常弹性方差模型下保险人的最优投资策略  

Insurer's optimal investment strategy under constant elasticity of variance model

作　　者：荣喜民[1] 范立鑫[1] 

机构地区：[1]天津大学理学院,天津300072

出　　处：《系统工程理论与实践》2012年第12期2619-2628,共10页Systems Engineering-Theory & Practice

基　　金：天津市自然科学基金(09JCYBLJC01800)

摘　　要：假设风险资产价格服从常弹性方差(CEV)模型,保险人面临的风险过程是带漂移的布朗运动.投资过程与承保风险过程完全相关.根据随机最优控制理论,建立保险基金投资问题的HJB方程.由于该方程是非线性偏微分方程,不易求解,因此采用Legendre变换将其转换成对偶问题进行研究.最后针对特定参数值分别得到以CARA和CRRA效用函数为目标的保险人的最优投资策略,这样的投资策略更符合金融市场的实际要求.Research insurance funds investment based on constant elasticity of variance （CEV） model, consider a model which the risky asset is modeled by CEV model and the aggregate claims are modeled by a Brownian motion with drift. As employment of premium is different from ordinary, which means that the insurer should keep an eye on underwrite risk when he use insurance funds, assume that investment risk has a linear correlation with underwrite risk. According to stochastic control theory, derive the HJB equation related with insurance problem. This equation is non-linear partial differential equation, yet it is difficult to solve it, change primary problem to the dual problem by using Legendre transform. Through setting the parameter values, the optimal investment strategy for an insurer with CARA or CRRA utility function is presented and the relevant analysis is given, which provides important practical significance for an insurer to invest.

关 键 词：保险基金 CEV模型 效用函数 随机控制理论 HJB方程 LEGENDRE变换 

分 类 号：O211.6[理学—概率论与数理统计]