基于相对财富效用的多阶段投资组合博弈模型

doi:10.16381/j.cnki.issn1003-207x.2019.01.004

中国管理科学 ›› 2019, Vol. 27 ›› Issue (1): 34-43.doi: 10.16381/j.cnki.issn1003-207x.2019.01.004

基于相对财富效用的多阶段投资组合博弈模型

周忠宝¹, 任甜甜¹, 肖和录², 吴士健³, LIU Wenbin⁴

1. 湖南大学工商管理学院, 湖南长沙 410082;
2. 湖南师范大学商学院, 湖南长沙 410082;
3. 山东科技大学经济管理学院, 山东青岛 266510;
4. Business School, University of Kent, England Kent CT2 7PE

收稿日期:2017-05-26 修回日期:2018-01-03 出版日期:2019-01-20 发布日期:2019-03-25
通讯作者: 吴士健(1977-),男(汉族),山东齐河人,山东科技大学经济管理学院副教授,研究方向:系统优化与决策,E-mail:everwsj@163.com. E-mail:everwsj@163.com
基金资助:
国家自然科学基金面上项目（71771082，71371067，71801091）；湖南省杰出青年科学基金资助项目（2017JJ1012）

Multi-period Portfolio Game Model Based on Relative Wealth Utility

ZHOU Zhong-bao¹, REN Tian-tian¹, XIAO He-lu², WU Shi-jian³, LIU Wen-bin⁴

1. School of Business Administration, Hunan University, Changsha 410082, China;
2. Business School, Hunan Normal University, Changsha 410081, China;
3. College of Economics and Management, Shandong University of Science and Technology, Qingdao 266510, China;
4. Business School, University of Kent, Kent CT2 7PE, England

Received:2017-05-26 Revised:2018-01-03 Online:2019-01-20 Published:2019-03-25

摘要/Abstract

摘要： 现有投资组合优化模型普遍假设投资者之间是相互独立的，然而在实际投资过程中投资者往往是相互影响的，尤其是对于机构投资者而言，考虑这种相互影响显得尤为重要。本文基于多阶段投资组合理论和纳什均衡思想，考虑投资者决策之间的影响关系，以每个投资者自身终端相对财富的期望效用水平最大化为目标，构建了多阶段投资组合博弈模型，并给出了纳什均衡投资策略和相应值函数的解析解。最后，采用累计经验分布函数和确定性等价等指标，对纳什均衡投资策略与传统策略进行了比较，结果表明纳什均衡策略更具优越性。

关键词: 多阶段投资组合, 博弈模型, 纳什均衡, 相对财富效用

Abstract: Most existing portfolio optimization models assume that investors are independent. However, the investors especially institutional investors, usually affect each other in actual investment. Based on the portfolio optimization and Nash game theories, the competition relationship is considered into investors' decision-making, and a multi-period portfolio game model is constructed by maximizing the expected utility of the relative terminal wealth of each competitor. The close forms of the Nash equilibrium investment strategy and the corresponding value function are obtained. By using the empirical cumulative distribution function and the certainty equivalent, the Nash equilibrium investment strategy is compared with the traditional strategy in our simulations. The results show that the Nash equilibrium strategy is more effective for investors.

Key words: multi-period portfolio optimization, game model, Nash equilibrium, relative wealth utility

中图分类号:

F830

周忠宝, 任甜甜, 肖和录, 吴士健, LIU Wenbin. 基于相对财富效用的多阶段投资组合博弈模型[J]. 中国管理科学, 2019, 27(1): 34-43.

ZHOU Zhong-bao, REN Tian-tian, XIAO He-lu, WU Shi-jian, LIU Wen-bin. Multi-period Portfolio Game Model Based on Relative Wealth Utility[J]. Chinese Journal of Management Science, 2019, 27(1): 34-43.

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基于相对财富效用的多阶段投资组合博弈模型

Multi-period Portfolio Game Model Based on Relative Wealth Utility

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