of Risk And Practitioners from Industries, Perceive as Significant over the Next Few Years. Dans: RTLC Research workshop."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "RTLC Research workshop"
          "keywords" => []
          "updatedAt" => "2021-04-19 17:57:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      109 => Essec\Faculty\Model\Contribution {#2460
        #_index: "academ_contributions"
        #_id: "2070"
        #_source: array:18 [
          "id" => "2070"
          "slug" => "modeling-macroeconomic-effects-and-expert-judgements-in-operational-risk-a-bayesian-approach"
          "yearMonth" => "2012-12"
          "year" => "2012"
          "title" => "Modeling Macroeconomic Effects and Expert Judgements in Operational Risk: A Bayesian Approach"
          "description" => "CAPA SANTOS, H., KRATZ, M. et MOSQUERA MUNOZ, F. (2012). Modeling Macroeconomic Effects and Expert Judgements in Operational Risk: A Bayesian Approach. <i>Journal of Operational Risk</i>, 7(4), pp. 3-23."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CAPA SANTOS H."
            ]
            2 => array:1 [
              "name" => "MOSQUERA MUNOZ F."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:7 [
            0 => "Quantitative risk management"
            1 => "Solvency 2"
            2 => "Basel II"
            3 => "Bayesian inference"
            4 => "Operational risk"
            5 => "Macroeconomics dependence"
            6 => "Loss distribution approach"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://hal-essec.archives-ouvertes.fr/hal-00690448"
          "publicationInfo" => array:3 [
            "pages" => "3-23"
            "volume" => "7"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              We present in this paper a contribution on operational risk modeling. We consider a general Bayesian context incorporating information on market risk profile, experts opinion and operational losses, taking into account the general macroeconomic environment as well. This modeling aims at estimating a characteristic parameter of the operational risk severity distribution function, using those sources of information.\n
              It generalizes under more realistic conditions a study realized by Lambrigger, Shevchenko and Wüthrich, and analyses the influence of macroeconomic effects on operational risk. Our theoretical model suggests that severities of operational losses are more related to the macroeconomic environment than usually assumed.
              """
            "en" => """
              We present in this paper a contribution on operational risk modeling. We consider a general Bayesian context incorporating information on market risk profile, experts opinion and operational losses, taking into account the general macroeconomic environment as well. This modeling aims at estimating a characteristic parameter of the operational risk severity distribution function, using those sources of information.\n
              It generalizes under more realistic conditions a study realized by Lambrigger, Shevchenko and Wüthrich, and analyses the influence of macroeconomic effects on operational risk. Our theoretical model suggests that severities of operational losses are more related to the macroeconomic environment than usually assumed.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      110 => Essec\Faculty\Model\Contribution {#2461
        #_index: "academ_contributions"
        #_id: "2085"
        #_source: array:18 [
          "id" => "2085"
          "slug" => "multinomial-var-backtests-a-simple-implicit-approach-to-backtesting-expected-shortfall"
          "yearMonth" => "2018-03"
          "year" => "2018"
          "title" => "Multinomial VaR Backtests: A Simple Implicit Approach to Backtesting Expected Shortfall"
          "description" => "KRATZ, M., LOK, Y.H. et MCNEIL, A.J. (2018). Multinomial VaR Backtests: A Simple Implicit Approach to Backtesting Expected Shortfall. <i>Journal of Banking & Finance</i>, 88(C), pp. 393-407."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LOK Y. H."
            ]
            2 => array:1 [
              "name" => "MCNEIL A. J."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Backtesting"
            1 => "Banking regulation"
            2 => "Expected shortfall"
            3 => "Financial risk management"
            4 => "Statistical test"
            5 => "Value-at-Risk"
          ]
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.sciencedirect.com/science/article/abs/pii/S0378426618300086"
          "publicationInfo" => array:3 [
            "pages" => "393-407"
            "volume" => "88"
            "number" => "C"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Under the Fundamental Review of the Trading Book, capital charges are based on the coherent Expected Shortfall (ES) risk measure, which is sensitive to tail risk. We argue that backtesting of the forecasting models used to derive ES can be based on a multinomial test of Value-at-Risk (VaR) exceptions at several levels. Using simulation experiments with heavy-tailed distributions and GARCH volatility models, we design a statistical procedure to show that at least four VaR levels are required to obtain tests for misspecified trading book models that are more powerful than single-level (or even two-level) binomial exception tests. A traffic-light system for model approval is proposed and illustrated with three real-data examples spanning the 2008 financial crisis."
            "en" => "Under the Fundamental Review of the Trading Book, capital charges are based on the coherent Expected Shortfall (ES) risk measure, which is sensitive to tail risk. We argue that backtesting of the forecasting models used to derive ES can be based on a multinomial test of Value-at-Risk (VaR) exceptions at several levels. Using simulation experiments with heavy-tailed distributions and GARCH volatility models, we design a statistical procedure to show that at least four VaR levels are required to obtain tests for misspecified trading book models that are more powerful than single-level (or even two-level) binomial exception tests. A traffic-light system for model approval is proposed and illustrated with three real-data examples spanning the 2008 financial crisis."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      111 => Essec\Faculty\Model\Contribution {#2462
        #_index: "academ_contributions"
        #_id: "2100"
        #_source: array:18 [
          "id" => "2100"
          "slug" => "new-results-for-tails-of-probability-distributions-according-to-their-asymptotic-decay"
          "yearMonth" => "2016-02"
          "year" => "2016"
          "title" => "New Results for Tails of Probability Distributions According to Their Asymptotic Decay"
          "description" => "CADENA, M. et KRATZ, M. (2016). New Results for Tails of Probability Distributions According to Their Asymptotic Decay. <i>Statistics & Probability Letters</i>, 109, pp. 178-183."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Asymptotic behavior"
            1 => "Maximum domains of attraction"
            2 => "Fréchet"
            3 => "Gumbel"
            4 => "Pickands–Balkema–de Haan Theorem"
            5 => "Regularly varying function"
          ]
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://www.sciencedirect.com/science/article/abs/pii/S0167715215300237"
          "publicationInfo" => array:3 [
            "pages" => "178-183"
            "volume" => "109"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This paper provides new properties for tails of probability distributions belonging to a class defined according to the asymptotic decay of the tails. This class contains the one of regularly varying tails of distributions. The main results concern the relation between this larger class and the maximum domains of attraction of Fréchet and Gumbel."
            "en" => "This paper provides new properties for tails of probability distributions belonging to a class defined according to the asymptotic decay of the tails. This class contains the one of regularly varying tails of distributions. The main results concern the relation between this larger class and the maximum domains of attraction of Fréchet and Gumbel."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      112 => Essec\Faculty\Model\Contribution {#2463
        #_index: "academ_contributions"
        #_id: "2105"
        #_source: array:18 [
          "id" => "2105"
          "slug" => "normex-a-new-method-for-evaluating-the-distribution-of-aggregated-heavy-tailed-risks"
          "yearMonth" => "2014-12"
          "year" => "2014"
          "title" => "Normex, a New Method for Evaluating the Distribution of Aggregated Heavy Tailed Risks"
          "description" => "KRATZ, M. (2014). Normex, a New Method for Evaluating the Distribution of Aggregated Heavy Tailed Risks. <i>Extremes</i>, 17(4), pp. 661-691."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-02-02 16:16:18"
          "publicationUrl" => "https://www.researchgate.net/publication/284837102_Normex_a_new_method_for_evaluating_the_distribution_of_aggregated_heavy_tailed_risks"
          "publicationInfo" => array:3 [
            "pages" => "661-691"
            "volume" => "17"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-at-Risk of the yearly log returns of financial assets."
            "en" => "We develop theoretically as well as numerically a new method, Normex, for the sum of independent heavy tailed distributed random variables, to obtain the most accurate evaluation of its entire distribution. Normex provides sharp results, whatever the number of summands and the tail index are. It is particularly suited when the Central Limit Theorem (CLT) applies but with slow convergence of the mean and with a poor approximation for the tail. Hence, it is filling up a gap in the literature by giving an appropriate limit distribution in this case, in general better than with most standard methods. An application is developed to evaluate the Value-at-Risk of the yearly log returns of financial assets."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      113 => Essec\Faculty\Model\Contribution {#2464
        #_index: "academ_contributions"
        #_id: "2122"
        #_source: array:18 [
          "id" => "2122"
          "slug" => "on-functions-bounded-by-karamata-functions"
          "yearMonth" => "2019-03"
          "year" => "2019"
          "title" => "On functions bounded by Karamata functions"
          "description" => "CADENA, M., KRATZ, M. et OMEY, E. (2019). On functions bounded by Karamata functions. <i>Journal of Mathematical Sciences</i>, 237(5), pp. 621-630."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
            2 => array:1 [
              "name" => "OMEY E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2023-05-24 16:21:49"
          "publicationUrl" => "https://link.springer.com/article/10.1007/s10958-019-04187-z"
          "publicationInfo" => array:3 [
            "pages" => "621-630"
            "volume" => "237"
            "number" => "5"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The results are extended to functions that are bounded by O-regularly varying functions."
            "en" => "We define a new class of positive and measurable functions that are bounded by regularly varying functions (which were introduced by Karamata). We study integrals and Laplace transforms of these functions. We use the obtained results to study the tail of convolutions of distribution functions. The results are extended to functions that are bounded by O-regularly varying functions."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      114 => Essec\Faculty\Model\Contribution {#2465
        #_index: "academ_contributions"
        #_id: "2129"
        #_source: array:18 [
          "id" => "2129"
          "slug" => "on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-r%c2%b2"
          "yearMonth" => "2016-09"
          "year" => "2016"
          "title" => "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²"
          "description" => "KRATZ, M. et NAGEL, W. (2016). On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R². <i>Advances in Applied Probability</i>, 48(3), pp. 712-725."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "NAGEL W."
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:10 [
            0 => "Capacity functional"
            1 => "Crossings"
            2 => "Excursion set"
            3 => "Gaussian field"
            4 => "Growing circle method"
            5 => "Rice formula"
            6 => "Second moment measure"
            7 => "Sweeping line method"
            8 => "Stereology"
            9 => "Stochastic geometry"
          ]
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.cambridge.org/core/journals/advances-in-applied-probability/article/abs/on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-2/3A82FDC50E850497837BA1457551B43E"
          "publicationInfo" => array:3 [
            "pages" => "712-725"
            "volume" => "48"
            "number" => "3"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "When a random field (X_t, t in R²) is thresholded on a given level u, the excursion set is given by its indicator 1(X_t>u). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as, e.g., the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry."
            "en" => "When a random field (X_t, t in R²) is thresholded on a given level u, the excursion set is given by its indicator 1(X_t>u). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as, e.g., the capacity functional as well as the second moment measure of the boundary length. It extends results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossings theory, in particular Rice methods, and from integral and stochastic geometry."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      115 => Essec\Faculty\Model\Contribution {#2466
        #_index: "academ_contributions"
        #_id: "8040"
        #_source: array:18 [
          "id" => "8040"
          "slug" => "explicit-diversification-benefit-for-dependent-risks"
          "yearMonth" => "2015-12"
          "year" => "2015"
          "title" => "Explicit Diversification Benefit for Dependent Risks"
          "description" => "DACOROGNA, M., ELBAHTOURI, L. et KRATZ, M. (2015). <i>Explicit Diversification Benefit for Dependent Risks</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
            2 => array:1 [
              "name" => "ELBAHTOURI L."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence."
            "en" => "We propose a new approach to analyse the effect of diversification on a portfolio of risks. By means of mixing techniques, we provide an explicit formula for the probability density function of the portfolio. These techniques allow to compute analytically risk measures as VaR or TVaR, and consequently the associated diversification benefit. The explicit formulas constitute ideal tools to analyse the properties of risk measures and diversification benefit. We use standard models, which are popular in the reinsurance industry, Archimedean survival copulas and heavy tailed marginals. We explore numerically their behavior and compare them to the aggregation of independent random variables, as well as of linearly dependent ones. Moreover, the numerical convergence of Monte Carlo simulations of various quantities is tested against the analytical result. The speed of convergence appears to depend on the fatness of the tail; the higher the tail index, the faster the convergence."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      116 => Essec\Faculty\Model\Contribution {#2467
        #_index: "academ_contributions"
        #_id: "15172"
        #_source: array:18 [
          "id" => "15172"
          "slug" => "confronting-emerging-risks-with-flexible-general-models-a-focus-on-cyber-risk"
          "yearMonth" => "2024-09"
          "year" => "2024"
          "title" => "Confronting emerging risks with flexible general models: a focus on cyber risk"
          "description" => "KRATZ, M. (2024). Confronting emerging risks with flexible general models: a focus on cyber risk. Dans: 6th edition of the European Actuarial Journal Conference (EAJC). Lisbon."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "6th edition of the European Actuarial Journal Conference (EAJC)"
          "keywords" => []
          "updatedAt" => "2024-09-30 13:32:49"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      117 => Essec\Faculty\Model\Contribution {#2468
        #_index: "academ_contributions"
        #_id: "15173"
        #_source: array:18 [
          "id" => "15173"
          "slug" => "cyber-risk-analysis-with-a-focus-on-extremes"
          "yearMonth" => "2023-06"
          "year" => "2023"
          "title" => "Cyber Risk Analysis, with a Focus on Extremes"
          "description" => "KRATZ, M. (2023). Cyber Risk Analysis, with a Focus on Extremes. Dans: Workshop on Insurance and Financial Mathematics: Cyber Risk and Insurance. Hannover."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Workshop on Insurance and Financial Mathematics: Cyber Risk and Insurance"
          "keywords" => []
          "updatedAt" => "2024-09-19 01:01:32"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      118 => Essec\Faculty\Model\Contribution {#2469
        #_index: "academ_contributions"
        #_id: "15174"
        #_source: array:18 [
          "id" => "15174"
          "slug" => "efficient-estimation-for-ev-regression-models-of-tail-risks"
          "yearMonth" => "2023-05"
          "year" => "2023"
          "title" => "Efficient estimation for EV regression models of tail risks"
          "description" => "KRATZ, M. (2023). Efficient estimation for EV regression models of tail risks. Dans: Les 30 ans du LMM - Journées ‘Risque’. Le Mans."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Les 30 ans du LMM - Journées ‘Risque’"
          "keywords" => []
          "updatedAt" => "2024-09-30 14:02:19"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      119 => Essec\Faculty\Model\Contribution {#2470
        #_index: "academ_contributions"
        #_id: "8228"
        #_source: array:18 [
          "id" => "8228"
          "slug" => "living-in-a-stochastic-world-and-managing-complex-risks"
          "yearMonth" => "2015-10"
          "year" => "2015"
          "title" => "Living in a Stochastic World and Managing Complex Risks"
          "description" => "DACOROGNA, M. et KRATZ, M. (2015). <i>Living in a Stochastic World and Managing Complex Risks</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this paper, we review the concept of risk, its evolution in history and the big changes we experienced in the last 50 years. We conclude that peak risks are growing and the need for risk management is becoming a societal demand. Two phenomena are identified to render risks more complex, increasing interconnectedness of the world and faster time scale whereby actors have little time to adapt. We conclude in showing the complementary between qualitative and quantitative risk management."
            "en" => "In this paper, we review the concept of risk, its evolution in history and the big changes we experienced in the last 50 years. We conclude that peak risks are growing and the need for risk management is becoming a societal demand. Two phenomena are identified to render risks more complex, increasing interconnectedness of the world and faster time scale whereby actors have little time to adapt. We conclude in showing the complementary between qualitative and quantitative risk management."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      120 => Essec\Faculty\Model\Contribution {#2471
        #_index: "academ_contributions"
        #_id: "8271"
        #_source: array:18 [
          "id" => "8271"
          "slug" => "modelling-macroeconomic-effects-and-expert-judgements-in-operational-risk-a-bayesian-approach"
          "yearMonth" => "2012-03"
          "year" => "2012"
          "title" => "Modelling Macroeconomic Effects and Expert Judgements in Operational Risk: A Bayesian Approach"
          "description" => "CAPA SANTOS, H., KRATZ, M. et MOSQUERA MUÑOZ, F.V. (2012). <i>Modelling Macroeconomic Effects and Expert Judgements in Operational Risk: A Bayesian Approach</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CAPA SANTOS H."
            ]
            2 => array:1 [
              "name" => "MOSQUERA MUÑOZ F.V."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This work presents a contribution on operational risk under a general Bayesian context incorporating information on market risk profile, experts and operational losses, taking into account the general macroeconomic environment as well. It aims at estimating a characteristic parameter of the distributions of the sources, market risk profile, experts and operational losses, chosen here at a location parameter. It generalizes under more realistic conditions a study realized by Lambrigger, Shevchenko and Wüthrich, and analyses macroeconomic effects on operational risk. It appears that severities of operational losses are more related to the macroeconomics environment than usually assumed."
            "en" => "This work presents a contribution on operational risk under a general Bayesian context incorporating information on market risk profile, experts and operational losses, taking into account the general macroeconomic environment as well. It aims at estimating a characteristic parameter of the distributions of the sources, market risk profile, experts and operational losses, chosen here at a location parameter. It generalizes under more realistic conditions a study realized by Lambrigger, Shevchenko and Wüthrich, and analyses macroeconomic effects on operational risk. It appears that severities of operational losses are more related to the macroeconomics environment than usually assumed."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      121 => Essec\Faculty\Model\Contribution {#2472
        #_index: "academ_contributions"
        #_id: "8283"
        #_source: array:18 [
          "id" => "8283"
          "slug" => "multinomial-var-backtests-a-simple-implicit-approach-to-backtesting-expected-shortfall"
          "yearMonth" => "2016-11"
          "year" => "2016"
          "title" => "Multinomial VaR Backtests: A Simple Implicit Approach to Backtesting Expected Shortfall"
          "description" => "KRATZ, M., LOK, Y.H. et MCNEIL, A.J. (2016). <i>Multinomial VaR Backtests: A Simple Implicit Approach to Backtesting Expected Shortfall</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LOK Y. H."
            ]
            2 => array:1 [
              "name" => "MCNEIL A. J."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calculated - can be based on a simultaneous multinomial test of value-at-risk (VaR) exceptions at different levels, an idea supported by an approximation of ES in terms of multiple quantiles of a distribution proposed in Emmer et al.. By comparing Pearson, Nass and likelihood-ratio tests (LRTs) for different numbers of VaR levels N, it is shown in a series of simulation experiments that multinomial tests with N>=4 are much more powerful at detecting misspecifications of trading book loss models than standard binomial exception tests corresponding to the case N=1. Each test has its merits: Pearson offers simplicity; Nass is robust in its size properties to the choice of N; the LRT is very powerful though slightly over-sized in small samples and more computationally burdensome. A traffic-light system for trading book models based on the multinomial test is proposed and the recommended procedure is applied to a real-data example spanning the 2008 financial crisis."
            "en" => "Under the Fundamental Review of the Trading Book (FRTB) capital charges for the trading book are based on the coherent expected shortfall (ES) risk measure, which show greater sensitivity to tail risk. In this paper it is argued that backtesting of expected shortfall - or the trading book model from which it is calculated - can be based on a simultaneous multinomial test of value-at-risk (VaR) exceptions at different levels, an idea supported by an approximation of ES in terms of multiple quantiles of a distribution proposed in Emmer et al.. By comparing Pearson, Nass and likelihood-ratio tests (LRTs) for different numbers of VaR levels N, it is shown in a series of simulation experiments that multinomial tests with N>=4 are much more powerful at detecting misspecifications of trading book loss models than standard binomial exception tests corresponding to the case N=1. Each test has its merits: Pearson offers simplicity; Nass is robust in its size properties to the choice of N; the LRT is very powerful though slightly over-sized in small samples and more computationally burdensome. A traffic-light system for trading book models based on the multinomial test is proposed and the recommended procedure is applied to a real-data example spanning the 2008 financial crisis."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      122 => Essec\Faculty\Model\Contribution {#2473
        #_index: "academ_contributions"
        #_id: "8286"
        #_source: array:18 [
          "id" => "8286"
          "slug" => "new-results-on-the-order-of-functions-at-infinity"
          "yearMonth" => "2017-06"
          "year" => "2017"
          "title" => "New Results on the Order of Functions at Infinity"
          "description" => "CADENA, M., KRATZ, M. et OMEY, E. (2017). <i>New Results on the Order of Functions at Infinity</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CADENA M."
            ]
            2 => array:1 [
              "name" => "OMEY E."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Recently, new classes of positive and measurable functions, M(p) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type lim log U(x)/H(x) = p < ∞ for a large class of normalizing functions H. It provides subclasses of M(0) and M(±∞)."
            "en" => "Recently, new classes of positive and measurable functions, M(p) and M(±∞), have been defined in terms of their asymptotic behaviour at infinity, when normalized by a logarithm (Cadena et al., 2015, 2016, 2017). Looking for other suitable normalizing functions than logarithm seems quite natural. It is what is developed in this paper, studying new classes of functions of the type lim log U(x)/H(x) = p < ∞ for a large class of normalizing functions H. It provides subclasses of M(0) and M(±∞)."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      123 => Essec\Faculty\Model\Contribution {#2474
        #_index: "academ_contributions"
        #_id: "8294"
        #_source: array:18 [
          "id" => "8294"
          "slug" => "on-the-capacity-functional-of-excursion-sets-of-gaussian-random-fields-on-r%c2%b2"
          "yearMonth" => "2014-11"
          "year" => "2014"
          "title" => "On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²"
          "description" => "KRATZ, M. et NAGEL, W. (2014). <i>On the Capacity Functional of Excursion Sets of Gaussian Random Fields on R²</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "NAGEL W."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "When a random field (Xt, t € R²) is thresholded on a given level u, the excursion set is given by its indicator 1[u,∞)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extend results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossing theory,  in particular Rice methods, and from integral and stochastic geometry."
            "en" => "When a random field (Xt, t € R²) is thresholded on a given level u, the excursion set is given by its indicator 1[u,∞)(Xt). The purpose of this work is to study functionals (as established in stochastic geometry) of these random excursion sets, as e.g. the capacity functional as well as the second moment measure of the boundary length. It extend results obtained for the one-dimensional case to the two-dimensional case, with tools borrowed from crossing theory,  in particular Rice methods, and from integral and stochastic geometry."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      124 => Essec\Faculty\Model\Contribution {#2475
        #_index: "academ_contributions"
        #_id: "8295"
        #_source: array:18 [
          "id" => "8295"
          "slug" => "on-the-dependence-between-quantiles-and-dispersion-estimators"
          "yearMonth" => "2018-12"
          "year" => "2018"
          "title" => "On The Dependence Between Quantiles And Dispersion Estimators"
          "description" => "BRÄUTIGAM, M. et KRATZ, M. (2018). <i>On The Dependence Between Quantiles And Dispersion Estimators</i>. ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this study, we derive the joint asymptotic distributions of functionals of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile) and functionals of measure of dispersion estimators (the sample standard deviation, sample mean absolute deviation, sample median absolute deviation) - assuming an underlying identically and independently distributed sample. Additionally, for location-scale distributions, we show that asymptotic correlations of such functionals do not depend on the mean and variance parameter of the distribution. Further, we compare the impact of the choice of the quantile estimator (sample quantile vs. parametric location-scale quantile) in terms of speed of convergence of the asymptotic covariance and correlations respectively. As application, we show in simulations a good finite sample performance of the asymptotics. Further, we show how the theoretical dependence results can be applied to the most well-known risk measures (Value-at-Risk, Expected Shortfall, expectile). Finally, we relate the theoretical results to empirical findings in the literature of the dependence between risk measure prediction (on historical samples) and the estimated volatility."
            "en" => "In this study, we derive the joint asymptotic distributions of functionals of quantile estimators (the non-parametric sample quantile and the parametric location-scale quantile) and functionals of measure of dispersion estimators (the sample standard deviation, sample mean absolute deviation, sample median absolute deviation) - assuming an underlying identically and independently distributed sample. Additionally, for location-scale distributions, we show that asymptotic correlations of such functionals do not depend on the mean and variance parameter of the distribution. Further, we compare the impact of the choice of the quantile estimator (sample quantile vs. parametric location-scale quantile) in terms of speed of convergence of the asymptotic covariance and correlations respectively. As application, we show in simulations a good finite sample performance of the asymptotics. Further, we show how the theoretical dependence results can be applied to the most well-known risk measures (Value-at-Risk, Expected Shortfall, expectile). Finally, we relate the theoretical results to empirical findings in the literature of the dependence between risk measure prediction (on historical samples) and the estimated volatility."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      125 => Essec\Faculty\Model\Contribution {#2476
        #_index: "academ_contributions"
        #_id: "8335"
        #_source: array:18 [
          "id" => "8335"
          "slug" => "predicting-risk-with-risk-measures-an-empirical-study"
          "yearMonth" => "2018-02"
          "year" => "2018"
          "title" => "Predicting Risk with Risk Measures: An Empirical Study"
          "description" => "BRÄUTIGAM, M., DACOROGNA, M. et KRATZ, M. (2018). <i>Predicting Risk with Risk Measures: An Empirical Study</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this study we consider the risk estimation as a stochastic process based on the Sample Quantile Process (SQP) - which is a generalization of the Value-at-Risk calculated on a rolling sample. Using SQP's, we are able to show and quantify the pro-cyclicality of the current way financial institutions measure their risk. Analysing 11 stock indices, we show that, if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in periods of high volatility, the risk measure overestimates the risk. Moreover, using a simple GARCH(1,1) model, we conclude that this pro-cyclical effect is related to the clustering of volatility. We argue that this has important consequences for the regulation in times of crisis."
            "en" => "In this study we consider the risk estimation as a stochastic process based on the Sample Quantile Process (SQP) - which is a generalization of the Value-at-Risk calculated on a rolling sample. Using SQP's, we are able to show and quantify the pro-cyclicality of the current way financial institutions measure their risk. Analysing 11 stock indices, we show that, if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in periods of high volatility, the risk measure overestimates the risk. Moreover, using a simple GARCH(1,1) model, we conclude that this pro-cyclical effect is related to the clustering of volatility. We argue that this has important consequences for the regulation in times of crisis."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      126 => Essec\Faculty\Model\Contribution {#2477
        #_index: "academ_contributions"
        #_id: "8383"
        #_source: array:18 [
          "id" => "8383"
          "slug" => "risk-measure-estimates-in-quiet-and-turbulent-times-an-empirical-study"
          "yearMonth" => "2016-12"
          "year" => "2016"
          "title" => "Risk Measure Estimates in Quiet and Turbulent Times: An Empirical Study"
          "description" => "CHOTARD, R., DACOROGNA, M. et KRATZ, M. (2016). <i>Risk Measure Estimates in Quiet and Turbulent Times: An Empirical Study</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CHOTARD R."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this study we empirically explore the capacity of historical VaR to correctly predict the future risk of a financial institution. We observe that rolling samples are better able to capture the dynamics of future risks. We thus introduce another risk measure, the Sample Quantile Process, which is a generalization of the VaR calculated on a rolling sample, and study its behavior as a predictor by varying its parameters. Moreover, we study the behavior of the future risk as a function of past volatility. We show that if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in period of high volatility, the risk measure overestimates the risk, confirming that the current way financial institutions measure their risk is highly procyclical."
            "en" => "In this study we empirically explore the capacity of historical VaR to correctly predict the future risk of a financial institution. We observe that rolling samples are better able to capture the dynamics of future risks. We thus introduce another risk measure, the Sample Quantile Process, which is a generalization of the VaR calculated on a rolling sample, and study its behavior as a predictor by varying its parameters. Moreover, we study the behavior of the future risk as a function of past volatility. We show that if the past volatility is low, the historical computation of the risk measure underestimates the future risk, while in period of high volatility, the risk measure overestimates the risk, confirming that the current way financial institutions measure their risk is highly procyclical."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      127 => Essec\Faculty\Model\Contribution {#2478
        #_index: "academ_contributions"
        #_id: "8384"
        #_source: array:18 [
          "id" => "8384"
          "slug" => "risk-neutral-versus-real-world-distribution-of-publicly-listed-bank-corporations"
          "yearMonth" => "2016-07"
          "year" => "2016"
          "title" => "Risk Neutral Versus Real-World Distribution of Publicly Listed Bank Corporations"
          "description" => "DACOROGNA, M., FRANCISCO MIGUELEZ, J.J. et KRATZ, M. (2016). <i>Risk Neutral Versus Real-World Distribution of Publicly Listed Bank Corporations</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA M."
            ]
            2 => array:1 [
              "name" => "FRANCISCO MIGUELEZ J.-J."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this study, we examine different quantitative methods to recover the risk neutral distribution function associated to the prices of option on bank shares. This is useful for a wide range of applications, such as determining the implicit State guarantee that systemic financial institutions benefit from the State, or looking if the market prices correctly the fat tails of financial returns. We assess the performance of these techniques in various ways, including comparing market option prices and historical Values-at-Risk to option prices and Value-at- Risk implied by the estimated risk neutral distribution. We find that, contrary to what is expected for a market composed of risk averse investors, the latter is much smaller than the one obtained from real data. We discuss our results with respect to the theory of risk neutral valuation and investor risk preference."
            "en" => "In this study, we examine different quantitative methods to recover the risk neutral distribution function associated to the prices of option on bank shares. This is useful for a wide range of applications, such as determining the implicit State guarantee that systemic financial institutions benefit from the State, or looking if the market prices correctly the fat tails of financial returns. We assess the performance of these techniques in various ways, including comparing market option prices and historical Values-at-Risk to option prices and Value-at- Risk implied by the estimated risk neutral distribution. We find that, contrary to what is expected for a market composed of risk averse investors, the latter is much smaller than the one obtained from real data. We discuss our results with respect to the theory of risk neutral valuation and investor risk preference."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      128 => Essec\Faculty\Model\Contribution {#2479
        #_index: "academ_contributions"
        #_id: "8457"
        #_source: array:18 [
          "id" => "8457"
          "slug" => "the-impact-of-systemic-risk-on-the-diversification-benefits-of-a-risk-portfolio"
          "yearMonth" => "2013-12"
          "year" => "2013"
          "title" => "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio"
          "description" => "BUSSE, M., DACOROGNA, M. et KRATZ, M. (2013). <i>The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BUSSE M."
            ]
            2 => array:1 [
              "name" => "DACOROGNA M."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low."
            "en" => "Risk diversification is the basis of insurance and investment. It is thus crucial to study the effects that could limit it. One of them is the existence of systemic risk that affects all the policies at the same time. We introduce here a probabilistic approach to examine the consequences of its presence on the risk loading of the premium of a portfolio of insurance policies. This approach could be easily generalized for investment risk. We see that, even with a small probability of occurrence, systemic risk can reduce dramatically the diversification benefits. It is clearly revealed via a non-diversifiable term that appears in the analytical expression of the variance of our models. We propose two ways of introducing it and discuss their advantages and limitations. By using both VaR and TVaR to compute the loading, we see that only the latter captures the full effect of systemic risk when its probability to occur is low."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      129 => Essec\Faculty\Model\Contribution {#2480
        #_index: "academ_contributions"
        #_id: "8485"
        #_source: array:18 [
          "id" => "8485"
          "slug" => "there-is-a-var-beyond-usual-approximations"
          "yearMonth" => "2013-11"
          "year" => "2013"
          "title" => "There is a VaR Beyond Usual Approximations"
          "description" => "KRATZ, M. (2013). <i>There is a VaR Beyond Usual Approximations</i>. ESSEC Business School."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 21:00:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the use of the Central Limit Theorem (CLT), when assuming aggregation of independent and identically distributed (iid) observations in the portfolio model. Such a choice of modeling, in particular using light tail distributions, has proven during the crisis of 2008/2009 to be an inadequate approximation when dealing with the presence of extreme returns; as a consequence, it leads to a gross underestimation of the risks.\n
              The main objective of our study is to obtain the most accurate evaluations of the aggregated risks distribution and risk measures when working on financial or insurance data under the presence of heavy tail and to provide practical solutions for accurately estimating high quantiles of aggregated risks. We explore a new method, called Normex, to handle this problem numerically as well as theoretically, based on properties of upper order statistics. Normex provides accurate results, only weakly dependent upon the sample size and the tail index. We compare it with existing methods.
              """
            "en" => """
              Basel II and Solvency 2 both use the Value-at Risk (VaR) as the risk measure to compute the Capital Requirements. In practice, to calibrate the VaR, a normal approximation is often chosen for the unknown distribution of the yearly log returns of financial assets. This is usually justified by the use of the Central Limit Theorem (CLT), when assuming aggregation of independent and identically distributed (iid) observations in the portfolio model. Such a choice of modeling, in particular using light tail distributions, has proven during the crisis of 2008/2009 to be an inadequate approximation when dealing with the presence of extreme returns; as a consequence, it leads to a gross underestimation of the risks.\n
              The main objective of our study is to obtain the most accurate evaluations of the aggregated risks distribution and risk measures when working on financial or insurance data under the presence of heavy tail and to provide practical solutions for accurately estimating high quantiles of aggregated risks. We explore a new method, called Normex, to handle this problem numerically as well as theoretically, based on properties of upper order statistics. Normex provides accurate results, only weakly dependent upon the sample size and the tail index. We compare it with existing methods.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      130 => Essec\Faculty\Model\Contribution {#2481
        #_index: "academ_contributions"
        #_id: "8520"
        #_source: array:18 [
          "id" => "8520"
          "slug" => "what-is-the-best-risk-measure-in-practice-a-comparison-of-standard-measures"
          "yearMonth" => "2013-12"
          "year" => "2013"
          "title" => "What Is the Best Risk Measure in Practice? A Comparison of Standard Measures"
          "description" => "EMMER, S., KRATZ, M. et TASCHE, D. (2013). <i>What Is the Best Risk Measure in Practice? A Comparison of Standard Measures</i>. ESSEC Business School."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "EMMER S."
            ]
            2 => array:1 [
              "name" => "TASCHE D."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2020-12-17 18:37:46"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straight-forward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES."
            "en" => "Expected Shortfall (ES) has been widely accepted as a risk measure that is conceptually superior to Value-at-Risk (VaR). At the same time, however, it has been criticized for issues relating to backtesting. In particular, ES has been found not to be elicitable which means that backtesting for ES is less straight-forward than, e.g., backtesting for VaR. Expectiles have been suggested as potentially better alternatives to both ES and VaR. In this paper, we revisit commonly accepted desirable properties of risk measures like coherence, comonotonic additivity, robustness and elicitability. We check VaR, ES and Expectiles with regard to whether or not they enjoy these properties, with particular emphasis on Expectiles. We also consider their impact on capital allocation, an important issue in risk management. We find that, despite the caveats that apply to the estimation and backtesting of ES, it can be considered a good risk measure. In particular, there is no sufficient evidence to justify an all-inclusive replacement of ES by Expectiles in applications, especially as we provide an alternative way for backtesting of ES."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      131 => Essec\Faculty\Model\Contribution {#2482
        #_index: "academ_contributions"
        #_id: "9737"
        #_source: array:18 [
          "id" => "9737"
          "slug" => "on-the-convergence-of-the-number-of-exceedances-of-nonstationary-normal-sequences"
          "yearMonth" => "1994-05"
          "year" => "1994"
          "title" => "On the convergence of the number of exceedances of nonstationary normal sequences"
          "description" => "KRATZ, M. et HÜSLER, J. (1994). On the convergence of the number of exceedances of nonstationary normal sequences. Dans: <i>Extreme Value Theory and Applications</i>. Gaithersburg:  Journal of Research of the National Institute of Standards and Technology, pp. 539-542."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "HÜSLER Jürg"
            ]
          ]
          "ouvrage" => "Extreme Value Theory and Applications"
          "keywords" => array:1 [
            0 => "AMS classification extreme value theory"
          ]
          "updatedAt" => "2021-07-13 14:31:19"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "539-542"
            "volume" => "99"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Actes d'une conférence"
            "en" => "Conference Proceedings"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We analyze the rate of convergence of the number of exceedances of normal sequences to the Poisson limit and extend the result to the nonstationary case by using the Stein-Chen method. In addition, we consider the cases of exceedances of a constant level as well as of a particular nonconstant level."
            "en" => "We analyze the rate of convergence of the number of exceedances of normal sequences to the Poisson limit and extend the result to the nonstationary case by using the Stein-Chen method. In addition, we consider the cases of exceedances of a constant level as well as of a particular nonconstant level."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      132 => Essec\Faculty\Model\Contribution {#2483
        #_index: "academ_contributions"
        #_id: "9759"
        #_source: array:18 [
          "id" => "9759"
          "slug" => "rate-of-poisson-approximation-of-the-number-of-exceedances-of-nonstationary-normal-sequences"
          "yearMonth" => "1995-05"
          "year" => "1995"
          "title" => "Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences"
          "description" => "KRATZ, M. et HÜSLER, J. (1995). Rate of Poisson approximation of the number of exceedances of nonstationary normal sequences. <i>Stochastic Processes and their Applications</i>, 55, pp. 301-313."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "HÜSLER Jürg"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:4 [
            0 => "AMS classification -Stein-Chen approximation"
            1 => "rate of convergence"
            2 => "exceedances -maxima"
            3 => "nonstationary Gaussian sequences"
          ]
          "updatedAt" => "2021-07-13 14:31:20"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "301-313"
            "volume" => "55"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved."
            "en" => "It is known that the partial maximum of nonstationary Gaussian sequences converges in distribution and that the number of exceedances of a boundary is asymptotically a Poisson random variable, under certain restrictions. We investigate the rate of Poisson approximation for the number of exceedances. We generalize the result known in the stationary case, showing that the given bound of the rate depends on the largest positive auto-correlation value (less than 1) and the lowest values of the nonconstant boundary. We show that for special cases this bound cannot be improved."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      133 => Essec\Faculty\Model\Contribution {#2484
        #_index: "academ_contributions"
        #_id: "9781"
        #_source: array:18 [
          "id" => "9781"
          "slug" => "parameter-estimation-for-moving-averages-with-positive-innovations"
          "yearMonth" => "1996-01"
          "year" => "1996"
          "title" => "Parameter estimation for moving averages with positive innovations"
          "description" => "KRATZ, M., RESNICK, S. et FEIGIN, P. (1996). Parameter estimation for moving averages with positive innovations. <i>Annals of Applied Probability</i>, 6, pp. 1157-1190."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "RESNICK Sidney"
            ]
            2 => array:1 [
              "name" => "FEIGIN Paul"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:1 [
            0 => "AMS classification -ARMA"
          ]
          "updatedAt" => "2021-07-13 14:31:20"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "1157-1190"
            "volume" => "6"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This paper continues the study of time series models generated by non-negative innovations which was begun in Feigin and Resnick (1992,1994). We concentrate on moving average processes. Estimators for moving average coefficients are proposed and consistency and asymptotic distributions established for the case of an order one moving average assuming either the right or left tail of the innovation distribution is regularly varying. The rate of convergence can be superior to that of the Yule--Walker or maximum likelihood estimators."
            "en" => "This paper continues the study of time series models generated by non-negative innovations which was begun in Feigin and Resnick (1992,1994). We concentrate on moving average processes. Estimators for moving average coefficients are proposed and consistency and asymptotic distributions established for the case of an order one moving average assuming either the right or left tail of the innovation distribution is regularly varying. The rate of convergence can be superior to that of the Yule--Walker or maximum likelihood estimators."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      134 => Essec\Faculty\Model\Contribution {#2485
        #_index: "academ_contributions"
        #_id: "9788"
        #_source: array:18 [
          "id" => "9788"
          "slug" => "the-q-q-estimator-and-heavy-tails"
          "yearMonth" => "1996-04"
          "year" => "1996"
          "title" => "The Q-Q estimator and heavy tails"
          "description" => "KRATZ, M. et RESNICK, S. (1996). The Q-Q estimator and heavy tails. <i>Stochastic Models</i>, 12(4), pp. 699-724."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "RESNICK Sidney"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:3 [
            0 => "AMS classification -parameter estimation"
            1 => "weak convergence"
            2 => "consistency -time series analysis -qq-plot -heavy tails -regular variation"
          ]
          "updatedAt" => "2021-07-13 14:31:20"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "699-724"
            "volume" => "12"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "A common visual technique for assessing goodness of fit and estimating location and scale is the qq--plot. We apply this technique to data from a Pareto distribution and more generally to data generated by a distribution with a heavy tail. A procedure for assessing the presence of heavy tails and for estimating the parameter of regular variation is discussed which can supplement other standard techniques such as the Hill plot. Some examples are given using telecommunications data."
            "en" => "A common visual technique for assessing goodness of fit and estimating location and scale is the qq--plot. We apply this technique to data from a Pareto distribution and more generally to data generated by a distribution with a heavy tail. A procedure for assessing the presence of heavy tails and for estimating the parameter of regular variation is discussed which can supplement other standard techniques such as the Hill plot. Some examples are given using telecommunications data."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      135 => Essec\Faculty\Model\Contribution {#2486
        #_index: "academ_contributions"
        #_id: "9806"
        #_source: array:18 [
          "id" => "9806"
          "slug" => "hermite-polynomial-expansion-for-non-smooth-functionals-of-stationary-gaussian-processes-crossings-and-extremes"
          "yearMonth" => "1997-03"
          "year" => "1997"
          "title" => "Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes"
          "description" => "KRATZ, M. et LEON, J. (1997). Hermite polynomial expansion for non-smooth functionals of stationary Gaussian processes: crossings and extremes. <i>Stochastic Processes and their Applications</i>, 66(2), pp. 237-252."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON José"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:5 [
            0 => "AMS classification"
            1 => "Gaussian processes"
            2 => "Crossings"
            3 => "Extremes"
            4 => "Hermite polynomial expansion"
          ]
          "updatedAt" => "2021-07-13 14:31:20"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "237-252"
            "volume" => "66"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process."
            "en" => "We propose a new method to get the Hermite polynomial expansion of crossings of any level by a stationary Gaussian process, as well as the one of the number of maxima in an interval, under some assumptions on the spectral moments of the process."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      136 => Essec\Faculty\Model\Contribution {#2487
        #_index: "academ_contributions"
        #_id: "9815"
        #_source: array:18 [
          "id" => "9815"
          "slug" => "on-the-rate-of-convergence-for-extremes-of-mean-square-differentiable-stationary-normal-processes"
          "yearMonth" => "1997-12"
          "year" => "1997"
          "title" => "On the rate of convergence for extremes of mean square differentiable stationary normal processes"
          "description" => "KRATZ, M. et ROOTZÉN, H. (1997). On the rate of convergence for extremes of mean square differentiable stationary normal processes. <i>Journal of Applied Probability</i>, 34(4), pp. 908-923."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ROOTZÉN Holger"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:1 [
            0 => """
              AMS classification -\n
              60G70 -60G15 -60F05rate of convergence -extremes -normal processes -Poisson convergence
              """
          ]
          "updatedAt" => "2021-07-13 14:31:21"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "908-923"
            "volume" => "34"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Let ${\xi(t); t\geq 0}$ be a normalized continuous mean square differentiable stationary normal process with covariance function $r(t)$. Further, let $$ \rho(t)=\frac{(1-r(t))^2}{1-r(t)^2+r'(t)|r'(t)|} $$ and set $$ \delta=\frac{1}{2}\wedge \inf_{t\geq 0} \rho(t). $$ We give bounds which are roughly of the order $T^{-\delta}$ for the rate of convergence of the distribution of the maximum and of the number of upcrossings of a high level by $\xi(t)$ in the interval $[0,T]$. The results assume that $r(t)$ and $r'(t)$ decay polynomially at infinity and that $r''(t)$ is suitably bounded. For the number of upcrossings it is in addition assumed that $r(t)$ is non-negative. Some applications are developed."
            "en" => "Let ${\xi(t); t\geq 0}$ be a normalized continuous mean square differentiable stationary normal process with covariance function $r(t)$. Further, let $$ \rho(t)=\frac{(1-r(t))^2}{1-r(t)^2+r'(t)|r'(t)|} $$ and set $$ \delta=\frac{1}{2}\wedge \inf_{t\geq 0} \rho(t). $$ We give bounds which are roughly of the order $T^{-\delta}$ for the rate of convergence of the distribution of the maximum and of the number of upcrossings of a high level by $\xi(t)$ in the interval $[0,T]$. The results assume that $r(t)$ and $r'(t)$ decay polynomially at infinity and that $r''(t)$ is suitably bounded. For the number of upcrossings it is in addition assumed that $r(t)$ is non-negative. Some applications are developed."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      137 => Essec\Faculty\Model\Contribution {#2488
        #_index: "academ_contributions"
        #_id: "9871"
        #_source: array:18 [
          "id" => "9871"
          "slug" => "central-limit-theorems-for-the-number-of-maxima-and-some-estimator-of-the-second-spectral-moment-of-a-stationary-gaussian-process-applications-in-hydroscience"
          "yearMonth" => "2000-03"
          "year" => "2000"
          "title" => "Central limit theorems for the number of maxima and some estimator of the second spectral moment of a stationary Gaussian process. Applications in hydroscience"
          "description" => "KRATZ, M. et LEON, J. (2000). Central limit theorems for the number of maxima and some estimator of the second spectral moment of a stationary Gaussian process. Applications in hydroscience. <i>Extremes</i>, 3(1), pp. 57-86."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON José"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:9 [
            0 => "AMS classification -asymptotic variance"
            1 => "central limit theorem"
            2 => "crossings"
            3 => "estimation"
            4 => "Gaussian processes"
            5 => "Hermite polynomials"
            6 => "hydroscience"
            7 => "maxima"
            8 => "spectral moment"
          ]
          "updatedAt" => "2021-07-13 14:31:22"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "57-86"
            "volume" => "3"
            "number" => "1"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Let X = (Xt, t  0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima."
            "en" => "Let X = (Xt, t  0) be a mean zero stationary Gaussian process with variance one, assumed to satisfy some conditions on its covariance function r. Central limit theorems and asymptotic variance formulas are provided for estimators of the square root of the second spectral moment of the process and for the number of maxima in an interval, with some applications in hydroscience. A consistent estimator of the asymptotic variance is proposed for the number of maxima."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      138 => Essec\Faculty\Model\Contribution {#2489
        #_index: "academ_contributions"
        #_id: "9872"
        #_source: array:18 [
          "id" => "9872"
          "slug" => "chaos-expansions-and-level-crossings"
          "yearMonth" => "2000-09"
          "year" => "2000"
          "title" => "Chaos expansions and level crossings"
          "description" => "KRATZ, M. (2000). <i>Chaos expansions and level crossings</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:22"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              In this paper we show that the number of crossings at any \n
              level by a smooth stationary Gaussian process X on the interval [0,t] can be defined as $N_t(x)= \int_0^t \delta_x(X_s)\n
              | \dot X_s| ds$ in the Sobolev space D(2,alpha) for any alpha <1/4.
              """
            "en" => """
              In this paper we show that the number of crossings at any \n
              level by a smooth stationary Gaussian process X on the interval [0,t] can be defined as $N_t(x)= \int_0^t \delta_x(X_s)\n
              | \dot X_s| ds$ in the Sobolev space D(2,alpha) for any alpha <1/4.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      139 => Essec\Faculty\Model\Contribution {#2490
        #_index: "academ_contributions"
        #_id: "9894"
        #_source: array:18 [
          "id" => "9894"
          "slug" => "central-limit-theorems-for-level-functionals-of-stationary-gaussian-processes-and-fields"
          "yearMonth" => "2001-07"
          "year" => "2001"
          "title" => "Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields"
          "description" => "KRATZ, M. et LEON, J. (2001). Central Limit Theorems for Level Functionals of Stationary Gaussian Processes and Fields. <i>Journal of Theoretical Probability</i>, 14(3), pp. 639-672."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON José"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:9 [
            0 => """
              AMS classification -\n
              asymptotic variance
              """
            1 => "central limit theorem"
            2 => "crossings"
            3 => "Gaussian fields"
            4 => "Gaussian processes"
            5 => "Hermite polynomials"
            6 => "level curve"
            7 => "maxima"
            8 => "sojourn time"
          ]
          "updatedAt" => "2020-12-17 18:37:46"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "639-672"
            "volume" => "14"
            "number" => "3"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We introduce a general method, which combines the one developed by authors in 1997 and one derived from the work of Malevich, Cuzick and mainly Berman, to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field."
            "en" => "We introduce a general method, which combines the one developed by authors in 1997 and one derived from the work of Malevich, Cuzick and mainly Berman, to provide in an easy way a CLT for level functionals of a Gaussian process, as well as a CLT for the length of a level curve of a Gaussian field."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      140 => Essec\Faculty\Model\Contribution {#2491
        #_index: "academ_contributions"
        #_id: "10020"
        #_source: array:18 [
          "id" => "10020"
          "slug" => "on-a-representation-of-gibbs-measure-for-r-e-m"
          "yearMonth" => "2004-05"
          "year" => "2004"
          "title" => "On a representation of Gibbs measure for R.E.M."
          "description" => "KRATZ, M. et PICCO, P. (2004). On a representation of Gibbs measure for R.E.M. <i>Annals of Applied Probability</i>, 14(2), pp. 651-677."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PICCO Pierre"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:7 [
            0 => """
              AMS classification -\n
              62G30
              """
            1 => "82B44"
            2 => """
              62G32\n
              Extremes
              """
            3 => "Gaussian r.v."
            4 => "order statistics"
            5 => "random spin systems"
            6 => "uniform r.v."
          ]
          "updatedAt" => "2021-07-13 14:31:25"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "651-677"
            "volume" => "14"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature."
            "en" => "In this work we consider a problem related to the equilibrium statistical mechanics of spin glasses, namely the study of the Gibbs measure of the random energy model. For solving this problem, new results of independent interest on sums of spacings for i.i.d. Gaussian random variables are presented. Then we give a precise description of the support of the Gibbs measure below the critical temperature."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      141 => Essec\Faculty\Model\Contribution {#2492
        #_index: "academ_contributions"
        #_id: "10086"
        #_source: array:18 [
          "id" => "10086"
          "slug" => "some-contributions-in-probability-and-statistics-of-extremes"
          "yearMonth" => "2005-11"
          "year" => "2005"
          "title" => "Some contributions in probability and statistics of extremes"
          "description" => "KRATZ, M. (2005). <i>Some contributions in probability and statistics of extremes</i>."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-07-13 14:31:26"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Synthèse de mes travaux de recherche sur plusieurs thèmes regroupés en deux axes. Le premier axe est constitué de l'étude des franchissements de niveau par des processus gaussiens, ou de façon plus générale, l'étude de fonctionnelles non linéaires de processus gaussiens. Le second axe traite de problèmes de statistique et de mécanique statistique en temps discret tels l'étude du processus des excédences, l’estimation de paramètres et leur validité lors de la modélisation par des processus de distribution à queue épaisse (heavy tailed), et enfin l'étude de fonctions liées aux statistiques d’ordre de processus gaussiens en vue d’application à la mécanique statistique."
            "en" => "Synthèse de mes travaux de recherche sur plusieurs thèmes regroupés en deux axes. Le premier axe est constitué de l'étude des franchissements de niveau par des processus gaussiens, ou de façon plus générale, l'étude de fonctionnelles non linéaires de processus gaussiens. Le second axe traite de problèmes de statistique et de mécanique statistique en temps discret tels l'étude du processus des excédences, l’estimation de paramètres et leur validité lors de la modélisation par des processus de distribution à queue épaisse (heavy tailed), et enfin l'étude de fonctions liées aux statistiques d’ordre de processus gaussiens en vue d’application à la mécanique statistique."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      142 => Essec\Faculty\Model\Contribution {#2493
        #_index: "academ_contributions"
        #_id: "10115"
        #_source: array:18 [
          "id" => "10115"
          "slug" => "curve-crossings-and-specular-points-dapres-longuet-higgins"
          "yearMonth" => "2006-07"
          "year" => "2006"
          "title" => "Curve crossings and specular points, d'après Longuet-Higgins."
          "description" => "KRATZ, M. et LEON, J. (2006). Curve crossings and specular points, d'après Longuet-Higgins. Dans: 31th Conference on Stochastic Processes and their Applications. Paris."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON José"
            ]
          ]
          "ouvrage" => "31th Conference on Stochastic Processes and their Applications"
          "keywords" => array:7 [
            0 => "crossings"
            1 => "CLT"
            2 => "Gaussian fields"
            3 => "Hermite polynomials"
            4 => "level curve"
            5 => "specular point"
            6 => "twinkle"
          ]
          "updatedAt" => "2021-07-13 14:31:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              We use the Hermite expansion for the number of crossings of a differentiable curve by a stationary process to study\n
              the number of specular points of a curve and to understand its dynamical behavior, in particular asymptotically (CLT).
              """
            "en" => """
              We use the Hermite expansion for the number of crossings of a differentiable curve by a stationary process to study\n
              the number of specular points of a curve and to understand its dynamical behavior, in particular asymptotically (CLT).
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      143 => Essec\Faculty\Model\Contribution {#2494
        #_index: "academ_contributions"
        #_id: "10123"
        #_source: array:18 [
          "id" => "10123"
          "slug" => "funciones-de-distribucion-de-cuerdas-en-medios-porosos"
          "yearMonth" => "2006-11"
          "year" => "2006"
          "title" => "Funciones de distribucion de cuerdas en medios porosos."
          "description" => "KRATZ, M., ESTRADE, A. et IRIBARREN, I. (2006). Funciones de distribucion de cuerdas en medios porosos. Dans: Rencontres France-Espagne-Venezuela de probabilité et statistique mathématique. Choroni."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ESTRADE Anne"
            ]
            2 => array:1 [
              "name" => "IRIBARREN Ileana"
            ]
          ]
          "ouvrage" => "Rencontres France-Espagne-Venezuela de probabilité et statistique mathématique"
          "keywords" => array:6 [
            0 => "chords"
            1 => "(up/down) crossings"
            2 => "level-cut process"
            3 => "Palm measure"
            4 => "porous media"
            5 => "Rice formula"
          ]
          "updatedAt" => "2021-07-13 14:31:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              We consider a two-phases model to describe a porous medium; an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or\n
              greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase.\n
              Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point\n
              correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics\n
              literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato).
              """
            "en" => """
              We consider a two-phases model to describe a porous medium; an image of this medium, seen as a random level surface of a process X, is divided into two phases (pore and solid) according to whether X is less or\n
              greater than some threshold. The statistical approach is made by observing the chord functions, i.e. the lengths of time intervals when X is in the same phase.\n
              Based on excursions theory, in particular on level crossings number, this work provides the exact formula of the chord-distribution functions and the two-point\n
              correlation function obtained from cross-sectional micrographs, proving in a rigorous way, as well as generalizing, some results published in the physics\n
              literature in the 90s (see for instance Berk, Teubner, Roberts or Torquato).
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      144 => Essec\Faculty\Model\Contribution {#2495
        #_index: "academ_contributions"
        #_id: "10143"
        #_source: array:18 [
          "id" => "10143"
          "slug" => "on-the-second-moment-of-the-number-of-crossings-by-a-stationary-gaussian-process"
          "yearMonth" => "2006-07"
          "year" => "2006"
          "title" => "On the second moment of the number of crossings by a stationary Gaussian process"
          "description" => "KRATZ, M. et LEON, J. (2006). On the second moment of the number of crossings by a stationary Gaussian process. <i>Annals of Probability</i>, 34(4), pp. 1601-1607."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "LEON José"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:4 [
            0 => """
              AMS classification -\n
              60G15 -60G10 -60G70Crossings
              """
            1 => "Gaussian processes"
            2 => "Geman condition"
            3 => "Hermite polynomials -level curve -spectral moment"
          ]
          "updatedAt" => "2021-07-13 14:31:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => "1601-1607"
            "volume" => "34"
            "number" => "4"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Cramér and Leadbetter introduced a sufficient condition  to have a finite variance of the zeros number of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows taht the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman conditiion."
            "en" => "Cramér and Leadbetter introduced a sufficient condition  to have a finite variance of the zeros number of a centered stationary Gaussian process with twice differentiable covariance function r. This condition is known as the Geman condition since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows taht the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman conditiion."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      145 => Essec\Faculty\Model\Contribution {#2496
        #_index: "academ_contributions"
        #_id: "10190"
        #_source: array:18 [
          "id" => "10190"
          "slug" => "fixed-points-of-the-abe-formulation-of-stochastic-hopfield-networks"
          "yearMonth" => "2007-09"
          "year" => "2007"
          "title" => "Fixed points of the Abe formulation of Stochastic Hopfield Networks"
          "description" => "KRATZ, M., ATENCIA, M. et JOYA, G. (2007). Fixed points of the Abe formulation of Stochastic Hopfield Networks. Dans: 17th ICANN. Porto."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "ATENCIA Miguel"
            ]
            2 => array:1 [
              "name" => "JOYA Gonzalo"
            ]
          ]
          "ouvrage" => "17th ICANN"
          "keywords" => array:1 [
            0 => "Hopfield network"
          ]
          "updatedAt" => "2021-07-13 14:31:29"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be\n
              unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization.
              """
            "en" => """
              The stability of stochastic Hopfield neural networks, in the Abe formulation, is studied. The aim is to determine whether the ability of the deterministic system to solve combinatorial optimization problems is preserved after the addition of random noise. In particular, the stochastic stability of the attractor set is analyzed: vertices, which are feasible points of the problem, should be stable, whereas interior points, which are unfeasible, should be\n
              unstable. Conditions on the noise intensity are stated, so that these properties are guaranteed. This theoretical investigation establishes the foundations for practical application of stochastic networks to combinatorial optimization.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      146 => Essec\Faculty\Model\Contribution {#2497
        #_index: "academ_contributions"
        #_id: "10789"
        #_source: array:18 [
          "id" => "10789"
          "slug" => "probabilistic-forecasting-of-bubbles-and-flash-crashes"
          "yearMonth" => "2020-05"
          "year" => "2020"
          "title" => "Probabilistic Forecasting of Bubbles and Flash Crashes"
          "description" => "BANERJEE, A., CHEVILLON, G. et KRATZ, M. (2020). Probabilistic Forecasting of Bubbles and Flash Crashes. <i>Econometrics Journal</i>, 23(2)."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "CHEVILLON Guillaume"
              "bid" => "B00072304"
              "slug" => "chevillon-guillaume"
            ]
            1 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            2 => array:1 [
              "name" => "BANERJEE A."
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.researchgate.net/publication/339273040_Probabilistic_Forecasting_of_Bubbles_and_Flash_Crashes"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => "23"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We propose a near explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T−α) distance of unity, with α ∈ (0, 1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. In empirical illustrations, we estimate predictive probabilities of bubbles or flash crashes in financial asset prices."
            "en" => "We propose a near explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T−α) distance of unity, with α ∈ (0, 1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. In empirical illustrations, we estimate predictive probabilities of bubbles or flash crashes in financial asset prices."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      147 => Essec\Faculty\Model\Contribution {#2498
        #_index: "academ_contributions"
        #_id: "10947"
        #_source: array:18 [
          "id" => "10947"
          "slug" => "risk-concentration-under-second-order-regular-variation"
          "yearMonth" => "2020-06"
          "year" => "2020"
          "title" => "Risk Concentration Under Second Order Regular Variation"
          "description" => "DAS, S. et KRATZ, M. (2020). Risk Concentration Under Second Order Regular Variation. <i>Extremes</i>, 23, pp. 381-410."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DAS Shubhabrata"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-020-00382-3"
          "publicationInfo" => array:3 [
            "pages" => "381-410"
            "volume" => "23"
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to study their convergence rates. In this paper, we provide the asymptotic rate of convergence of the measure of risk concentration for a portfolio of heavy-tailed risk factors, when the portfolio admits the so-called second order regular variation property. Moreover, we explore the relationship between multivariate second order regular variation for a vector (e.g., risk factors) and the second order regular variation property for the sum of its components (e.g., the portfolio of risk factors). Results are illustrated with a variety of examples."
            "en" => "Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to study their convergence rates. In this paper, we provide the asymptotic rate of convergence of the measure of risk concentration for a portfolio of heavy-tailed risk factors, when the portfolio admits the so-called second order regular variation property. Moreover, we explore the relationship between multivariate second order regular variation for a vector (e.g., risk factors) and the second order regular variation property for the sum of its components (e.g., the portfolio of risk factors). Results are illustrated with a variety of examples."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      148 => Essec\Faculty\Model\Contribution {#2499
        #_index: "academ_contributions"
        #_id: "11613"
        #_source: array:18 [
          "id" => "11613"
          "slug" => "lapproche-statistique-au-service-de-lhumain-mieux-comprendre-les-risques-cyber-pour-une-societe-plus-resiliente"
          "yearMonth" => "2019-12"
          "year" => "2019"
          "title" => "L’approche statistique au service de l’humain : mieux comprendre les risques cyber pour une société plus résiliente"
          "description" => "KRATZ, M. (2019). L’approche statistique au service de l’humain : mieux comprendre les risques cyber pour une société plus résiliente. <i>Revue de la Gendarmerie Nationale</i>, (266), pp. 61-62."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => ""
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://www.gendarmerie.interieur.gouv.fr/crgn/content/download/1170/document/Revue%20gendarmerie%20266%20FIC.pdf"
          "publicationInfo" => array:3 [
            "pages" => "61-62"
            "volume" => null
            "number" => "266"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue professionnelle"
            "en" => "Professional journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      149 => Essec\Faculty\Model\Contribution {#2500
        #_index: "academ_contributions"
        #_id: "11965"
        #_source: array:18 [
          "id" => "11965"
          "slug" => "moving-from-uncertainty-to-risk-the-case-of-cyber-risk"
          "yearMonth" => "2020-10"
          "year" => "2020"
          "title" => "Moving from Uncertainty to Risk: the Case of Cyber Risk."
          "description" => "KRATZ, M. et DACOROGNA, M. (2020). Moving from Uncertainty to Risk: the Case of Cyber Risk. Dans: Hugo Loiseau, Daniel Ventre, Hartmut Aden eds. <i>Cybersecurity in Humanities and Social Sciences. A Research Methods Approach</i>. 1st ed. London & Hoboken: ISTE - WILEY, pp. 123-152."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "Cybersecurity in Humanities and Social Sciences. A Research Methods Approach"
          "keywords" => array:1 [
            0 => "cyber risk, cyber threats,  cybercrime,  cybersecurity, data cleansing"
          ]
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => "https://doi.org/10.1002/9781119777588.ch5"
          "publicationInfo" => array:3 [
            "pages" => "123-152"
            "volume" => "1"
            "number" => "5"
          ]
          "type" => array:2 [
            "fr" => "Chapitres"
            "en" => "Book chapters"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "This chapter describes the quantitative methods to cope with cyber‐threats problem. It illustrates the methodological aspects along with the study conducted on the French Gendarmerie Nationale (GN) database on cybercrime complaints registered at their offices. The chapter explains the scientific approach to move from the uncertainty created in society by cybercrimes to a measurable cyber risk. It discusses data cleansing as an inescapable step to develop valuable models for exploration of dataset in the GN database. The chapter deals with the problem of learning important behaviors from the data from statistical exploration on the various variables of the dataset"
            "en" => "This chapter describes the quantitative methods to cope with cyber‐threats problem. It illustrates the methodological aspects along with the study conducted on the French Gendarmerie Nationale (GN) database on cybercrime complaints registered at their offices. The chapter explains the scientific approach to move from the uncertainty created in society by cybercrimes to a measurable cyber risk. It discusses data cleansing as an inescapable step to develop valuable models for exploration of dataset in the GN database. The chapter deals with the problem of learning important behaviors from the data from statistical exploration on the various variables of the dataset"
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      150 => Essec\Faculty\Model\Contribution {#2501
        #_index: "academ_contributions"
        #_id: "12240"
        #_source: array:18 [
          "id" => "12240"
          "slug" => "on-the-regularity-of-functionals-for-stationary-gaussian-processes-invited-session"
          "yearMonth" => "2019-07"
          "year" => "2019"
          "title" => "On the regularity of functionals for stationary Gaussian processes [invited session]"
          "description" => "KRATZ, M. (2019). On the regularity of functionals for stationary Gaussian processes [invited session]. Dans: 41th SPA (Stochastic Processes and its Applications) conference, Northwestern Univ."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "41th SPA (Stochastic Processes and its Applications) conference, Northwestern Univ."
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      151 => Essec\Faculty\Model\Contribution {#2502
        #_index: "academ_contributions"
        #_id: "12242"
        #_source: array:18 [
          "id" => "12242"
          "slug" => "pro-cyclicality-of-traditional-risk-measurements-quantifying-and-highlighting-factors-at-its-source"
          "yearMonth" => "2019-11"
          "year" => "2019"
          "title" => "Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source"
          "description" => "KRATZ, M. (2019). Pro-Cyclicality of Traditional Risk Measurements: Quantifying and Highlighting Factors at its Source. Dans: Zurich-Hannover workshop on Insurance and Financial Mathematics. Hannover."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "Zurich-Hannover workshop on Insurance and Financial Mathematics"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      152 => Essec\Faculty\Model\Contribution {#2503
        #_index: "academ_contributions"
        #_id: "12244"
        #_source: array:18 [
          "id" => "12244"
          "slug" => "how-does-market-price-extremes-of-underlying-shares-in-the-options-market"
          "yearMonth" => "2019-12"
          "year" => "2019"
          "title" => "How does market price extremes of underlying shares in the options market?"
          "description" => "KRATZ, M. (2019). How does market price extremes of underlying shares in the options market? Dans: 14th International Conference on Computational and Financial Econometrics (CFE 2020). London."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "14th International Conference on Computational and Financial Econometrics (CFE 2020)"
          "keywords" => []
          "updatedAt" => "2021-09-24 10:33:27"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => null
            "number" => null
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => null
            "en" => null
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      153 => Essec\Faculty\Model\Contribution {#2504
        #_index: "academ_contributions"
        #_id: "12568"
        #_source: array:18 [
          "id" => "12568"
          "slug" => "combining-machine-learning-extreme-value-theory-for-modelling-multimodal-non-homogeneous-data"
          "yearMonth" => "2021-07"
          "year" => "2021"
          "title" => "Combining Machine Learning & Extreme Value Theory for modelling multimodal non homogeneous data"
          "description" => "KRATZ, M. et CHAAR, A. (2021). Combining Machine Learning & Extreme Value Theory for modelling multimodal non homogeneous data. Dans: 63rd World Statistics Congress 2021, Invited Session: Extreme Value Statistics. Virtual."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "CHAAR A"
            ]
          ]
          "ouvrage" => "63rd World Statistics Congress 2021, Invited Session: Extreme Value Statistics"
          "keywords" => []
          "updatedAt" => "2022-11-02 12:47:22"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      154 => Essec\Faculty\Model\Contribution {#2505
        #_index: "academ_contributions"
        #_id: "12775"
        #_source: array:18 [
          "id" => "12775"
          "slug" => "multi-normex-distributions-for-the-sum-of-random-vectors-rates-of-convergence"
          "yearMonth" => "2021-07"
          "year" => "2021"
          "title" => "Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence"
          "description" => "KRATZ, M. et PROKOPENKO, E. (2021). <i>Multi-Normex Distributions for the Sum of Random Vectors. Rates of Convergence</i>. 2102, ESSEC Business School."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO Evgeny"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:12 [
            0 => "aggregation"
            1 => "central limit theorem"
            2 => "dependence"
            3 => "extreme value theorem"
            4 => "geometrical quantiles"
            5 => "multivariate regular variation"
            6 => "(multivariate) Pareto distribution"
            7 => "ordered statistics"
            8 => "QQ-plots"
            9 => "rate of convergence"
            10 => "second order regular variation"
            11 => "sum of random vectors"
          ]
          "updatedAt" => "2023-01-27 01:00:41"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Cahier de Recherche"
            "en" => "Working Papers"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed - random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ - approach from a univariate to a multivariate framework. We propose two possible multinormex - distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution - for describing the mean behavior, via the CLT, while the difference between the - two versions comes from using the exact distribution or the EV theorem for the maximum. - The main theorems provide the rate of convergence for each version of the multi-normex - distributions towards the distribution of the sum, assuming second order regular variation - property for the norm of the parent random vector when considering the MRV-normex - case. Numerical illustrations and comparisons are proposed with various dependence structures - on the parent random vector, using QQ-plots based on geometrical quantiles."
            "en" => "We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed - random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ - approach from a univariate to a multivariate framework. We propose two possible multinormex - distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution - for describing the mean behavior, via the CLT, while the difference between the - two versions comes from using the exact distribution or the EV theorem for the maximum. - The main theorems provide the rate of convergence for each version of the multi-normex - distributions towards the distribution of the sum, assuming second order regular variation - property for the norm of the parent random vector when considering the MRV-normex - case. Numerical illustrations and comparisons are proposed with various dependence structures - on the parent random vector, using QQ-plots based on geometrical quantiles."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      155 => Essec\Faculty\Model\Contribution {#2506
        #_index: "academ_contributions"
        #_id: "12797"
        #_source: array:18 [
          "id" => "12797"
          "slug" => "multi-normex-distributions"
          "yearMonth" => "2021-12"
          "year" => "2021"
          "title" => "Multi-Normex Distributions"
          "description" => "KRATZ, M. et PROKOPENKO, P. (2021). Multi-Normex Distributions. Dans: 14th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2021). London."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO P"
            ]
          ]
          "ouvrage" => "14th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2021)"
          "keywords" => []
          "updatedAt" => "2023-01-27 01:00:42"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      156 => Essec\Faculty\Model\Contribution {#2507
        #_index: "academ_contributions"
        #_id: "13090"
        #_source: array:18 [
          "id" => "13090"
          "slug" => "multi-normex-approach-based-on-ordered-statistics-for-evaluating-the-sum-of-heavy-tailed-random-vectors"
          "yearMonth" => "2022-05"
          "year" => "2022"
          "title" => "Multi-Normex Approach based on Ordered Statistics for evaluating the Sum of Heavy-tailed Random Vectors"
          "description" => "KRATZ, M. et PROKOPENKO, E. (2022). Multi-Normex Approach based on Ordered Statistics for evaluating the Sum of Heavy-tailed Random Vectors. Dans: 14th International Conference on Ordered Statistical Data. Vietri."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO Evgeny"
            ]
          ]
          "ouvrage" => "14th International Conference on Ordered Statistical Data"
          "keywords" => []
          "updatedAt" => "2023-01-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      157 => Essec\Faculty\Model\Contribution {#2508
        #_index: "academ_contributions"
        #_id: "13091"
        #_source: array:18 [
          "id" => "13091"
          "slug" => "multi-normex-for-evaluating-the-distribution-of-aggregated-heavy-tailed-risks"
          "yearMonth" => "2022-06"
          "year" => "2022"
          "title" => "Multi-Normex for evaluating the Distribution of Aggregated Heavy-tailed Risks"
          "description" => "KRATZ, M. et PROKOPENKO, E. (2022). Multi-Normex for evaluating the Distribution of Aggregated Heavy-tailed Risks. Dans: 53èmes Journées de Statistique de la Société Française de Statistique (SFdS). Lyon."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO Evgeny"
            ]
          ]
          "ouvrage" => "53èmes Journées de Statistique de la Société Française de Statistique (SFdS)"
          "keywords" => []
          "updatedAt" => "2023-07-20 12:44:58"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      158 => Essec\Faculty\Model\Contribution {#2509
        #_index: "academ_contributions"
        #_id: "13092"
        #_source: array:18 [
          "id" => "13092"
          "slug" => "consequences-for-risk-management-of-the-analysis-of-the-gn-database-on-cyber-attacks"
          "yearMonth" => "2022-05"
          "year" => "2022"
          "title" => "Consequences for risk management of the analysis of the GN database on cyber attacks"
          "description" => "DACOROGNA, M. et KRATZ, M. (2022). Consequences for risk management of the analysis of the GN database on cyber attacks. Dans: ASTIN Cyber Workshop – Capacity Crunch in the Cyber Market. London."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "ASTIN Cyber Workshop – Capacity Crunch in the Cyber Market"
          "keywords" => []
          "updatedAt" => "2023-07-20 12:46:14"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      159 => Essec\Faculty\Model\Contribution {#2510
        #_index: "academ_contributions"
        #_id: "13409"
        #_source: array:18 [
          "id" => "13409"
          "slug" => "pro-cyclicality-beyond-business-cycle"
          "yearMonth" => "2023-05"
          "year" => "2023"
          "title" => "Pro-cyclicality beyond business cycle"
          "description" => "BRÄUTIGAM, M., DACOROGNA, M. et KRATZ, M. (2023). Pro-cyclicality beyond business cycle. <i>Mathematical Finance</i>, 33(2), pp. 308-341."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
            2 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Bahadur representation"
            1 => "estimation"
            2 => """
              financial risk management -\n
              joint asymptotic normality
              """
            3 => "market state"
            4 => "regulation"
            5 => """
              riskmeasure -\n
              statistics
              """
          ]
          "updatedAt" => "2024-10-31 13:51:19"
          "publicationUrl" => "https://onlinelibrary.wiley.com/doi/full/10.1111/mafi.12369"
          "publicationInfo" => array:3 [
            "pages" => "308-341"
            "volume" => "33"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We show that pro-cyclicality is inherent in risk measure estimates based on historical data. Taking the example of VaR, we show that the empirical VaR measure is mean-reverting over a 1-year horizon when the portfolio is held fixed. It means that a capital requirement rule based on historical measurements of VaR tends in calm times to understate future required capital and tends in volatile times to overstate it. To quantify this pro-cyclicality, we develop a simple and efficient methodology, which we apply to major equity market indices. We make the interesting point that the pro-cyclicality property holds true even in a world with constant volatility, though the empirical magnitude of the mean-reversion is greater than what would be observed in that special case."
            "en" => "We show that pro-cyclicality is inherent in risk measure estimates based on historical data. Taking the example of VaR, we show that the empirical VaR measure is mean-reverting over a 1-year horizon when the portfolio is held fixed. It means that a capital requirement rule based on historical measurements of VaR tends in calm times to understate future required capital and tends in volatile times to overstate it. To quantify this pro-cyclicality, we develop a simple and efficient methodology, which we apply to major equity market indices. We make the interesting point that the pro-cyclicality property holds true even in a world with constant volatility, though the empirical magnitude of the mean-reversion is greater than what would be observed in that special case."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      160 => Essec\Faculty\Model\Contribution {#2511
        #_index: "academ_contributions"
        #_id: "13430"
        #_source: array:18 [
          "id" => "13430"
          "slug" => "multi-normex-distributions-for-the-sum-of-random-vectors-rates-of-convergence"
          "yearMonth" => "2023-01"
          "year" => "2023"
          "title" => "Multi-normex distributions for the sum of random vectors. Rates of convergence"
          "description" => "KRATZ, M. et PROKOPENKO, E. (2023). Multi-normex distributions for the sum of random vectors. Rates of convergence. <i>Extremes</i>, 26, pp. 509-544."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO Evgeny"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:10 [
            0 => "aggregation"
            1 => "central limit theorem"
            2 => "dependence"
            3 => "extreme value theorem"
            4 => "geometrical quantiles"
            5 => "multivariate regular variation"
            6 => "(multivariate) Pareto distribution"
            7 => "ordered statistics"
            8 => "QQ-plots"
            9 => "rate of convergence"
          ]
          "updatedAt" => "2024-03-18 09:59:05"
          "publicationUrl" => "https://link.springer.com/article/10.1007/s10687-022-00461-7"
          "publicationInfo" => array:3 [
            "pages" => "509-544"
            "volume" => "26"
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ approach from a univariate to a multivariate framework. We propose two possible multi-normex distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution for describing the mean behavior, via the CLT, while the difference between the two versions comes from using the exact distribution or the EV theorem for the maximum. The main theorems provide the rate of convergence for each version of the multi-normex distributions towards the distribution of the sum, assuming second order regular variation property for the norm of the parent random vector when considering the MRV-normex case. Numerical illustrations and comparisons are proposed with various dependence structures on the parent random vector, using QQ-plots based on geometrical quantiles."
            "en" => "We build a sharp approximation of the whole distribution of the sum of iid heavy-tailed random vectors, combining mean and extreme behaviors. It extends the so-called ’normex’ approach from a univariate to a multivariate framework. We propose two possible multi-normex distributions, named d-Normex and MRV-Normex. Both rely on the Gaussian distribution for describing the mean behavior, via the CLT, while the difference between the two versions comes from using the exact distribution or the EV theorem for the maximum. The main theorems provide the rate of convergence for each version of the multi-normex distributions towards the distribution of the sum, assuming second order regular variation property for the norm of the parent random vector when considering the MRV-normex case. Numerical illustrations and comparisons are proposed with various dependence structures on the parent random vector, using QQ-plots based on geometrical quantiles."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      161 => Essec\Faculty\Model\Contribution {#2512
        #_index: "academ_contributions"
        #_id: "13717"
        #_source: array:18 [
          "id" => "13717"
          "slug" => "on-the-relation-between-extremal-dependence-and-concomitants"
          "yearMonth" => "2023-01"
          "year" => "2023"
          "title" => "On the relation between extremal dependence and concomitants"
          "description" => "KRATZ, M. et KHORAMI CHOKAMI, A. (2023). <i>On the relation between extremal dependence and concomitants</i>. WP 2301, ESSEC Business School Research Center."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "KHORAMI CHOKAMI Amir"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:14 [
            0 => "Asymptotic Theorems"
            1 => "Concomitants"
            2 => "Copula"
            3 => "(Tail) Dependence"
            4 => "Extremes"
            5 => "Gaussian"
            6 => "Logistic"
            7 => "Maxima"
            8 => "Order Statistics"
            9 => "Pareto"
            10 => "Slowly/Regularly"
            11 => "Varying Functions"
            12 => "Tail Equivalence"
            13 => "Weak Convergence"
          ]
          "updatedAt" => "2023-02-09 09:23:33"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Cahier de Recherche"
            "en" => "Working Papers"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The study of concomitants has recently met a renewed interest due to its applications in selection procedures. For instance, concomitants are used in rankedset sampling, to achieve efficiency and reduce cost when compared to the simple random sampling. In parallel, the search for new methods to provide a rich description of extremal dependence among multiple time series has rapidly grown, due also to its numerous practical implications and the lack of suitable models to assess it. Here, our aim is to investigate extremal dependence when choosing the concomitants approach. In this study, we show how the extremal dependence of a vector (X, Y) impacts the asymptotic behavior of the maxima over subsets of concomitants. Furthermore, discussing the various conditions and results, we investigate how transformations of the marginal distributions of X and Y influence the degeneracy of the limit."
            "en" => "The study of concomitants has recently met a renewed interest due to its applications in selection procedures. For instance, concomitants are used in rankedset sampling, to achieve efficiency and reduce cost when compared to the simple random sampling. In parallel, the search for new methods to provide a rich description of extremal dependence among multiple time series has rapidly grown, due also to its numerous practical implications and the lack of suitable models to assess it. Here, our aim is to investigate extremal dependence when choosing the concomitants approach. In this study, we show how the extremal dependence of a vector (X, Y) impacts the asymptotic behavior of the maxima over subsets of concomitants. Furthermore, discussing the various conditions and results, we investigate how transformations of the marginal distributions of X and Y influence the degeneracy of the limit."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      162 => Essec\Faculty\Model\Contribution {#2513
        #_index: "academ_contributions"
        #_id: "13718"
        #_source: array:18 [
          "id" => "13718"
          "slug" => "managing-cyber-risk-a-science-in-the-making"
          "yearMonth" => "2023-02"
          "year" => "2023"
          "title" => "Managing Cyber Risk, a Science in the Making"
          "description" => "KRATZ, M. et DACOROGNA, M. (2023). <i>Managing Cyber Risk, a Science in the Making</i>. WP 2302, ESSEC Business School Research Center."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Cyber risk"
            1 => "Cyber security"
            2 => "Cyber resilience"
            3 => "Insurance"
            4 => "Modelling"
            5 => "Risk management"
          ]
          "updatedAt" => "2023-02-09 09:19:50"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Documents de travail"
            "en" => "Working Papers"
          ]
          "support_type" => array:2 [
            "fr" => "Cahier de Recherche"
            "en" => "Working Papers"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => """
              Not a day goes by without news about a cyber attack. Fear spreads out and lots of wrong ideas circulate. This survey aims at showing how all these uncertainties about cyber can be transformed into manageable risk. After reviewing the main characteristics of cyber risk, we consider the three layers of\n
              cyber space: hardware, software and psycho-cognitive layer. We ask ourselves how is this risk different from others, how modelling has been tackled and needs to evolve, and what are the multi-facettedbaspects of cyber risk management. This wide exploration pictures a science in the making and points out the questions to be solved for building a resilient society.
              """
            "en" => """
              Not a day goes by without news about a cyber attack. Fear spreads out and lots of wrong ideas circulate. This survey aims at showing how all these uncertainties about cyber can be transformed into manageable risk. After reviewing the main characteristics of cyber risk, we consider the three layers of\n
              cyber space: hardware, software and psycho-cognitive layer. We ask ourselves how is this risk different from others, how modelling has been tackled and needs to evolve, and what are the multi-facettedbaspects of cyber risk management. This wide exploration pictures a science in the making and points out the questions to be solved for building a resilient society.
              """
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      163 => Essec\Faculty\Model\Contribution {#2514
        #_index: "academ_contributions"
        #_id: "13936"
        #_source: array:18 [
          "id" => "13936"
          "slug" => "how-do-empirical-estimators-of-popular-risk-measures-impact-pro-cyclicality"
          "yearMonth" => "2023-09"
          "year" => "2023"
          "title" => "How do empirical estimators of popular risk measures impact pro-cyclicality?"
          "description" => "BRÄUTIGAM, M. et KRATZ, M. (2023). How do empirical estimators of popular risk measures impact pro-cyclicality? <i>Annals of Actuarial Science</i>, 17(3), pp. 547-579."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRÄUTIGAM Marcel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:7 [
            0 => "Asymptotic normality"
            1 => "Expected shortfall -Expectile -Estimators -(Filtered)"
            2 => """
              \n
              Historical simulation
              """
            3 => "Measure of dispersion"
            4 => "Pro-cyclicality"
            5 => "Risk measure"
            6 => """
              Sample quantile\n
              Value-at-risk
              """
          ]
          "updatedAt" => "2023-11-28 15:10:22"
          "publicationUrl" => "https://urldefense.proofpoint.com/v2/url?u=https-3A__doi.org_10.1017_S1748499523000039&d=DwMFaQ&c=oS_0xOYps7FNW56RWijYeQ&r=XOcJOIAyw3LSRph5STbvfQ&m=uECq2vftznPMs-bTe36CXi9TELU1awhSUE-eVMIYLUleDXDDGkUrNnX7u084JHm8&s=j8NO6jE4RliMrXEzDgvlTIZBCV8R6flxrrvESVKL"
          "publicationInfo" => array:3 [
            "pages" => "547-579"
            "volume" => "17"
            "number" => "3"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Risk measurements are clearly central to risk management, in particular for banks, (re)insurance companies, and investment funds. The question of the appropriateness of risk measures for evaluating the risk of financial institutions has been heavily debated, especially after the financial crisis of 2008/2009. Another concern for financial institutions is the pro-cyclicality of risk measurements. In this paper, we extend existing work on the pro-cyclicality of the Value-at-Risk to its main competitors, Expected Shortfall, and Expectile: We compare the pro-cyclicality of historical quantile-based risk estimation, taking into account the market state. To characterise the latter, we propose various estimators of the realised volatility. Considering the family of augmented GARCH(p, q) processes (containing well-known GARCH models and iid models, as special cases), we prove that the strength of pro-cyclicality depends on the three factors: the choice of risk measure and its estimators, the realised volatility estimator and the model considered, but, no matter the choices, the pro-cyclicality is always present. We complement this theoretical analysis by performing simulation studies in the iid case and developing a case study on real data."
            "en" => "Risk measurements are clearly central to risk management, in particular for banks, (re)insurance companies, and investment funds. The question of the appropriateness of risk measures for evaluating the risk of financial institutions has been heavily debated, especially after the financial crisis of 2008/2009. Another concern for financial institutions is the pro-cyclicality of risk measurements. In this paper, we extend existing work on the pro-cyclicality of the Value-at-Risk to its main competitors, Expected Shortfall, and Expectile: We compare the pro-cyclicality of historical quantile-based risk estimation, taking into account the market state. To characterise the latter, we propose various estimators of the realised volatility. Considering the family of augmented GARCH(p, q) processes (containing well-known GARCH models and iid models, as special cases), we prove that the strength of pro-cyclicality depends on the three factors: the choice of risk measure and its estimators, the realised volatility estimator and the model considered, but, no matter the choices, the pro-cyclicality is always present. We complement this theoretical analysis by performing simulation studies in the iid case and developing a case study on real data."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      164 => Essec\Faculty\Model\Contribution {#2515
        #_index: "academ_contributions"
        #_id: "13965"
        #_source: array:18 [
          "id" => "13965"
          "slug" => "managing-cyber-risk-a-science-in-the-making"
          "yearMonth" => "2023-10"
          "year" => "2023"
          "title" => "Managing cyber risk, a science in the making"
          "description" => "DACOROGNA, M. et KRATZ, M. (2023). Managing cyber risk, a science in the making. <i>Scandinavian Actuarial Journal</i>, 2023(10), pp. 1000-1021."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:6 [
            0 => "Cyber risk"
            1 => "cyber security"
            2 => "cyber resilience"
            3 => "insurance"
            4 => "modelling"
            5 => "risk management"
          ]
          "updatedAt" => "2024-10-31 13:51:19"
          "publicationUrl" => "https://doi.org/10.1080/03461238.2023.2191869"
          "publicationInfo" => array:3 [
            "pages" => "1000-1021"
            "volume" => "2023"
            "number" => "10"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Not a day goes by without news about a cyber attack. Fear spreads out and lots of wrong ideas circulate. This survey aims at showing how all these uncertainties about cyber can be transformed into manageable risk. After reviewing the main characteristics of cyber risk, we consider the three layers of cyber space: hardware, software and psycho-cognitive layer. We ask ourselves how is this risk different from others, how modelling has been tackled and needs to evolve, and what are the multi-facetted aspects of cyber risk management. This wide exploration pictures a science in the making and points out the questions to be solved for building a resilient society."
            "en" => "Not a day goes by without news about a cyber attack. Fear spreads out and lots of wrong ideas circulate. This survey aims at showing how all these uncertainties about cyber can be transformed into manageable risk. After reviewing the main characteristics of cyber risk, we consider the three layers of cyber space: hardware, software and psycho-cognitive layer. We ask ourselves how is this risk different from others, how modelling has been tackled and needs to evolve, and what are the multi-facetted aspects of cyber risk management. This wide exploration pictures a science in the making and points out the questions to be solved for building a resilient society."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      165 => Essec\Faculty\Model\Contribution {#2516
        #_index: "academ_contributions"
        #_id: "14041"
        #_source: array:18 [
          "id" => "14041"
          "slug" => "building-up-cyber-resilience-by-better-grasping-cyber-risk-via-a-new-algorithm-for-modelling-heavy-tailed-data"
          "yearMonth" => "2023-12"
          "year" => "2023"
          "title" => "Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data"
          "description" => "DACOROGNA, M., DEBBABI, N. et KRATZ, M. (2023). Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data. <i>European Journal of Operational Research</i>, 311(2), pp. 708-729."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
            2 => array:1 [
              "name" => "DEBBABI Nehla"
            ]
          ]
          "ouvrage" => ""
          "keywords" => array:5 [
            0 => "Risk statistical analysis"
            1 => "Cyber risk"
            2 => "Extreme value theory"
            3 => "Probabilistic modelling"
            4 => "Risk management"
          ]
          "updatedAt" => "2024-03-18 10:54:11"
          "publicationUrl" => "https://doi.org/10.1016/j.ejor.2023.05.003"
          "publicationInfo" => array:3 [
            "pages" => "708-729"
            "volume" => "311"
            "number" => "2"
          ]
          "type" => array:2 [
            "fr" => "Articles"
            "en" => "Journal articles"
          ]
          "support_type" => array:2 [
            "fr" => "Revue scientifique"
            "en" => "Scientific journal"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "Cyber security and resilience are major challenges in our modern economies; this is why they are top priorities on the agenda of governments, security and defense forces, management of companies and organizations. Hence, the need of a deep understanding of cyber risks to improve resilience. We propose here an analysis of the database of the cyber complaints filed at the Gendarmerie Nationale. We perform this analysis with a new algorithm developed for non-negative asymmetric heavy-tailed data, which could become a handy tool for applied fields, including operations research. This method gives a good estimation of the full distribution including the tail. Our study confirms the finiteness of the loss expectation, necessary condition for insurability. Finally, we draw the consequences of this model for risk management, compare its results to other standard EVT models, and lay the ground for a classification of attacks based on the fatness of the tail"
            "en" => "Cyber security and resilience are major challenges in our modern economies; this is why they are top priorities on the agenda of governments, security and defense forces, management of companies and organizations. Hence, the need of a deep understanding of cyber risks to improve resilience. We propose here an analysis of the database of the cyber complaints filed at the Gendarmerie Nationale. We perform this analysis with a new algorithm developed for non-negative asymmetric heavy-tailed data, which could become a handy tool for applied fields, including operations research. This method gives a good estimation of the full distribution including the tail. Our study confirms the finiteness of the loss expectation, necessary condition for insurability. Finally, we draw the consequences of this model for risk management, compare its results to other standard EVT models, and lay the ground for a classification of attacks based on the fatness of the tail"
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      166 => Essec\Faculty\Model\Contribution {#2517
        #_index: "academ_contributions"
        #_id: "14371"
        #_source: array:18 [
          "id" => "14371"
          "slug" => "plenary-speaker-efficient-estimation-in-extreme-value-regression-models-of-hedge-fund-tail-risk"
          "yearMonth" => "2023-08"
          "year" => "2023"
          "title" => "[Plenary speaker] Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risk"
          "description" => "HAMBUCKERS, J., KRATZ, M. et USSEGLIO-CARLEVE, A. (2023). [Plenary speaker] Efficient Estimation in Extreme Value Regression Models of Hedge Fund Tail Risk. Dans: 2023 JAFEE-ISM International Symposium. Tokyo."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "HAMBUCKERS Julien"
            ]
            2 => array:1 [
              "name" => "USSEGLIO-CARLEVE Antoine "
            ]
          ]
          "ouvrage" => "2023 JAFEE-ISM International Symposium"
          "keywords" => array:3 [
            0 => "Extreme value theory"
            1 => "generalized Pareto regression"
            2 => "censored maximum likelihood"
          ]
          "updatedAt" => "2024-05-16 11:48:18"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Invité dans une conférence académique (Keynote speaker)"
            "en" => "Invited speaker at an academic conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions of investment vehicles such as hedge funds. However, a major limitation is the need to select ex ante a threshold below which data are discarded, leading to estimation inefficiencies. To solve these issues, we extend the tail regression model to non-tail observations with an auxiliary splicing density, enabling the threshold to be selected automatically. We then apply an artificial censoring mechanism of the likelihood contributions in the bulk of the data to decrease specification issues at the estimation stage. We illustrate the superiority of our approach for inference over classical peaks-over-threshold methods in a simulation study. Empirically, we investigate the determinants of hedge fund tail risks over time, using pooled returns of 1,484 hedge funds. We find a significant link between tail risks and factors such as equity momentum, financial stability index, and credit spreads. Moreover, sorting funds along exposure to our tail risk measure discriminates between high and low alpha funds, supporting the existence of a fear premium."
            "en" => "We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions of investment vehicles such as hedge funds. However, a major limitation is the need to select ex ante a threshold below which data are discarded, leading to estimation inefficiencies. To solve these issues, we extend the tail regression model to non-tail observations with an auxiliary splicing density, enabling the threshold to be selected automatically. We then apply an artificial censoring mechanism of the likelihood contributions in the bulk of the data to decrease specification issues at the estimation stage. We illustrate the superiority of our approach for inference over classical peaks-over-threshold methods in a simulation study. Empirically, we investigate the determinants of hedge fund tail risks over time, using pooled returns of 1,484 hedge funds. We find a significant link between tail risks and factors such as equity momentum, financial stability index, and credit spreads. Moreover, sorting funds along exposure to our tail risk measure discriminates between high and low alpha funds, supporting the existence of a fear premium."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      167 => Essec\Faculty\Model\Contribution {#2518
        #_index: "academ_contributions"
        #_id: "14384"
        #_source: array:18 [
          "id" => "14384"
          "slug" => "joint-asymptotics-for-the-sample-quantile-and-measures-of-dispersion-for-functionals-of-mixing-processes"
          "yearMonth" => "2023-07"
          "year" => "2023"
          "title" => "Joint Asymptotics for the Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes"
          "description" => "KRATZ, M. et BRAUTIGAM, M. (2023). Joint Asymptotics for the Sample Quantile and Measures of Dispersion for Functionals of Mixing Processes. Dans: 43rd Conference on Stochastic Processes and their Applications 2023. Lisbon."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "BRAUTIGAM Marcel"
            ]
          ]
          "ouvrage" => "43rd Conference on Stochastic Processes and their Applications 2023"
          "keywords" => []
          "updatedAt" => "2023-09-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      168 => Essec\Faculty\Model\Contribution {#2519
        #_index: "academ_contributions"
        #_id: "14402"
        #_source: array:18 [
          "id" => "14402"
          "slug" => "multi-normex-for-evaluating-the-distribution-of-aggregated-heavy-tailed-risks"
          "yearMonth" => "2023-06"
          "year" => "2023"
          "title" => "Multi-Normex for Evaluating the Distribution of Aggregated Heavy Tailed Risks"
          "description" => "KRATZ, M. et PROKOPENKO, E. (2023). Multi-Normex for Evaluating the Distribution of Aggregated Heavy Tailed Risks. Dans: 13th Conference on Extreme Value Analysis, Probabilistic and Statistical Models and their Applications 2023. Milan."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "PROKOPENKO Evgeny"
            ]
          ]
          "ouvrage" => "13th Conference on Extreme Value Analysis, Probabilistic and Statistical Models and their Applications 2023"
          "keywords" => []
          "updatedAt" => "2023-09-27 01:00:43"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      169 => Essec\Faculty\Model\Contribution {#2520
        #_index: "academ_contributions"
        #_id: "14676"
        #_source: array:18 [
          "id" => "14676"
          "slug" => "efficient-estimation-for-ev-regression-models-of-tail-risks"
          "yearMonth" => "2023-12"
          "year" => "2023"
          "title" => "Efficient estimation for EV regression models of tail risks"
          "description" => "HAMBUCKERS, J., KRATZ, M. et USSEGLIO-CARLEVE, A. (2023). Efficient estimation for EV regression models of tail risks. Dans: 2023 Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2023). Berlin."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "HAMBUCKERS Julien "
            ]
            2 => array:1 [
              "name" => "USSEGLIO-CARLEVE Antoine "
            ]
          ]
          "ouvrage" => "2023 Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2023)"
          "keywords" => []
          "updatedAt" => "2024-05-16 11:50:19"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      170 => Essec\Faculty\Model\Contribution {#2521
        #_index: "academ_contributions"
        #_id: "14894"
        #_source: array:18 [
          "id" => "14894"
          "slug" => "developing-ot-and-related-graphical-tools-application-in-risk-analysis-management"
          "yearMonth" => "2024-05"
          "year" => "2024"
          "title" => "Developing OT (and related) graphical tools. Application in Risk Analysis & Management"
          "description" => "SINGHA, S., KRATZ, M. et VADLAMANI, S. (2024). Developing OT (and related) graphical tools. Application in Risk Analysis & Management. Dans: 55e Journées de Statistique de la Société Française de Statistique (SFdS) 2024. Paris."
          "authors" => array:3 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "SINGHA S"
            ]
            2 => array:1 [
              "name" => "VADLAMANI Sreekar"
            ]
          ]
          "ouvrage" => "55e Journées de Statistique de la Société Française de Statistique (SFdS) 2024"
          "keywords" => []
          "updatedAt" => "2024-07-10 01:01:22"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      171 => Essec\Faculty\Model\Contribution {#2522
        #_index: "academ_contributions"
        #_id: "14929"
        #_source: array:18 [
          "id" => "14929"
          "slug" => "new-methods-for-evaluating-the-distribution-of-heavy-tailed-data-based-on-asymptotic-mean-and-extreme-behaviours"
          "yearMonth" => "2024-04"
          "year" => "2024"
          "title" => "New methods for evaluating the distribution of heavy tailed data, based on (asymptotic) mean and extreme behaviours"
          "description" => "KRATZ, M. (2024). New methods for evaluating the distribution of heavy tailed data, based on (asymptotic) mean and extreme behaviours. Dans: 8th Ritsumeikan-Monash Symposium on Probability and Related Fields 2024. Kusatsu."
          "authors" => array:1 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
          ]
          "ouvrage" => "8th Ritsumeikan-Monash Symposium on Probability and Related Fields 2024"
          "keywords" => []
          "updatedAt" => "2024-07-16 19:38:13"
          "publicationUrl" => null
          "publicationInfo" => array:3 [
            "pages" => ""
            "volume" => ""
            "number" => ""
          ]
          "type" => array:2 [
            "fr" => "Communications dans une conférence"
            "en" => "Presentations at an Academic or Professional conference"
          ]
          "support_type" => array:2 [
            "fr" => null
            "en" => null
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => ""
            "en" => ""
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
      172 => Essec\Faculty\Model\Contribution {#2523
        #_index: "academ_contributions"
        #_id: "15175"
        #_source: array:18 [
          "id" => "15175"
          "slug" => "research-in-cyber-risk-an-important-step-for-building-resilience"
          "yearMonth" => "2022-04"
          "year" => "2022"
          "title" => "Research in Cyber Risk, an Important Step for Building Resilience"
          "description" => "DACOROGNA, M. et KRATZ, M. (2022). Research in Cyber Risk, an Important Step for Building Resilience. <i>MDPI</i>, 10(112)."
          "authors" => array:2 [
            0 => array:3 [
              "name" => "KRATZ Marie"
              "bid" => "B00072305"
              "slug" => "kratz-marie"
            ]
            1 => array:1 [
              "name" => "DACOROGNA Michel"
            ]
          ]
          "ouvrage" => "Risks - Special Issue “Cyber Risk and Security”"
          "keywords" => array:2 [
            0 => "risks"
            1 => "cyber risk"
          ]
          "updatedAt" => "2024-10-31 13:51:19"
          "publicationUrl" => "https://doi.org/10.3390/risks10060112"
          "publicationInfo" => array:3 [
            "pages" => null
            "volume" => "10"
            "number" => "112"
          ]
          "type" => array:2 [
            "fr" => "Préfaces / Introductions de revue"
            "en" => "Prefaces of a journal"
          ]
          "support_type" => array:2 [
            "fr" => "Editeur"
            "en" => "Publisher"
          ]
          "countries" => array:2 [
            "fr" => null
            "en" => null
          ]
          "abstract" => array:2 [
            "fr" => "The COVID-19 pandemic and now the war in Ukraine, have raised the risks to levels not seen in the last 30 years. This Special Issue of Risks was planned before these events, but comes at the right moment to contribute to the progress in our understanding of cyber risk. The last two years have demonstrated our acute dependence on IT systems and the weakness of our defenses against cyber attacks. With climate changes and pandemics, cyber risk constitutes one of the main challenges to building more resilience in our society. Thus, this Special Issue is very topical and will help us advance our knowledge on this emerging risk."
            "en" => "The COVID-19 pandemic and now the war in Ukraine, have raised the risks to levels not seen in the last 30 years. This Special Issue of Risks was planned before these events, but comes at the right moment to contribute to the progress in our understanding of cyber risk. The last two years have demonstrated our acute dependence on IT systems and the weakness of our defenses against cyber attacks. With climate changes and pandemics, cyber risk constitutes one of the main challenges to building more resilience in our society. Thus, this Special Issue is very topical and will help us advance our knowledge on this emerging risk."
          ]
          "authors_fields" => array:2 [
            "fr" => "Systèmes d'Information, Data Analytics et Opérations"
            "en" => "Information Systems, Data Analytics and Operations"
          ]
          "indexedAt" => "2024-12-21T17:21:43.000Z"
        ]
        +lang: "fr"
        +"_type": "_doc"
        +"_score": 4.302359
        +"parent": null
      }
    ]
    "avatar" => "https://faculty.essec.edu/wp-content/uploads/avatars/B00072305.jpg"
    "contributionCounts" => 173
    "personalLinks" => array:1 [
      0 => "<a href="https://orcid.org/0000-0001-5160-2042" target="_blank">ORCID</a>"
    ]
    "docTitle" => "Marie KRATZ"
    "docSubtitle" => "Professeur"
    "docDescription" => "Département: Systèmes d'Information, Data Analytics et Opérations<br>Campus de Cergy"
    "docType" => "cv"
    "docPreview" => "<img src="https://faculty.essec.edu/wp-content/uploads/avatars/B00072305.jpg"><span><span>Marie KRATZ</span><span>B00072305</span></span>"
    "academ_cv_info" => ""
  ]
  #_index: "academ_cv"
  +lang: "fr"
  +"_type": "_doc"
  +"_score": 5.0369525
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}