Pareto-optimal reinsurance policies with maximal synergy

Optimal reinsurance policies have been studied extensively in the economics and insurance literature. Two types of optimality criteria, expected utility (EU) maximization and risk minimization, are commonly used. Understandably, applying the two types of criteria usually will result in different “optimal” policies. To reconcile the conflicting interests of the insurer and reinsurer and strike a balance between EU maximization and risk minimization, we follow the approach in Borch (1960b) but assume that the involved two parties both apply distortion risk measures instead of variance. We first identify a set of reinsurance policies that minimize the total risk borne by the two parties, then we take this set of policies as admissible and derive the Pareto-optimal policies that maximize the weighted EU of these two parties. A Nash bargaining model is applied to identify the “best” weights allocated to the two parties. In addition, we extend our results to a situation where the insurer’s decision making is dictated by the rank-dependent expected utility (RDEU) theory. Finally, we present numerical examples to show the applicability of our methodology and some implications of the obtained results.