具有熵约束的多阶段均值—半绝对偏差投资组合优化

doi:10.16381/j.cnki.issn1003-207x.2019.0897

中国管理科学 ›› 2021, Vol. 29 ›› Issue (9): 36-43.doi: 10.16381/j.cnki.issn1003-207x.2019.0897

具有熵约束的多阶段均值—半绝对偏差投资组合优化

曾永泉¹, 张鹏²

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

收稿日期:2019-06-19 修回日期:2019-09-30 出版日期:2021-09-20 发布日期:2021-09-20
通讯作者: 曾永泉(1975-),女(汉族),湖北麻城人,仲恺农业工程学院人文与社会科学学院,博士,讲师,研究方向:风险管理,E-mail:151499768@qq.com. E-mail:151499768@qq.com
基金资助:
国家自然科学基金资助项目（71271161）；广东省软科学项目（2019A101002066，2019A101002052）；广东省社科项目（GD19CGL32）

Multi-period Mean-semi-absolute Deviation Portfolio Selection with Entropy Constraint

ZENG Yong-quan¹, ZHANG Peng²

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

Received:2019-06-19 Revised:2019-09-30 Online:2021-09-20 Published:2021-09-20

摘要/Abstract

摘要： 考虑投资者面临金融市场随机不确定性，将证券收益率视为随机变量，文章运用半绝对偏差度量风险，采用投资组合的熵度量分散化程度，同时，考虑交易成本和借款限制，提出多阶段投资组合模型。由于投资过程存在交易成本，上述模型为路径依赖性的动态优化问题。文章运用离散近似迭代法求解，并证明了该算法是线性收敛的。最后，通过实证研究得出熵的取值越大，投资组合的最终财富越小。

关键词: 多阶段投资组合, 均值-半绝对偏差, 熵, 交易成本, 离散近似迭代法

Abstract: A mean semi-absolute deviation model for multi-period portfolio selection in random environment is presented by taking into account transaction cost, borrowing constraints and diversification degree of portfolio. In the proposed model, the risk level is characterized by the semi-absolute deviation of return, and the diversification degree of portfolio is measured by the originally presented entropy. Because of the transaction costs, the multi-period portfolio selection is the dynamic optimization problem with path dependence. Furthermore, the discrete approximate iteration method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the different entropy model is provided by a numerical example to illustrate that the entropy is more and the terminal wealth is less.

Key words: multi-period portfolio selection, mean semi-absolute deviation, entropy, transaction costs, discrete approximate iteration

中图分类号:

F224.9

曾永泉, 张鹏. 具有熵约束的多阶段均值—半绝对偏差投资组合优化[J]. 中国管理科学, 2021, 29(9): 36-43.

ZENG Yong-quan, ZHANG Peng. Multi-period Mean-semi-absolute Deviation Portfolio Selection with Entropy Constraint[J]. Chinese Journal of Management Science, 2021, 29(9): 36-43.

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具有熵约束的多阶段均值—半绝对偏差投资组合优化

Multi-period Mean-semi-absolute Deviation Portfolio Selection with Entropy Constraint

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