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 measure, while seeking reinsurance with finitely many reinsurers. The reinsurers use principles, they are allowed to have beliefs regarding underlying probability distribution. We provide characterization of optimal indemnities, we show that layer-insurance type. is done both without budget constraint, i.e., an upper bound constraint aggregate premium. Moreover, indemnities enable us identify representative reinsurer in situations. Finally, two examples Conditional Value-at-Risk illustrate our results.