基于随机微分博弈的保险公司最优决策模型

The optimal decision-making model for insurance companies based on the dynamical differential game

本文研究了基于保险公司与自然之间二人-零和随机微分博弈的最优投资及再保险问题。假设保险公司具有指数效用,自然是博弈的"虚拟"对手,通过求解最优控制问题对应的HJB I方程,得到了保险公司的最优投资和再保险策略以及最优值函数的闭式解。结果显示,在完全分保时(即自留比例为零),保险公司应该将全部财富购买无风险资产,即风险资产投资额为零;在不完全分保时保险公司将卖空风险资产,且卖空数量及保险自留比例都随保险公司盈余过程与风险资产间的相关性的提高而增大,随终止时刻T的临近而增加,但随市场中无风险资产回报率的增加而减少。

The paper studied the optimal investment and reinsurance arrangements of an insurance company according to the two-person zero sum dynamical differential game theory between the insurer and the nature. Assuming the insurer having the index effect, and the nature as the ＂hypothetical＂ counterpart, it arrived at the optimal investment plan and reinsurance strategy and the closed-form solution of the optimal value function by solving the HJBI equation corresponding to optimal control problems. The results indicated that in the situation of full cession （ i. e. zero retention by the insurer）, the insurance company should invest all its wealth into risk-free assets,namely ,maintain none risk assets portfolio. In the situation of partial cession, the insurance company should short risk assets, and the short position and the rate of retention should increase along with the increase of correlation between the surplus realization and risk assets, and increase as the approaching of the termination day T, but should decrease as the rise of the risk-free return rate in the market.