跳扩散环境下考虑红利支付的动态资产配置问题研究  

Research of dynamic asset allocation with dividend payment under jump-diffusion environment

作　　者：蔡振球[1] 费为银[1] 潘磊[1] 

机构地区：[1]安徽工程大学数理学院,安徽芜湖241000

出　　处：《纯粹数学与应用数学》2013年第1期99-105,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金(71171003);安徽省自然科学基金(090416225);安徽省高校自然科学基金(KJ2010A037)

摘　　要：研究资产价格带跳环境下红利支付对投资者资产配置的影响,投资者将其财富在风险资产和无风险资产中进行分配,在终端财富预期效用最大化标准下,利用动态规划原理建立的HJB方程推导最优配置策略,并得到最优动态资产配置策略的近似解.最后通过数值模拟,分析了跳和红利支付对投资者最优配置策略的影响.结果表明在跳发生的情况下,不管跳的大小和方向如何,投资者都会减少其在风险资产中的配置头寸,同时带有红利支付的资产比不带红利支付的资产对投资者更具吸引力.The impacts of the dividend on asset allocations of an investor under an environment with jump asset prices are studied.An investor allocates his wealth to the risky asset and the riskless asset.Under maximizing the expected utility of the terminal wealth,by using HJB equation derived by the dynamic programming principle,the optimal allocation strategy is provided,and an approximate solution of the optimal dynamic asset allocation is obtained.Finally,we analyze the impacts of jump and dividend on the optimal allocation strategy of an investor through the numerical simulation.The results indicate that when a jump happens,no matter what size and direction of a jump are,the investor will reduce the position of risky asset,and the assets with dividend are more attractive to investors than the ones without dividend.

关 键 词：跳扩散过程 红利支付 资产配置 HJB方程 效用最大化 

分 类 号：O211.63[理学—概率论与数理统计] F830.9[理学—数学]