Optimal reinsurance with general premium principles based on RVaR and WVaR

Abstract

This paper studies the problem of optimal reinsurance design. Assuming that both the ceded and retained loss functions are increasing, we establish two optimal reinsurance models by minimizing the RVaR and WVaR risk measures of the total risk exposure of the insurer, respectively. Under RVaR, assuming that the premium principle satisfies distribution invariance, risk loading and preserving stop-loss order, we provide the optimal reinsurance treaty, which is a composition of two layer reinsurance treaties. Under WVaR, assuming that the premium principle satisfies distribution invariance, risk loading and preserving second-order stochastic dominance, we obtain the optimal reinsurance treaty, which is a stop-loss reinsurance. Finally, examples are given to illustrate the obtained results. Especially, when the claim is exponentially distributed, the explicit expressions for the optimal reinsurance treaties are given.