Robust optimal dynamic reinsurance policies under the mean-RVaR premium principle

This work investigates a robust optimal dynamic reinsurance problem for an ambiguity averse insurer (AAI) concerned about potential ambiguity of claim intensity. The study aims to determine a robust optimal reinsurance contract to minimize the discounted ruin probability imposed a penalization owing to model ambiguity, including discounting for the time of ruin. We suppose that the surplus process is modeled by a diffusion model. The AAI purchases reinsurance from the reinsurer to manage risk, subject to the incentive compatibility constraint, which rules out moral hazard. Moreover, the reinsurance premium is calculated based on the mean-RVaR premium principle, which generalizes the expected value premium principle and the mean-CVaR premium principle and reflects the different risk preferences of reinsurers. Based on the dynamic programming approach, we obtain the value function and optimal reinsurance policies (the dual excess-of-loss reinsurance). Finally, we show a numerical example to illustrate the effects of premium and ambiguity averse on the discounted ruin probability and the robust optimal contract.