Optimal dynamic reinsurance with common shock dependence and state-dependent risk aversion

Abstract

This paper studies an optimal dynamic proportional reinsurance in a risk model with two dependent classes of insurance business. Under the criterion of maximizing the mean-variance utility of the terminal wealth with state-dependent risk aversion, we formulate the time-inconsistent problem within a game theoretic framework. By the technique of stochastic control theory, explicit expressions of the optimal results are derived not only for diffusion risk model but also for compound Poisson risk model. Furthermore, the similar problem with constant risk aversion is studied as well. Finally, some numerical examples are presented to show the impact of model parameters on the optimal strategies for both compound Poisson and diffusion cases.