Mean-variance problem for an insurer with default risk under a jump-diffusion risk model

Abstract

This paper considers an optimal investment-reinsurance problem with default risk under the mean-variance criterion. We assume that the insurer is allowed to purchase proportional reinsurance and invest his/her surplus in a risk-free asset, a stock and a defaultable bond. The goal is to maximize the expectation and minimize the variance of the terminal wealth. We first formulate the problem to stochastic linear-quadratic (LQ) control problem with constraints. Then the optimal investment-reinsurance strategies and the corresponding value functions are obtained via the viscosity solutions of Hamilton-Jacobi-Bellman (HJB) equations for the post-default case and pre-default case, respectively. Finally, we provide numerical examples to illustrate the effects of model parameters on the optimal strategies and value functions.