多目标规划最优化数学模型在组合投资中的应用
Application of Multi-Objective Planning Optimization Mathematical Model in Portfolio Investment
DOI: 10.12677/orf.2025.152061, PDF,  被引量   
作者: 马佳欢, 车丽萍：上海理工大学管理学院，上海
关键词: 多目标规划；组合投资；风险；收益；Multi-Objective Optimization； Portfolio Investment； Risks； Benefits
摘要: 投资者将资金以特定比例分别投放于一篮子有价证券的行为就可以构建一个投资组合，证券投资的收益特性和风险特性使得证券投资组合管理构成了现代投资决策理论非常重要的一部分。本文以现代投资理论重要基石——马科维茨的均值–方差理论为基础，简化假设投资者都追求利益最大化和风险最小化，首先简要介绍了多目标规划初等数学模型，然后将其与证券领域里的有关指标有机结合建立了在证券组合投资里的多目标规划模型，引入风险偏好系数，将其优化为更便于计算的单目标规划模型，最后代入搜集到的有关数据运用Matlab进行求解，满足了不同风险偏好投资者的不同需求。
Abstract: The behavior of investors investing funds in a certain proportion of a basket of securities can form a portfolio investment. The income characteristics and risk characteristics of securities investment make securities portfolio management an important part of financial management and investment decision-making. This article is based on Markowitz’s Mean-variance Theory—an important cornerstone of modern investment theory and it simplifies the assumption that investors are pursuing the maximization of profits and the minimization of risks. First, it briefly introduces the elementary mathematical model of multi-objective programming, and then it organically combines the relevant indicators in the securities field so we can establish a multi-objective programming model in portfolio investment, introduce a risk preference coefficient, optimize this model into a single-objective programming model which is more convenient to calculate, and finally extract the collected data into it to solve the problem with Matlab. The model could meet the different needs of investors with different risk preferences.
文章引用：马佳欢, 车丽萍. 多目标规划最优化数学模型在组合投资中的应用[J]. 运筹与模糊学, 2025, 15(2): 22-31. https://doi.org/10.12677/orf.2025.152061

参考文献

[1] 叶博韬. 投资组合的最优化设计[J]. 大众投资指南, 2017(10): 189.
[2] 任立民, 邓芳. 投资组合中多目标规划最优化数学模型的应用[J]. 海峡科学, 2007(7): 72-73.
[3] 易静. 多目标最优化方法及应用的探讨[J]. 时代教育, 2015(14): 117.
[4] 陈科燕, 肖冬荣. 多目标证券组合投资决策[J]. 统计与决策, 2003(4): 23-24.
[5] 孙靖, 熊岩, 张恒, 刘志平. 多期证券投资组合问题的区间多目标规划求解方法[J]. 控制与决策, 2020, 35(3): 645-650.
[6] 黄婧颖, 杨超进, 陈威, 梁景敏. 证券投资组合中的多目标规划应用[J]. 科技致富向导, 2014(8): 290.
[7] 袁从伦, 陈晨. 多目标投资组合优化[J]. 金融经济, 2015(22): 123-125.
[8] 杨桂元, 郑亚豪. 多目标决策问题及其求解方法研究[J]. 数学的实践与认识, 2012, 42(2): 108-115.
[9] 严应超, 张传新. 多目标投资组合研究[J]. 全国商情(经济理论研究), 2008(2): 80-81.
[10] 胡达沙, 吴炜. 目标规划法在证券组合投资中的应用[J]. 运筹与管理, 2004(3): 116-119.
[11] 刘敏. 数学规划在证券组合优化投资中的应用[J]. 湖南科技学院学报, 2005(11): 27-31.
[12] 杨伍梅, 刘权. 基于MATLAB的多目标规划最优投资组合方法的探讨[J]. 长沙大学学报, 2014, 28(5): 9-11.
[13] Markowitz, H. (1952) Portfolio Selection. The Journal of Finance, 7, 77-91. [Google Scholar] [CrossRef] 
[14] Shang, Z. and Liu, H. (2010). The Research on Portfolio Optimization Model and Strategy for Multiple Objectives. 2010 IEEE 2nd Symposium on Web Society, Beijing, 16-17 August 2010, 291-295.[CrossRef] 
[15] Anagnostopoulos, K.P. and Mamanis, G. (2010) A Portfolio Optimization Model with Three Objectives and Discrete Variables. Computers & Operations Research, 37, 1285-1297. [Google Scholar] [CrossRef] 

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