一类终端财富期望效用最大化问题:通货膨胀情形  

A Kind of Problem of Maximizing the Expected Utility from the Terminal Wealth:the Case of Inflation

作　　者：王光臣[1] 吴臻[2] 

机构地区：[1]山东师范大学数学科学学院,济南250014 [2]山东大学数学学院,济南250100

出　　处：《应用概率统计》2009年第4期345-353,共9页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(10671112);国家重点基础研究发展计划(973项目:2007CB814904);山东省自然科学基金(JQ200801和2008BS01024);教育部博士点基金资助

摘　　要：本文研究了一类受通货膨胀影响的终端财富期望效用最大化问题.对常数相对风险厌恶(CRRA)情形的效用函数,用直接构造的方法得到了代理人的显式最优投资策略和最大期望效用,并给出其经济含义.该思想来自线性二次最优控制问题中的完全平方技术.根据股票价格和通货膨胀率的历史数据,我们用SAS软件估计出模型中参数的近似值,并给出代理人的最优投资策略和最大期望效用.This paper is concerned with a kind of problem of maximizing the expected utility from the terminal wealth in the case of inflation. For a class of CRRA utility, we obtain by a direct method an agent＇s explicit optimal portfolio strategy and the corresponding maximum expected utility. Moreover, we give some economical interpretations. This idea comes from the completion-of-square technique of linear quadratic optimal control problems. In Section 3, based on the history data of the stock price and the inflation rate, the values of the parameters in models are estimated with SAS software. And then, the explicit optimal portfolio strategy and the maximum expected utility are also given.

关 键 词：效用最大化 常数相对风险厌恶(CRRA) 通货膨胀 居民消费价格总指数 投资组合 

分 类 号：O211.63[理学—概率论与数理统计]