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.
KRATZ, M. et SHUBHABRATA, D. (2008). On efficiency and Alarm System in Reinsurance Contracts. Dans: 7th World Congress in Probability and Statistics.