现实约束下多阶段模糊投资组合的时间一致性策略研究

doi:10.16381/j.cnki.issn1003-207x.2020.1759

中国管理科学 ›› 2022, Vol. 30 ›› Issue (4): 42-51.doi: 10.16381/j.cnki.issn1003-207x.2020.1759cstr: 32146.14.j.cnki.issn1003-207x.2020.1759

现实约束下多阶段模糊投资组合的时间一致性策略研究

张鹏¹, 李影¹, 曾永泉²

1.华南师范大学经济与管理学院，广东广州510006；2.仲恺农业工程学院人文与社会科学学院，广东广州510225

收稿日期:2020-09-12 修回日期:2021-02-25 出版日期:2022-04-20 发布日期:2022-04-26
通讯作者: 张鹏(1975-)，男(汉族)，江西吉安人，华南师范大学经济与管理学院，教授，博士，研究方向：投资组合优化、金融工程，Email:zhangpeng300478@aliyun.com. E-mail:zhangpeng300478@aliyun.com
基金资助:
国家自然科学基金资助项目(71271161)；广东省社科项目(GD19CGL32)

Time-consistent Strategy for Themultiperiod Fuzzy Portfolio Selection with Real Constraints

ZHANG Peng¹, LI Ying¹, ZENG Yong-quan²

1. School of Economics and Management, South China Normal University, Guangzhou 510006, China;2. College of Humanities and Social sciences, Zhongkai University of Agriculture and Engineering, Guangzhou 510225, China

Received:2020-09-12 Revised:2021-02-25 Online:2022-04-20 Published:2022-04-26
Contact: 张鹏 E-mail:zhangpeng300478@aliyun.com

摘要/Abstract

摘要： 考虑交易成本约束、借款约束、阈值约束、收益需求约束和基数约束，本文提出多阶段均值—标准下半方差模糊投资组合模型并讨论了该模型的时间一致性最优投资策略。具体如下：首先，基于可能性理论，将模型转化为非线性动态优化问题；由于标准半方差是不可离散的，模型的最优解不具有时间一致性。其次，为获得时间一致的最优投资策略，本文采用博弈论，将该模型转化为时间一致性动态优化问题，并运用离散近似迭代方法求解。最后，通过具体算例比较不同风险偏好系数、不同基数约束和不同借款约束的最优投资策略，以验证模型和算法的有效性。

关键词: 多阶段模糊投资组合模型; 均值—标准下半方差; 收益需求; 时间一致性; 离散近似迭代方法

Abstract: Considering the borrowing constraints, threshold constraints, return demand and cardinality constraints, a new multiperiod possibislistic mean standard lower semi-variance portfolio selection model is proposed. Based on the possibilistic theory, the proposed model can be transformed into a crisp nonlinear dynamic optimization problem. Because the standard deviation operator is not separable, the optimal solution of the model is not time-consistent. By applying the game theory, the model is transformed into a time-consistentdynamic optimization problem. The discrete iteration method is used to obtain the optimal time-consistent strategy.Finally, the comparison analyses of trade-off parameters, different desired number of risk assets and different borrowing constraints are givento illustrate the idea of the model and the effectiveness of the designed algorithm.

Key words: multiperiod fuzzy portfolio selection; mean standard lower semi-variance; return demand; time-consistent strategy; a discrete approximate iteration method

中图分类号:

F830

张鹏,李影,曾永泉. 现实约束下多阶段模糊投资组合的时间一致性策略研究[J]. 中国管理科学, 2022, 30(4): 42-51.

ZHANG Peng,LI Ying,ZENG Yong-quan. Time-consistent Strategy for Themultiperiod Fuzzy Portfolio Selection with Real Constraints[J]. Chinese Journal of Management Science, 2022, 30(4): 42-51.

参考文献

［1］ Markowitz H M. Portfolio selection［J］. The Journal of Finance,1952, 7(1):77-91.
［2］ Markowitz H M. Portfolio selection: Efficient diversification of investments［M］. Wiley, New York, 1959.
［3］ Li Duan, Ng W L.Optimal dynamic portfolio selection: Multi-period mean-variance formulation［J］. Mathematical Finance, 2000,10(3):387-406.
［4］郭文旌, 胡奇英. 不确定终止时间的多阶段最优投资组合［J］. 管理科学学报,2005,8(2):13-19.Guo Wenjing, Hu Qiying. Multi-period portfolio optimization when exit time is uncertain［J］. Journal of Mangement Science in Chinese,2005,8(2):13–19.
［5］周忠宝, 任甜甜, 肖和录,等.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 Zhongbao, Ren Tiantian, Xiao Helu, et al. Multi-period portfolio game model based on relative wealth utility［J］. Chinese Journal of Management Science,2019,27(1): 34-43.
［6］张鹏,曾永泉. 具有卖空总量限制的多阶段M-SAD投资组合优化［J］.中国管理科学,2021,29(6):60-69.Zhang Peng, Zeng Yongquan. Multiperiod mean semi-absolute deviation portfolio selection with total short selling constraints［J］. Chinese Journal of Management Science,2021,29(1):60-69.
［7］ Li Xingmei, Fang Shucherng, Tian Ye, et al. Expanded model of the project portfolio selection problem with divisibility, time profile factors and cardinality constraints［J］.Journal of the Operational Research Society,2015, 66(7): 1132-1139.
［8］ Cui Xiangyu, Li Duan, Wang Shouyang, et al. Better than dynamic mean-variance: Time inconsistency and free cash flow stream［J］. Mathematical Finance, 2012,22(2):346-378.
［9］ Bjrk T, Murgoci A, Zhou Xunyu. Mean-variance portfolio optimization with state-dependent risk aversion［J］. Mathematical Finance, 2014, 24 (1): 1-24.
［10］ Basak S,Chabakauri G. Dynamic mean-variance asset allocation［J］. Review Financial Studies, 2010,23:2970-3016.
［11］郭文旌, 卢晖.在不允许卖空市场条件下均值-方差投资者的最优时间一致性资产配置策略［J］. 系统管理学报,2020,29(2):224-230.Guo Wenjing, Lu Hui. Optimal time-consistent asset allocation strategy for mean-variance investor with No short selling［J］. Journal of Systems&Management,2020,29(2):224-230.
［12］ Bjrk T, Davis M H A, Landén C. Optimal investment under partial information［J］. Mathematical Methods of Operations Research, 2010,71 (2):371-399.
［13］李方超, 张成科, 朱怀念.Heston模型下考虑工资风险和保费退还条款的DC型养老金时间一致性投资策略［J］.系统管理学报,2020,29(4):617-628.Li Fangchao, Zhang Chengke, Zhu Huainian. Time-Consistent investment strategy for DC pension with salary risk and premium refund clauses in heston model［J］. Journal of Systems & Management, 2020,29(4): 617-628.
［14］ Carlsson C, Fullér R, Majlender P. A possibilistic approach to selecting portfolios with highest utility score［J］. Fuzzy Sets and Systems,2002,131:13–21.
［15］金秀, 刘家和, 苑莹.加权极大-极小随机模糊投资组合模型及实证研究［J］.系统管理学报, 2015,24(1):78-84.Jin Xiu, Liu Jiahe, Yuan Ying. A portfolio selection model with random fuzzy returns and weighted max-min operator and its empirical study［J］. Journal of Systems&Management,2015,24(1):78-84.
［16］ Zhang Peng, Zhang Weiguo. Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints［J］. Fuzzy Sets and Systems,2014, 255: 74-91.
［17］ Zhang Weiguo, Wang Yingluo, Chen Zhiping, et al. Possibilistic mean-variance models and efficient frontiers for portfolio selection problem［J］.Information Sciences,2007, 177:2787-2801.
［18］ Heidergott B, Olsder G J, Woude J V. Max plus at work—modeling and analysis of synchronized systems: A course on max-plus algebra and its applications, Princeton University Press, 2006.
［19］ Vercher E, Bermdez J D. A possibilistic mean-downside risk-skewness model for efficient portfolio selection［J］. IEEE Transactions On Fuzzy Systems, 2013,3:585-595.

[1]	罗鹏飞, 姚彦铭, 谭英贤. 突发公共卫生事件下企业委托代理问题与最优资本结构[J]. 中国管理科学, 2025, 33(10): 47-56.
[2]	叶彦艺, 杨晓光. 股票市场知情交易如何影响信用债利差[J]. 中国管理科学, 2025, 33(9): 1-10.
[3]	甘柳, 蔡颖俐, 徐明玉, 谭英贤. 二级债券市场信息获取与可转债融资[J]. 中国管理科学, 2025, 33(9): 22-32.
[4]	姚银红, 王晓旭, 陈炜, 陈振松. 基于Transformer-LSTM分位数回归的全球股市极端风险溢出研究[J]. 中国管理科学, 2025, 33(8): 1-13.
[5]	吴伟平, 林雨, 金成能, 唐振鹏. 随机市场深度下基于风险管理和交易约束的最优执行问题[J]. 中国管理科学, 2025, 33(8): 14-25.
[6]	颜镜洲, 李仲飞, 毛杰, 李星毅. 模糊波动下的策略交易和市场质量[J]. 中国管理科学, 2025, 33(8): 26-36.
[7]	张维, 陈卓, 冯绪, 熊熊, 张永杰. 金融系统工程在中国：2010－2024[J]. 中国管理科学, 2025, 33(7): 11-23.
[8]	田军, 董赞强, 李雅丽. 基于预付账款融资模式的供应链融资策略研究[J]. 中国管理科学, 2025, 33(7): 272-283.
[9]	罗鹏飞, 刘新乐, 陆婷, 张勇. 碳减排下的企业并购决策[J]. 中国管理科学, 2025, 33(7): 337-345.
[10]	杨科, 刘鑫, 田凤平. 中国与其他主要新兴市场国家间股市极端风险的跨市场传染[J]. 中国管理科学, 2025, 33(7): 44-53.
[11]	文璐, 冯玲. 动态政府干预下银行风险传染与最优救助决策研究[J]. 中国管理科学, 2025, 33(6): 37-48.
[12]	欧阳资生, 周学伟. 中国金融机构系统性风险回测与关联研究[J]. 中国管理科学, 2025, 33(6): 14-26.
[13]	赵志明, 潘琼. 债权激励对公司再融资的影响研究[J]. 中国管理科学, 2025, 33(6): 27-36.
[14]	谭春萍, 秦学志, 尚勤, 王文华, 林先伟. 企业财务困境的激励相容式组合纾解策略[J]. 中国管理科学, 2025, 33(5): 13-25.
[15]	于辉, 王霜. 供应链金融：企业如何实现“鱼与熊掌”兼得？[J]. 中国管理科学, 2025, 33(5): 280-289.

现实约束下多阶段模糊投资组合的时间一致性策略研究

Time-consistent Strategy for Themultiperiod Fuzzy Portfolio Selection with Real Constraints

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0