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

This paper seeks to determine the optimal investment and reinsurance strategy for an insurer whose wealth follows a diffusion process. We extend Zhang and Siu (2009) in our model and establish the Hamilton†Jacobi†Bellman†Isaacs equations, for which we obtain the optimal solutions. The optimal solutions indicate the use of reinsurance and investment allocation to risky assets. Results show that when the utility function of the insurer’s terminal wealth is exponential, the optimal solutions are positively correlated with time, but independent of the insurer’s wealth. However, for the power utility function, the optimal solutions are uncorrelated with time and are increasing functions of the insurer’s wealth. We also demonstrate that the insurer’s investment and reinsurance strategies are dependent on the risk†free interest rate.