基于DEA博弈交叉效率和投资者心理的模糊投资组合研究

考虑到投资者并不是完全理性的,本文结合DEA博弈交叉效率方法研究了带有投资者心理因素的多目标模糊投资组合决策问题。首先,为了充分描绘投资者的心理因素和风险感知,本文基于可能性理论推导了带有风险态度的可能性均值和半绝对偏差。其次,将候选的风险资产视为互相竞争的博弈者,采用基于熵权法的DEA博弈交叉效率模型衡量它们的综合表现,从而得到每项资产的博弈交叉效率和奇异指数,并将其分别作为额外的收益和风险决策准则。基于此,提出了更加综合的可能性均值—半绝对偏差—博弈交叉效率—奇异指数模型。最后,通过一个应用实例验证了所提出的模型的合理性和有效性,从而为不同类型的投资者提供具有个性化的投资策略。

Research on Fuzzy Portfolios Based on DEA Game Cross-efficiency Method and Investor Psychology

Considering that investors are not completely rational, a multi-objective fuzzy portfolio selection problem with investor psychological factors is studied in this paper by combining with the DEA game cross-efficiency evaluation method. Firstly, to fully describe the psychology and risk perception of investors, the possibilistic mean and semi-absolute deviation with risk attitude are derived basedonthepossibility theory. Secondly, the candidate assets are regarded as competing players, and their comprehensive performance is measured by DEA game cross-efficiency model based on entropy weight method. In this way, the DEA game cross efficiency score and maverick index of each asset are obtained, which are used asadditional return and risk measures. Considering the four objectives of possibilistic mean, semi-absolute deviation, cross-efficiency score and the maverick index, a more comprehensive fuzzy portfolio optimization model is established. Finally, the rationality and effectiveness of the proposed model is illustrated by an application example, which can provide different investors with personalized investment strategies.