具有基数约束的多阶段均值-半方差可信性投资组合优化  

Credibilistic Multiperiod Mean-semivariance PortfolioSelection with Cardinality Constraints

作　　者：张鹏 崔淑琳 李璟欣 ZHANG Peng;CUI Shulin;LI Jingxin(School of Economics and Management,South China Normal University,Guangzhou 510006,China)

机构地区：[1]华南师范大学经济与管理学院,广东广州510006

出　　处：《运筹与管理》2023年第12期138-143,I0022-I0025,共10页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(71271161);中央高校基本科研业务费专项资金项目(175215003);武汉理工大学自主创新项目资助(171315005)。

摘　　要：文章探讨了一个多阶段模糊收益的投资组合优化问题。考虑交易成本、借贷约束、阈值约束和基数约束等现实约束,提出了一种新的多阶段均值-半方差可信性投资组合模型。在该模型中,本文分别运用可信性期望值和半方差来度量投资组合收益和风险。基于可信性理论,将该模型转化为一个动态优化问题。由于存在交易成本和基数约束,该模型是具有路径依赖性的混合整数动态优化问题。本文提出了一种新的离散近似迭代方法进行求解,并证明其线性收敛性。最后,文章运用了具体的算例以验证算法和模型的有效性。Asset preservation and appreciation are crucial for investors.The mean-variance model proposed by Markowitz in 1952 settled the foundation of modern portfolio theory.In the mean-variance model,the returns on risky assets are assumed stochastic variables.Investors try to find an optimal portfolio by trading off maximum return and minimum risk in a static environment.This model provides guidance for investors to make scientific investment decisions,however,the financial market is complex,and many constraints need to be considered when investing in financial assets.Based on this,many scholars improved the mean-variance model from different dimensions.Firstly,variance is used to measure the volatility of asset returns,which treats upward deviation and downward deviation from the mean of return as equally risky.For investors,only the downward deviation from the mean of returns is the risk,so using variance tends to overestimate the risk of a portfolio.Therefore,some scholars use downward deviation to measure portfolio risk,such as semi-variance,semi-absolute deviation,and so on.Secondly,the financial market is as uncertain as ever.The return of the asset is affected by the economic and social environment,and other factors,which are not rational to be described by using stochastic variables.Especially for sub-new stock,which lacks efficient history data,the mathematic expectation of estimated return is not an unbiased measure of returns.And people always evaluate it according to expert opinions.Therefore,some scholars have extended portfolio optimal to the fuzzy environment and used fuzzy variables to describe the assets’return,such as possibilistic variables,credibilistic variables,and uncertainty variables.Thirdly,in real investment transactions,investment is a continuous process.In different periods,asset returns,and investors’risk preferences are constantly changing,and long-term investors will adjust their investment portfolio positions in a timely manner as the environment changes.Therefore,portfolio problems

关 键 词：多阶段投资组合 可信性测度 均值-半方差 基数约束 离散近似迭代法 

分 类 号：F272[经济管理—企业管理]