股价服从Levy过程的投资组合优化策略研究  

Research on investment portfolio optimization strategy of stock prices obey Levy process

作　　者：张夏洁 刘宣会[1] 贾丹琴 ZHANG Xia-jie LIU Xuan-hui JIA Dan-qin(School of Science, Xihn Polytechnic University, Xihn 710048, China)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2017年第1期107-112,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：陕西省教育厅科研计划项目基金(2013JK0594);西安工程大学研究生创新基金(CX2015002)

摘　　要：当股票价格受到多个重大事件叠加影响时,股价会出现不连续的跳跃,一般可将股票价格考虑为服从Levy过程.基于随机微分对策,建立投资组合优化的数学模型,当股票价格服从Levy过程时,运用Ito-Levy过程的一维Ito公式和泛函变分法,采用对数效用函数,研究两人竞争的投资组合策略问题,运用随机微分对策得到两人竞争的最优投资策略.When stock price is impacted by many major things, the stock price will not jump continuously. Generally, the price of stock is considered to obey the Levy process. Based on the stochastic differential game, the mathematical model of investment portfolio optimization was established. In the course of stock price obeying Levy, the research on the investment portfolio strategy was studied by using the Ito formula of Ito - Levy process, functional varia- tional method and the logarithm utility function, the optimal investment strategy of the two person competition was obtained by using the stochastic differential game.

关 键 词：LEVY过程 随机微分对策 ITO公式 对数效用函数 最优策略 

分 类 号：O211[理学—概率论与数理统计]