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基于新型负指数期望效用的投资组合选择模型

付天文1,*  涂卓卓1  魏伯洋1   

  1. 1. 西安交通大学数学与统计学院, 西安 710049
  • 收稿日期:2015-01-04 出版日期:2016-03-15 发布日期:2016-03-15
  • 通讯作者: 付天文 twfu@stu.xjtu.edu.cn
  • 基金资助:

    国家基础科学人才培养基金 (No. J1210059)

Portfolio selection models with new negative exponential expected utilities

FU Tianwen1,*  TU Zhuozhuo1  WEI Boyang1   

  1. 1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2015-01-04 Online:2016-03-15 Published:2016-03-15

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摘要：

结合现有文献对最优投资决策问题的讨论, 提出了一类满足单调性和凹性的新型负指数效用函数, 并给出数学和经济学上的合理解释. 通过多种类型的加权函数以及对尾部的恰当描述, 损失分布的厚尾现象得到更加有效地控制. 利用$-统计量估计新型期望效用, 并说明其合理性. 进一步地, 构建了兼顾多种市场摩擦因素的实际投资组合选择模型. 选用中国和美国股票市场的数据进行实证研究. 结果表明了新期望效用的优越性和鲁棒性.

关键词: 负指数期望效用, 市场摩擦, 投资组合优化, 性能比率

Abstract:

With an overview of the literatures on discussions about optimal investment decision problems, we propose a new class of negative exponential utility function satisfying the monotonicity and concavity. And reasonable explanations are also given from the viewpoints of mathematics and economics. The fat-tail phenomenon of the loss distribution is controlled efficiently by different kinds of weighted function and proper description to the tail. We use L-statistics to estimate the new expected utility and the rationality is also illustrated. Moreover, we construct a realistic portfolio selection model with multiple market frictions. With the real data from Chinese and American stock market, we carry out a series of empirical studies. Empirical results show the superiority and robustness of our new expected utility.

Key words: negative exponential expected utility, market frictions, portfolio optimization, performance ratio