Optimal Dynamic Portfolio Section for Insurers with Investment and Reinsurance Based on Random Impulsive Model

In this paper an insurer is assumed to invest his reserve in a financial market, which consists of a risky asset and a risk-free asset. The random impulsive model for stock prices is used to depict the price of risky security. A controlled diffusion risk process is presented to describe such a dynamic setting. Explicit and closed-form solutions for the optimal dynamic choice are derived when excess-of-loss or proportional reinsurance is incorporated with an investment under the optimization criteria of maximizing the expectation of quadratic utility of the terminal wealth at a fixed terminal time, respectively. Based on the explicit solutions, the influence of the dependence between the finance risk and insurance risk on the optimal dynamic choice is illustrated numerically.