Heston模型下保险公司与再保险公司的博弈

A Game between Insurer and Reinsurer under the Heston Model

本文同时考虑保险公司和再保险公司的最优投资问题.假设保险公司可以向再保险公司购买比例再保险,保险公司和再保险公司都可以投资于一种无风险资产和一种价格过程服从Heston模型的风险资产.首先,在保险公司和再保险公司终端财富的指数效用期望最大化条件下建立目标函数;然后通过求解Hamilton-Jacobi-Bellman方程,分别得到了保险公司与再保险公司的最优投资和再保险策略以及最优价值函数的解析解;最后通过数值实例以及敏感性分析阐述了本文所得结果.

This paper considers an optimal investment problem for both insurer and reinsurer. The insurer is allowed to purchase proportional reinsurance and both the insurer and reinsurer are allowed to invest in a risk-free asset and a risky asset whose price process satisfies the Heston＇s stochastic volatility model. Firstly, we establish the objective function in the sense of maximizing the exponential utility of both the insurer and reinsurer on terminal wealth; Secondly, by solving the Hamilton-Jacobi-Bellman system, the closed-form expressions for the optimal reinsurance and investment strategies and the optimal value function are obtained; Finally, some numerical illustrations and sensitivity analysis for the proposed theoretical results are provided.