Optimal Dynamic Reinsurance Policies Under Mean CVaR A Generalized Denneberggs Absolute Deviation Principle

Abstract

This paper studies the optimal dynamic reinsurance policy for an insurance company whose surplus is modeled by the diffusion approximation of the classical Cramer-Lundberg model. We assume the reinsurance premium is calculated according to a proposed Mean-CVaR premium principle which generalizes Denneberg's absolute deviation principle and expected value principle. Moreover, we require that both ceded loss and retention functions are non-decreasing to rule out moral hazard. Under the objective of minimizing the ruin probability, we obtain the optimal reinsurance policy explicitly and we denote the resulting treaty as the dual excess-of-loss reinsurance. This form of optimal treaty is new to the literature. It also demonstrates that reinsurance treaties such as the proportional and the standard excess-of-loss, which are typically found to be optimal in the dynamic reinsurance model, need not be optimal when we consider a more general optimization model.