Optimal reinsurance and investment in a jump-diffusion financial market with common shock dependence

Abstract

In this paper, we study the optimal reinsurance and investment problem in a financial market with jump-diffusion risky asset. It is assumed that the insurance risk model is modulated by a compound Poisson process, and that the jumps in both the risky asset and insurance risk process are correlated through a common shock. Under the criterion of maximizing the expected exponential utility, we adopt a nonstandard approach to examine the existence and uniqueness of the optimal strategy. Using the technique of stochastic control theory, closed-form expressions for the optimal strategy and the value function are derived not only for the expected value principle but also for the variance premium principle. Also, we investigate the effect of the common shock parameter as well as some other important parameters on the optimal strategies. In particular, a numerical example shows that the optimal investment strategy decreases as the degree of common shock dependence increases but the optimal insurance retention level does not behave the same.