关键词: CIR随机利率模型, 投资策略, 再保险, 幂效用, 随机最优控制

Abstract: This paper considers an optimal reinsurance and optimal investment problem under the Cox-Ingersoll-Roll (CIR) stochastic interest rate framework. We assume that the insurer can invest in cash,zero coupon bond and several kinds of stocks in the financial market. Meanwhile, proportion reinsurance is purchased by an insurer to transfer the risk of insurance to other insurance companies. We further adopt an affine CIR model to characterize the interest rate while the surplus wealth process is approximated by a diffusion process, namely, the jump process is approximated by a continuous process. The goal of the insurer is to maximize the expected power utility of the terminal wealth. Due to the fact that the surplus process of the insurer is not a self-financing process, we firstly transform the original problem into a self-financing problem, establish the corresponding Hamilton-Jacobi-Bellman equation, and then derive an explicit solution via the stochastic optimal control method. We find that the percentage of quota invested in stocks would decrease with the increase of risk aversion parameters, while the terminal wealth would increase with the increase of initial interest rate. Finally, sensitivity analysis is carried out to show the impact of financial parameters on the optimal strategies and optimal utility.

Key words: CIR stochastic interest rate model, investment strategy, reinsurance, power utility, stochastic optimal control