Determining the Insurer’s Optimal Investment and Reinsurance Strategy Based on Stochastic Differential Game

In this paper, we discuss how to determine the optimal investment portfolio and reinsurance strategy of insurance company based on zero-sum stochastic differential game between the market and the insurer. We extend Zhang and Siu (2009)’s model by (1) including a risk-free asset, (2) considering risky assets instead of only one risky asset and (3) discussing the case of power utility function besides exponential utility when the wealth process of an insurance company is a diffusion process. We establish the Hamilton-Jacobi-Bellman-Issacs equations and obtain the optimal solutions of the amount invested in risky assets and retention of reinsurance. Our results show that the optimal solution is positively correlated to time but independent of the wealth of insurer, when the utility function of terminal wealth is exponential. However, the optimal solution is uncorrelated to time and is increasing function of the wealth of the insurer in the case of power utility function. Our results also show that the risk-free interest rate will affect the strategy of investment and reinsurance