On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures
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.
KRATZ, M. (2016). On the Estimation of the Distribution of Aggregated Heavy-Tailed Risks: Application to Risk Measures. In: Extreme Events in Finance: Handbook of Extreme Value Theory and Its Applications. 1st ed. Wiley, pp. 239-282.