Optimal Reinsurance with Multiple Reinsurers : Distortion Risk Measures, Distortion Premium Principles, and Heterogeneous Beliefs

This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,and heterogeneous beliefs. An insurer minimizes a distortion risk measure, while seekingreinsurance with finitely many reinsurers. The reinsurers use distortion premium principles, andthey are allowed to have heterogeneous beliefs regarding the underlying probability distribution.We provide a characterization of optimal reinsurance indemnities, and we show that they are ofa layer-insurance type. This is done both with and without a budget constraint, i.e., an upperbound constraint on the aggregate premium. Moreover, the optimal reinsurance indemnitiesenable us to identify a representative reinsurer in both situations. Finally, two examples withthe Conditional Value-at-Risk illustrate our results