Optimal Retention for Uncertain Stop-Loss Reinsurance Model

The optimal reinsurance is one of the important issues in actuarial science. In this paper, we discuss the optimal stop-loss reinsurance problem in uncertain environment. An uncertain optimal stop-loss reinsurance model is presented, where the reinsurance premium is calculated by expected value principle and the uncertain value-at-risk is chosen as the insurer’s total risk measure. Next, some conditions that the proposed uncertain stop-loss reinsurance model has optimal retention are provided. At last, a few numerical examples are given to illustrate the application.