| 一类终端财富期望效用最大化问题: 通货膨胀情形 |
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| 引用本文： | 王光臣,吴臻. 一类终端财富期望效用最大化问题: 通货膨胀情形[J]. 应用概率统计, 2009, 25(4): 345-353 |
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| 作者姓名： | 王光臣 吴臻 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金，国家重点基础研究发展计划，山东省自然科学基金，教育部博士点基金 |
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| 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.
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| 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. |
A Kind of Problem of Maximizing the Expected Utilityfrom the Terminal Wealth: the Case of Inflation |
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| WANG GUANGCHEN,WU ZHEN. A Kind of Problem of Maximizing the Expected Utilityfrom the Terminal Wealth: the Case of Inflation[J]. Chinese Journal of Applied Probability and Statisties, 2009, 25(4): 345-353 |
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| Authors: | WANG GUANGCHEN WU ZHEN |
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| Affiliation: | School of Mathematical Sciences,Shandong Normal UniversityJiangsu Institute of Economic and Trade Technology |
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| Abstract: | This paper is concerned with a kind of problemof maximizing the expected utility from the terminal wealth in thecase of inflation. For a class of CRRA utility, we obtain by adirect method an agent's explicit optimal portfolio strategy and thecorresponding maximum expected utility. Moreover, we give someeconomical interpretations. This idea comes from thecompletion-of-square technique of linear quadratic optimal controlproblems. In Section 3, based on the history data of the stock priceand the inflation rate, the values of the parameters in models areestimated with SAS software. And then, the explicit optimalportfolio strategy and the maximum expected utility are also given. |
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| Keywords: | Utility maximization CRRA inflation CPI portfolio. |
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