Optimal Reinsurance Models Defined By Distortion Risk Measures-From Both The Perspectives Of An Insurer And A Reinsurer

Optimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied extensively in the literature.However,as two parties of a rein-surance contract,an insurer and a reinsurer have conflicting interests.An optimal form of reinsurance from one party's point of view may be not acceptable to the other party.In this paper,we develop optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs.Our objective is to seek for all the optimal rein-surance strategies which minimize the convex combination of the distortion risk measures of the insurer's loss and the reinsurer's loss under four types of constraints.The optimal reinsurance strategy satisfying the constraints is presented in the four theorems of the paper.Constraints describe the maximum risk based on the distortion risk measure that an insurer or reinsurer can tolerate.The first type of constraints is the premium budget of the insurer,The second and the third type of constraints are a limit on the distortion risk measure of their own loss respectively.Combining the second and the third constraints is the fourth constraints.The first three optimal reinsurance problems only involving one constraint while the last optimal reinsurance problem involving two constraints.For those four types of constraint,we derive the optimal reinsurance forms in a class of ceded loss functions and under the distortion premium principle.It,needs to be mentioned that,when our general model is specified to the optimal reinsurance model defined by Value-at-Risk risk measures(VaR),our results coincides well with that of Cai et al.(2016).