跳跃扩散市场的最优保险投资决策

Optimal investment decision for insurer in a jump-diffusion market

假定保险公司的盈余为Crámer-Lundberg过程,保险公司的投资市场是由一个无风险债券和n个风险证券构成的资本市场.风险证券的价格服从带跳的扩散过程.在均值-方差准则下通过最优控制原理来研究保险公司的最优投资策略选择问题.得到了最优投资策略和有效边界的显式表达式.与在最大化最终财富期望效用准则下得到的最优投资策略不同,所得到的最优策略依赖保险索赔过程的所有因素.最后分析了最优投资策略随保险索赔过程各个因素变化的动态性质.

Assume that the surplus of an insurer follows the compound Poisson risk process and the insurer would invest its surplus in a financial market,which consists of one risk-free bond and n risky assets,whose prices follow an n-dimensional jump-diffusion process.The optimal investment strategy under the meanvariance principle for the insurer is studied by the stochastic control approach.The closed and explicit formulas for the optimal investment strategy and the efficient frontier are derived.Unlike optimal strategies derived under other criteria such as maximizing the expected exponential utility function of an insurer＇s terminal wealth,the optimal investment strategy derived in this paper depends on all model parameters for an insurer.Moreover,the effects of the model parameters on the optimal investment strategy and some dynamic properties of the efficient frontier are analyzed.