考虑交易费用的均值-VaR多阶段投资组合优化模型  

Multi-stage Mean-VaR Portfolio Selection Model with Transaction Costs

作　　者：王晓琴 高岳林 WANG Xiao-qin;GAO Yue-lin(School of Science and Chemical Engineering,Ningxia Institute of Science and Technology,Shizuishan 753000;School of Mathematics and Information Science,North Minzu University,Yinchuan 750021;The Key Laboratory of Intelligent Information and Big Data Processing of Ningxia Province,Yinchuan 750021)

机构地区：[1]宁夏理工学院理学与化学工程学院,石嘴山753000 [2]北方民族大学数学与信息科学学院,银川750021 [3]宁夏智能信息与大数据处理重点实验室,银川750021

出　　处：《工程数学学报》2020年第6期673-684,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(61561001);宁夏高等教育一流学科建设基金(NXYLXK2017B09);北方民族大学重大专项资助(ZDZX201901).

摘　　要：考虑到方差、下半方差和绝对偏差等度量投资组合风险的局限性以及单阶段投资决策不符合投资者的实际投资行为等因素,本文将风险价值(Value-at-Risk,简称VaR)作为风险度量标准应用到多阶段投资组合优化中.由于中国股票市场不允许卖空,因此本文在不允许卖空的情况下,在约束条件中同时考虑了交易费用和投资比例,建立了一个均值–VaR多阶段投资组合优化模型.考虑到粒子群算法具有收敛速度快,结构简单以及需要调控的参数比较少等优点,运用带有罚函数处理机制的粒子群算法对新建立的多阶段投资组合优化模型进行求解.求解得到了不同路径下各阶段资产的最优投资策略,从运算结果可以看出,在不同的投资路径下投资者的投资行为基本一致,在第一阶段对自己看好的股票买入,经过第一阶段股市的波动,在第二阶段对自己看好的股票继续买入,对不看好的股票不买入或者直接卖出,这种投资行为符合投资者的实际投资行为,说明本文所提出的模型具有合理性.Taking into account the limitations of risk measures such as variance,lower semivariance and absolute deviation,and the fact that single-stage investment decision does not accord with investors’actual investment behavior,Value-at-Risk(VaR)is applied in this paper as a measure of risk for multi-stage portfolio optimization.Because short selling is not allowed in Chinese stock market,we consider both transaction costs and investment proportions in constraints and establish a multi-stage mean-VaR portfolio optimization model.Considering that PSO has the advantages of fast convergence,simple structure and less parameters to be regulated,the proposed multi-stage portfolio optimization model is solved by using PSO with penalty function processing mechanism.The optimal investment strategy at each stage under different paths is obtained.It can be seen from the results that the investor’s investment behavior is consistent under different investment paths,buying the stocks they are optimistic about in the first stage.After the fluctuation of the stock market in the first stage,the investor continues to buy the stocks which are optimistic in the second stage.Meanwhile,the investor does not buy or sell stocks that are not good.This kind of investment behavior accords with the actual investment behavior of investors.Thus the proposed model is reasonable.

关 键 词：多阶段投资组合 粒子群算法 风险价值 交易费用 

分 类 号：F830[经济管理—金融学]