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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 ›› 2020, Vol. 37 ›› Issue (2): 155-164.doi: 10.3969/j.issn.1005-3085.2020.02.003

• • 上一篇    下一篇

带有交易成本的均值--方差--下半方差投资组合模型

王晓琴1,  高岳林1,2   

  1. 1- 北方民族大学数学与信息科学学院，银川  750021
    2- 宁夏智能信息与大数据处理重点实验室，银川  750021
  • 收稿日期:2018-01-18 接受日期:2018-06-25 出版日期:2020-04-15 发布日期:2020-06-15
  • 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; 61561001)；宁夏高等教育一流学科建设项目(NXYLXK2017B09)；北方民族大学重大专项(ZDZX201901).

Mean-variance Lower-semi-variance Portfolio Model with Transaction Costs

WANG Xiao-qin1,  GAO Yue-lin1,2   

  1. 1- School of Mathematics and Informational Science, North Minzu University, Yinchuan 750021
    2- Ningxia Province Key Laboratory of Intelligent Information and Big Data Processing, Yinchuan 750021
  • Received:2018-01-18 Accepted:2018-06-25 Online:2020-04-15 Published:2020-06-15
  • Contact: Y. Gao. E-mail address: gaoyuelin@263.net
  • Supported by:
    The National Natural Science Foundation of China (11961001; 61561001); the Construction Project of First-class Subjects in Ningxia Higher Education (NXYLXK2017B09); the Key Scientific Research Project of North Minzu University (ZDZX201901).

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摘要： 投资组合选择研究为投资决策和风险管理提供了可量化的途径和科学决策的依据．本文引入了非凹非凸的典型交易成本函数，建立了含有交易成本函数的均值--方差--下半方差投资组合模型．考虑到不同的投资者对风险的厌恶程度不同，引入风险厌恶系数，把双目标的投资组合优化模型转化为单目标的投资组合优化模型，并运用教与学算法对模型进行了求解，得到不同收益下的最优投资组合，同时给出了投资组合的有效边界，最后对算法的优越性进行了分析，得到了比较好的仿真结果．

关键词: 投资组合, 均值--方差, 下半方差, 交易成本, 教与学算法

Abstract: The research on portfolio selection provides a quantifiable way and scientific basis for investment decision and risk management. In this paper, we introduce a typical nonconcave and nonconvex transaction cost function, and establish a mean-variance lower-semi-variance portfolio model with transaction cost. Considering that different investors have different degrees of risk aversion, the risk aversion coefficient is introduced and the double objective portfolio optimization model is transformed into single objective portfolio optimization model. The model is solved by using Teaching and Learning algorithm, and the optimal portfolio under different returns is obtained. At the same time, the effective boundary of portfolio is given. Finally, the advantage of the algorithm is analyzed, and a good simulation result is presented.

Key words: portfolio, mean-variance, lower semi-variance, transaction cost, teaching-learning-based optimization

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