广东工业大学学报 ›› 2021, Vol. 38 ›› Issue (02): 39-47.doi: 10.12052/gdutxb.200100

• 综合研究 • 上一篇    下一篇

考虑限制性卖空的多期模糊投资组合优化模型

陈思豆, 黄卓铨, 杨兴雨   

  1. 广东工业大学 管理学院, 广东 广州 510520
  • 收稿日期:2020-08-13 出版日期:2021-03-10 发布日期:2021-01-13
  • 通信作者: 杨兴雨(1981-),男,教授,主要研究方向为金融工程与在线金融算法,E-mail:yangxy@gdut.edu.cn E-mail:yangxy@gdut.edu.cn
  • 作者简介:陈思豆(1996-)，女，硕士研究生，主要研究方向为投资组合与风险管理
  • 基金资助:
    国家自然科学基金资助项目(71501049)；教育部人文社会科学研究基金资助项目(18YJA630132)

A Multi-period Fuzzy Portfolio Optimization Model Considering Restricted Short Selling

Chen Si-dou, Huang Zhuo-quan, Yang Xing-yu   

  1. School of Management, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-08-13 Online:2021-03-10 Published:2021-01-13

HTML

PDF (PC)

2534

摘要： 在实际证券交易中, 卖空操作是一种重要的投资手段, 因此本文研究考虑限制性卖空的多期模糊投资组合优化问题。将风险资产的收益视为梯形模糊数。在允许卖空的情况下, 建立了带单期最低期望收益约束、破产控制约束和投资比例边界约束的多期可信性均值−下半方差−偏度投资组合优化模型。设计了一个改进的多种群粒子群算法对模型进行求解。最后, 采用真实股票数据进行数值算例分析, 说明了所提出的优化模型和算法的有效性。

关键词: 多期模糊投资组合, 限制性卖空, 破产控制约束, 多种群粒子群算法

Abstract: In the actual stock market, short selling is an important investment vehicle. A multi-period fuzzy portfolio optimization problem with restricted short selling is studied. Firstly, regarding the returns of risky assets as trapezoidal fuzzy numbers, within the situation of short selling, a multi-period credibilistic mean-lower-semi-variance-skewness portfolio optimization model is constructed with the minimum expected return constraint for each period, bankruptcy control constraint and bound constraint. Then, a modified multiple particle swarm optimization is designed to solve the model. Finally, a numerical example is given with real stock data to illustrate the effectiveness of the proposed optimization model and algorithm.

Key words: multi-period fuzzy portfolio selection, restricted short selling, bankruptcy control constraint, multiple particle swarm optimization

中图分类号: 

  • TP18
[1] MARKOWITZ H. Portfolio selection [J]. The Journal of Finance, 1952, 7(1): 77-91.
[2] 李佳, 徐维军, 张卫国. 含有背景风险的双目标投资组合模型研究[J]. 运筹与管理, 2017, 26(4): 118-123.
LI J, XU W J, ZHANG W G. Bi-objective portfolio selection model and algorithm with background risk [J]. Operations Research and Management Science, 2017, 26(4): 118-123.
[3] 杨兴雨, 刘伟龙, 井明月, 等. 基于模糊收益率的分散化投资组合调整策略[J]. 广东工业大学学报, 2020, 37(5): 13-21.
YANG X Y, LIU W L, JING M Y, et al. A diversified portfolio selection strategy based on fuzzy return rate [J]. Journal of Guangdong University of Technology, 2020, 37(5): 13-21.
[4] YUE W, WANG Y P, XUAN H J. Fuzzy multi-objective portfolio model based on semi-variance-semi-absolute deviation risk measures [J]. Soft Computing, 2019, 23(17): 8159-8179.
[5] ZADEH L A. Fuzzy sets [J]. Information and Control, 1965, 8(3): 338-353.
[6] LIU Y J, ZHANG W G. Fuzzy portfolio selection model with real features and different decision behaviors [J]. Fuzzy Optimization and Decision Making, 2018, 17(7): 1-20.
[7] KAR M B, KAR S, GUO S N, et al. A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms [J]. Soft Computing, 2019, 23(12): 4367-4381.
[8] 曾永泉, 张鹏. 具有现实约束的均值-方差模糊投资组合绩效评价[J]. 模糊系统与数学, 2020, 34(3): 134-145.
ZENG Y Q, ZHANG P. Measuring the efficiency of possibilistic mean-variance portfolio selection with real factors constraints [J]. Fuzzy Systems and Mathematics, 2020, 34(3): 134-145.
[9] LI W M, DENG X. Multi-parameter portfolio selection model with some novel score-deviation under dual hesitant fuzzy environment [J]. International Journal of Fuzzy Systems, 2020, 22(4): 1123-1141.
[10] LIU B D, LIU Y K. Expected value of fuzzy variable and fuzzy expected value models [J]. IEEE Transactions on Fuzzy Systems, 2002, 10(4): 445-450.
[11] KAMDEM J S, DEFFO C T, FONO L A. Moments and semi-moments for fuzzy portfolio selection [J]. Insurance Mathematics and Economics, 2012, 51(3): 517-530.
[12] 王灿杰, 邓雪. 基于可信性理论的均值-熵-偏度投资组合模型及其算法求解[J]. 运筹与管理, 2019, 28(2): 154-159.
WANG C J, DENG X. Mean-entropy-skewness portfolio model based on credibility theory and its algorithm solution [J]. Operations Research and Management Science, 2019, 28(2): 154-159.
[13] ZHANG P. Random credibilitic portfolio selection problem with different convex transaction costs [J]. Soft Computing, 2019, 23(24): 13309-13320.
[14] 刘明明, 高岩. 摩擦市场中允许卖空的最优投资组合选择[J]. 中国管理科学, 2006, 14(5): 23-27.
LIU M M, GAO Y. Portfolio selection with short sales in a frictional market [J]. Chinese Journal of Management Science, 2006, 14(5): 23-27.
[15] 张鹏, 张忠桢, 曾永泉. 限制性卖空的均值-方差投资组合优化[J]. 数理统计与管理, 2008, 27(1): 124-129.
ZHANG P, ZHANG Z Z, ZENG Y Q. The optimization of the portfolio selection with the restricted short sales [J]. Application and Statistics and Management, 2008, 27(1): 124-129.
[16] 李晨, 陆忠华, 胡嘉力, 等. 基于非凸交易成本的投资组合优化问题求解[J]. 计算机工程与设计, 2017, 38(12): 3258-3266.
LI C, LU Z H, HU J L, et al. Portfolio optimization problem solving under concave transaction costs [J]. Computer Engineering and Design, 2017, 38(12): 3258-3266.
[17] 孙薇, 张卫国, 张群, 等. 具有投资限制的风险资产模糊随机投资组合模型[J]. 数学的实践与认识, 2015, 45(24): 51-60.
SUN W, ZHANG W G, ZHANG Q, et al. Fuzzy random portfolio model with investment limited [J]. Fuzzy Systems and Mathematics, 2015, 45(24): 51-60.
[18] GUO S N, YU L, LI X, et al. Fuzzy multi-period portfolio selection with different investment horizons [J]. European Journal of Operational Research, 2016, 254(3): 1026-1035.
[19] GUPTA P, MEHLAWAT M K, YADAV S, et al. Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models [J]. Soft Computing, 2020, 24(16): 11931-11956.
[20] 徐维军, 罗伟强, 张卫国. 考虑破产风险约束的多项目投资组合决策模型[J]. 运筹与管理, 2013, 22(6): 92-98.
XU W J, LUO W Q, ZHANG W G. Multi-project portfolio model with bankruptcy risk [J]. Operations Research and Management Science, 2013, 22(6): 92-98.
[21] LIU Y J, ZHANG W G, ZHANG Q. Credibilistic multi-period portfolio optimization model with bankruptcy control and affine recourse [J]. Applied Soft Computing, 2016, 38: 890-906.
[22] CAO J L. Algorithm research based on multi period fuzzy portfolio optimization model [J]. Cluster Computing, 2019, 22(2): 3445-3452.
[23] GUERRA M L, STEFANINI L. Approximate fuzzy arithmetic operations using monotonic interpolations [J]. Fuzzy Sets and Systems, 2005, 150(1): 5-33.
[24] SAMUELSON P. The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments [J]. Review of Economic Studies, 1970, 37: 537-542.
[25] RAHIMI M, KUMAR P. Portfolio optimization based on fuzzy entropy [J]. International Journal on Interactive Design and Manufacturing, 2019, 13(2): 531-536.
[26] LIN C C. A weighted max-min model for fuzzy goal programming [J]. Fuzzy Sets and Systems, 2004, 142(3): 407-420.
[27] ZHANG W G, ZHANG X L, XU W J. A risk tolerance model for portfolio adjusting problem with transaction costs based on possibilistic moments [J]. Insurance: Mathematics and Economics, 2010, 46(3): 493-499.
[1] 章云, 王晓东. 基于受限样本的深度学习综述与思考[J]. 广东工业大学学报, 2022, 39(05): 1-8.
[2] 袁君, 章云, 张桂东, 李忠, 陈哲, 于晟龙. 基于自适应动态规划的能量管理系统研究综述[J]. 广东工业大学学报, 2022, 39(05): 21-28.
[3] 饶东宁, 易善桢. 基于蒙特卡洛树搜索的众包概率规划[J]. 广东工业大学学报, 2022, 39(04): 1-8.
[4] 丘展春, 费伦科, 滕少华, 张巍. 余弦相似度保持的掌纹识别算法[J]. 广东工业大学学报, 2022, 39(03): 55-62.
[5] 胡滨, 关治洪, 谢侃, 陈关荣. 复杂网络动力学与智能控制[J]. 广东工业大学学报, 2021, 38(06): 9-19.
[6] 王东, 黄瑞元, 李伟政, 黄之峰. 面向抓取任务的移动机器人停靠位置优化方法研究[J]. 广东工业大学学报, 2021, 38(06): 53-61.
[7] 崔铁军, 李莎莎. 人工智能与生产过程中本质安全的实现[J]. 广东工业大学学报, 2021, 38(06): 84-90.
[8] 胡斌, 周颖慧, 陶小梅. 情感智能与心理生理计算[J]. 广东工业大学学报, 2021, 38(04): 1-8.
[9] 汪培庄, 曾繁慧, 孙慧, 李兴森, 郭建威, 孟祥福, 何静. 知识图谱的拓展及其智能拓展库[J]. 广东工业大学学报, 2021, 38(04): 9-16.
[10] 饶东宁, 杨锦鹏, 刘越畅. 时态规划综述及研究现状[J]. 广东工业大学学报, 2021, 38(03): 9-16.
[11] 赖峻, 刘震宇, 刘圣海. 基于全局数据混洗的小样本数据预测方法[J]. 广东工业大学学报, 2021, 38(03): 17-21.
[12] 高红, 郗常清, 刘巍. 可拓分析与决策的应用研究：以高校招生体系为例[J]. 广东工业大学学报, 2021, 38(01): 13-20.
[13] 饶东宁, 林卓毅, 魏来. n-度中心度与k-压力中心度及其并行算法[J]. 广东工业大学学报, 2020, 37(03): 36-41.
[14] 吴家湖, 熊华, 宗睿, 赵曜, 周贤中. 基于循环神经网络的目标转弯机动类型识别[J]. 广东工业大学学报, 2020, 37(02): 67-73.
[15] 郑震霆, 杨春燕. 基于事元理论的机械运动系统行为知识表示研究[J]. 广东工业大学学报, 2019, 36(06): 1-8,23.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2017 《广东工业大学学报》编辑部
地址：广州市东风东路729号广东工业大学 邮编：510090
电话：020-37626653,020-37626139,020-37626396
邮箱：xbzrb@gdut.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发