基于DEA博弈交叉效率和投资者心理的模糊投资组合研究

doi:10.12005/orms.2022.0321

运筹与管理 ›› 2022, Vol. 31 ›› Issue (10): 68-74.DOI: 10.12005/orms.2022.0321

基于DEA博弈交叉效率和投资者心理的模糊投资组合研究

邓雪, 方雯

华南理工大学数学学院,广东广州 510640

收稿日期:2020-06-24 出版日期:2022-10-25 发布日期:2022-11-14
作者简介:邓雪(1974-),女,博士,教授,硕士生导师。
基金资助:
教育部人文社会科学青年基金项目(18YJAZH014-x2lxY9180090);2019广东省自然科学基金面上项目(2019A1515011038);广东省软科学研究项目(2018A070712006,2019A101002118);广东省研究生示范课程(2019SFKC07)

Research on Fuzzy Portfolios Based on DEA Game Cross-efficiency Method and Investor Psychology

DENG Xue, FANG Wen

School of Mathematics, South China University of Technology, Guangzhou 510640, China

Received:2020-06-24 Online:2022-10-25 Published:2022-11-14

摘要/Abstract

摘要： 考虑到投资者并不是完全理性的,本文结合DEA博弈交叉效率方法研究了带有投资者心理因素的多目标模糊投资组合决策问题。首先,为了充分描绘投资者的心理因素和风险感知,本文基于可能性理论推导了带有风险态度的可能性均值和半绝对偏差。其次,将候选的风险资产视为互相竞争的博弈者,采用基于熵权法的DEA博弈交叉效率模型衡量它们的综合表现,从而得到每项资产的博弈交叉效率和奇异指数,并将其分别作为额外的收益和风险决策准则。基于此,提出了更加综合的可能性均值—半绝对偏差—博弈交叉效率—奇异指数模型。最后,通过一个应用实例验证了所提出的模型的合理性和有效性,从而为不同类型的投资者提供具有个性化的投资策略。

关键词: 模糊投资组合, 风险态度, 半绝对偏差, DEA博弈交叉效率, 奇异指数

Abstract: Considering that investors are not completely rational, a multi-objective fuzzy portfolio selection problem with investor psychological factors is studied in this paper by combining with the DEA game cross-efficiency evaluation method. Firstly, to fully describe the psychology and risk perception of investors, the possibilistic mean and semi-absolute deviation with risk attitude are derived basedonthepossibility theory. Secondly, the candidate assets are regarded as competing players, and their comprehensive performance is measured by DEA game cross-efficiency model based on entropy weight method. In this way, the DEA game cross efficiency score and maverick index of each asset are obtained, which are used asadditional return and risk measures. Considering the four objectives of possibilistic mean, semi-absolute deviation, cross-efficiency score and the maverick index, a more comprehensive fuzzy portfolio optimization model is established. Finally, the rationality and effectiveness of the proposed model is illustrated by an application example, which can provide different investors with personalized investment strategies.

Key words: fuzzy portfolio, risk attitude, semi-absolute deviation, DEA game cross-efficiency, Maverick index

中图分类号:

F224

邓雪, 方雯. 基于DEA博弈交叉效率和投资者心理的模糊投资组合研究[J]. 运筹与管理, 2022, 31(10): 68-74.

DENG Xue, FANG Wen. Research on Fuzzy Portfolios Based on DEA Game Cross-efficiency Method and Investor Psychology[J]. Operations Research and Management Science, 2022, 31(10): 68-74.

参考文献

[1] Markowitz H M. Portfolio selection[J]. Journal of Finance, 1952, 7: 77-91.
[2] Sharpe W A. Simplified model for portfolio analysis[J]. Management Science, 1963, 9: 277-293.
[3] Zadeh L A. Fuzzy sets[J]. Information and Control, 1965, 8(3): 338-353.
[4] Zadeh L A. Fuzzy sets as a basis for a theory of possibility[J]. Fuzzy Sets and Systems, 1978, 1: 3-28.
[5] Carlsson C, Fullér R. On possibilistic mean value and variance of fuzzy numbers[J]. Fuzzy Sets and Systems, 2001(122): 315-326.
[6] Zhang W G, Nie Z K. On possibilistic variance of fuzzy numbers[J]. Lecture Notes in Computer Science, 2003, 2639: 398-402.
[7] Vercher E, Bermúdez J D, Segura J V. Fuzzy portfolio optimization under downside risk measures[J]. Fuzzy Sets and Systems, 2007, 158(7): 769-782.
[8] Maenhout P J. Robust portfolio rules and asset pricing[J]. The Review of Financial Studies, 2004, 17(4): 951-983.
[9] Tsaur R C. Fuzzy portfolio model with different investor risk attitudes[J]. European Journal of Operational Research, 2013, 227(2): 385-390.
[10] 金秀,曲晓洁,刘家和.考虑投资者心理的模糊多目标投资组合模型及交互式算法[J].系统管理学报,2017,6:1081-1088.
[11] Zhou X Y, Wang J, et al. Portfolio selection under different attitudes in fuzzy environment[J]. Information Sciences, 2018,462: 278-289.
[12] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision-making units[J]. European Journal of Operational Research, 1978, 2(6): 429-444.
[13] 周忠宝,丁慧,马超群,等.考虑交易成本的投资组合效率估计方法[J].中国管理科学,2015,23(1):25-33.
[14] Lim S, Oh K W, Zhu J. Use of DEA cross-efficiency evaluation in portfolio selection: an application to Korean stock market[J]. European Journal of Operational Research, 2014, 236: 361-368.
[15] Deng X, Fang W. A novel mean-variance-maverick DEA prospect cross-efficiency approach for fuzzy portfolio selection[J]. Journal of Intelligent and Fuzzy Systems, 2019, 37(1): 1-18.
[16] Essida H, Ganouati J, Vigeant S. A mean-maverick game cross-efficiency approach to portfolio selection: an application to Paris stock exchange[J]. Expert Systems with Applications, 2018, 113: 161-185.
[17] Chen W, Li S S, Zhang J, et al. A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model[J]. Soft Computing, 2020, 24: 2515-2526.
[18] Sexton T R, Silkman R H, Hogan A J. Data envelopment analysis: critique and extensions[J]. New Directions for Program Evaluation, 1986, 32: 73-105.
[19] Liang L, Wu J, Cook W D. The DEA game cross-efficiency model and its Nash equilibrium[J]. Operations Research, 2008, 56(5): 1278-1288.

基于DEA博弈交叉效率和投资者心理的模糊投资组合研究

Research on Fuzzy Portfolios Based on DEA Game Cross-efficiency Method and Investor Psychology

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