Vasicek利率下基于随机微分博弈的最优再保险和投资

Optimal reinsurance and investment based on stochastic differential games with Vasicek interest rate

研究了保险公司和金融市场之间的零和随机微分博弈.在无风险资产利率满足Vasicek随机利率情形下,通过保险公司和金融市场之间的博弈,寻找最优策略使得终止时刻财富的期望效用达到最大.在幂效用函数下,运用随机控制理论求得了最优策略和值函数的显式解,解释了所研究的结果在经济学上的意义,并通过数值计算分析了一些参数对最优策略的影响.

Zero-sum stochastic differential games between insurance company and financial market are considered. The goal is to obtain optimal strategies to maximize the expected utility of the terminal wealth by the game between insurance company and financial market. Under power utility function, by using stochastic control theory, the closed-form solutions for the value function as well as the strategies is obtained. Finally, the research results are explained in the economic sense and the influence of some parameters on the optimal strategies is given through numerical calculation.