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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2024, Vol. 41 ›› Issue (1): 39-52.doi: 10.3969/j.issn.1005-3085.2024.01.003

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模糊环境下基于遗传差分协同进化的多阶段投资组合模型

胡晨阳1,2,  高岳林1,3,  孙  滢2   

  1. 1. 北方民族大学数学与信息科学学院，银川 750021;
    2. 宁夏科学计算与智能信息处理协同创新中心，银川 750021;
    3. 宁夏智能信息与大数据处理重点实验室，银川  750021
  • 收稿日期:2021-07-05 接受日期:2022-08-12 出版日期:2024-02-15 发布日期:2024-04-15
  • 通讯作者: 高岳林 E-mail: gaoyuelin@263.net
  • 基金资助:
    国家自然科学基金 (11961001)；宁夏自然科学基金重点项目 (2022AAC02043)；宁夏高等教育一流学科建设基金 (NXYLXK2017B09)；南京证券支持基础学科研究项目 (NJZQJCXK202201).

A Multi-stage Portfolio Model Based on Genetic Differential Co-evolution in an Fuzzy Environment

HU Chenyang1,2,   GAO Yuelin1,3,   SUN Ying2   

  1. 1. School of Mathematics and Information Sciences, North Minzu University, Yinchuan 750021;
    2. The Collaborative Innovation Center of Scientific Computing and Intelligent Information Processing of Ningxia Province, Yinchuan 750021; 
    3. The Key Laboratory of Intelligent Information and Big Data Processing of Ningxia Province, Yinchuan 750021
  • Received:2021-07-05 Accepted:2022-08-12 Online:2024-02-15 Published:2024-04-15
  • Contact: Y. Gao.\quad E-mail address: gaoyuelin@263.net
  • Supported by:
    The National Natural Science Foundation of China (11961001); the Ningxia Natural Science Foundation Key Projects (2022AAC02043); the Construction Project of First-class Subjects in Ningxia Higher Education (NXYLXK2017B09); the Nanjing Securities Support Basic Discipline Research Project (NJZQJCXK202201).

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摘要：

现实经济活动中投资一般是不确定的和随机的，投资者对于风险资产的选择大多情况下是多阶段的。基于该现实因素，在模糊环境下考虑多个摩擦因素，利用交易限制引入资产的基数约束，建立可能性均值–下半方差–熵多阶段投资组合优化模型 (V-S-M)，
该模型是一个多阶段混合整数规划问题。同时，给出了求解该模型的一个遗传差分协同进化算法 (GAHDE)，并对不同风险态度下的投资组合策略进行了分析，同时将所得数值结果与可能性均值–下半方差模型 (V-M) 和可能性均值–熵模型 (S-M) 进行模型对比，与标准的遗传算法和差分进化算法进行了算法对比，结果验证了所建模型和设计算法的优越性与有效性。

关键词: 投资组合, 多阶段, 模糊环境, 遗传算法, 差分进化算法

Abstract:

Investment in real economic activities is generally uncertain and stochastic, and investors' choice of risky assets is of multi-stage in most cases. Based on this reality, multiple frictions in a fuzzy environment are considered and a base constraint is proposed on assets using transaction restrictions to develop a likelihood mean-lower half-variance-entropy multi-stage portfolio optimization model (V-S-M), which is a multi-stage mixed integer programming problem. A genetic differential co-evolutionary algorithm (GAHDE) for solving the model is presented to analyse the portfolio strategy under different risk attitudes, and the numerical results are compared with the likelihood mean-lower half variance model (V-M) and the likelihood mean-entropy model (S-M), as well as with standard genetic algorithms (GA) and differential evolution algorithms (DE). The results validated the superiority and effectiveness of the model and algorithm designed in this paper.

Key words: portfolio, multi-stage, fuzzy environment, genetic algorithm, differential evolution algorithm

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