跳扩散环境下红利支付对不确定厌恶投资者最优投资组合选择的影响  

Impacts of the Dividend Payment on the Optimal Portfolio Choice of an Investor with the Ambiguity Aversion under Jump-Diffusion

作　　者：梁勇[1] 费为银[1] 方和远 刘鹏[1] 

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000

出　　处：《东华大学学报（自然科学版）》2015年第2期273-276,共4页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金资助项目(71171003);安徽省高校自然科学基金资助项目(KJ2012B019;KJ2013B023)

摘　　要：面对例外事件的冲击,金融市场的股票价格会发生跳跃,当股票价格发生跳跃且支付红利时,不确定厌恶投资者的预期效用的刻画将会采用不同于传统的方法.利用跳扩散型随机微分方程理论和动态规划方法,建立了不确定厌恶投资者的最优投资策略所满足的Hamilton-JacobiBellman(HJB)方程.进一步,利用市场分解的技术求解HJB方程,从而推导出最优消费与投资策略.最后,利用数值分析定量地讨论了投资者风险厌恶因素对最优决策的影响.The stocks＇ prices in a financial market will jump when there is a shock of an rare event. And the utility of an ambiguity aversion investor with the environment of both the stock price＇s jump and the dividend payment is characterized by a new method. Through the theory of jump-diffusion stochastic differential equations and the dynamic programming principle, the value function of an investor＇s optimal consumption and portfolio satisfying the Hamilton-Jacobi-Bellman （HJB） equation is derived. Moreover, market decomposition technique is applied to solve the HJB equation, the optimal consumption and portfolio policy for investors is obtained. Finally, the effects of the risk aversion on the optimal portfolio choice of an investor are analyzed by numerical simulation.

关 键 词：不确定厌恶 跳扩散型随机微分方程 最优投资组合 例外事件 红利支付 

分 类 号：O211.63[理学—概率论与数理统计] F224.9[理学—数学]