随机微分博弈下带有负债的保险公司最优决策

Optimal Policies for Insurance Company with Liability under Stochastic Differential Games

应用线性-二次控制方法,假定市场是保险公司博弈的虚拟对手,研究带有负债情形下的保险公司与市场二人零和随机微分博弈问题.假设保险公司的目标是最大化终值财富期望效用,分别在指数效用和幂效用下,求得保险公司的最优投资策略与最优再保险策略,最优市场策略,并在最优策略下求得值函数的表达式.最后通过指数效用下的数值算例,在市场最坏的情形,分别给出有无负债及有负债时不同的负债参数对保险公司最优投资与再保险策略的影响.

Using linear-quadratic control theory, taking market as insurance company＇s virtual opponent, a zero-sum sto- chastic differential game problem between insurer and market with liability was investigated. Assuming that the aim of the insurer is to maximize the expected utility of terminal wealth, under exponential utility and power utility, the expression of optimal reinsurance strategies, investment strategies and the best marketing strategies as well as value function were obtained. Finally, a numerical analysis was given to show the impact of liabilities and market parameters on the optimal strategies under exponential utility.