考虑决策者心理行为的证券投资组合决策方法研究

Method for Portfolio Decision-Making Considering the Decision-Makers' Psychological Behaviors

在现实的证券投资组合决策中,决策者的心理行为是不可忽视的重要因素。本文针对考虑决策者心理行为的证券投资组合问题,给出了一种基于累积前景理论和心理账户的决策分析方法。首先,依据累积前景理论,将决策者对不同市场状态下的预期收益率作为参考点,计算各备选证券收益率相对于参照点的收益和损失,并计算不同市场状态下针对所有备选证券的综合前景价值;然后,依据决策者的心理账户,即以证券投资组合的收益总体综合前景价值最大为目标、以投资期末总财富阈值以及满足财富约束的概率不小于决策者设定的概率阈值为约束,构建了具有概率约束条件的证券投资组合优化模型,通过将概率约束转化为线性约束并求解优化模型,可得到最优的证券投资组合方案。最后,通过一个算例对本文提出方法的可行性和有效性进行了验证。研究结果表明,本文提出的方法能够较好地解决考虑决策者心理行为的证券投资组合问题。

Decision makers’ psychological behaviors cannot be ignored in the real portfolio decision-making. In this paper,a decision analysis method based on cumulative prospect theory and mental account is proposed to solve the portfolio decision-making problem considering the decision-makers’ psychological behaviors. First,decision makers’ expected returns are regarded as the reference points,according to cumulative prospect theory,the gain and loss of each security’s return with respect to reference points are calculated and comprehensive prospect values of all candidate securities in different market states are calculated. Then,according to the decision-makers’ mental account,an optimization model for portfolio decision-making with probability constraint is constructed,whose objective is to maximize decision-makers’ overall comprehensive prospect value,and whose constraints contain wealth threshold constraint and the probability constraint. After translating the probability constraint into linear constraints,portfolio alternative is obtained by solving the linear optimization model. Finally,a numerical example is used to verify the feasibility and validity of the method proposed in this paper. The results show that the method proposed in this paper can solve the securities portfolio problem considering decisionmakers’ psychological behaviors.