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中国管理科学

中国管理科学 ›› 2014, Vol. 22 ›› Issue (1): 1-9.

• 论文 •    下一篇

基于非参数估计框架的期望效用最大化最优投资组合

姚海祥1, 李仲飞2   

  1. 1. 广东外语外贸大学信息学院, 广东 广州 510006;
    2. 中山大学管理学院, 广东 广州 510275
  • 收稿日期:2011-12-16 修回日期:2013-06-30 出版日期:2014-01-20 发布日期:2014-01-20
  • 基金资助:
    国家自然科学基金重点项目（71231008）；广东省高等学校高层次人才项目；广东省自然科学基金项目（S2011010005503）；广东省高等院校科技创新项目（2012KJCX0050）；广东省科技计划项目（2012B040305009）；“全国统计科学”研究计划一般项目（2013LY101）

Expected Utility Maximization Optimal Portfolio Selection Based on Nonparametric Estimation Framework

YAO Hai-xiang1, LI Zhong-fei2   

  1. 1. School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, China;
    2. Business School, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2011-12-16 Revised:2013-06-30 Online:2014-01-20 Published:2014-01-20

PDF (PC)

2438

被引次数

10

摘要： 本文基于期望效用最大化和非参数估计框架研究了最优投资组合选择问题。和以往大多文献假定资产收益率服从某些特定分布不同资产收益率的分布类型无需作任何假设。首先在一般效用函数下，利用组合收益率密度函数的非参数核估计给出了期望效用的基本非参数估计公式，并建立了期望效用最大化投资组合选择问题的基本框架。然后，在投资者具有幂效用函数的假定下，给出了期望效用具体的非参数计算公式，并给出了求解最大期望效用的数值算法。最后，利用中国证券交易所11支股票日收益率的真实数据给出了一个数值算例。本文提出的非参数估计框架具有一般性，还可以进一步用来研究各种现实条件下（如各种现实不等式约束和具有交易成本）的投资组合管理问题。

关键词: 投资组合选择, 幂效用函数, 期望效用最大化模型, 非参数估计, 最优投资策略

Abstract: An optimal portfolio selection problem based on the expected utility maximization and nonparametric estimation framework is investigated in this paper. Unlike most studies in which the assets' returns are supposed to obey some special distribution forms, any assumption about the distributions of the asset returns are not required in this paper. Firstly in case of general utility function, using the nonparametric estimation of the portfolio return's density function, the basis nonparametric calculated formula for expected utility is given, and the basic framework for expected utility maximization portfolio selection problem is established. Then, under the assumption that investors hold the power utility function, the specific nonparametric estimated formula for expected utility is obtained, and the specific numerical algorithms for the optimal investment strategy of the utility maximization model is proposed. Finally, a numerical example based on real daily return data of 11 stocks from Chinese stock market is given to illustrate the usefulness and effectiveness of our results. The nonparametric estimation framework introduced in this paper is general and adaptive. It can be used to investigate the portfolio selection model under various realistic conditions, such as inequality constraints and transaction costs.

Key words: portfolio selection, power utility function, expected utility maximization model, nonparametric estimation, optimal investment strategy

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