基于模糊概率的行为投资组合优化模型

Optimization Model of Behavioral Portfolio Based on Fuzzy Probability

在Shefrin和Statman创立的行为投资组合优化模型中,投资者对于各种自然状态的主观认知概率是由Lopes的理论确定的,然而Lopes所给出的公式只是提供了一个理论分析的框架,实际操作起来极为困难。由于人们的认知具有模糊性,所以模糊集理论已成为认知研究领域的一个有力工具。本文用模糊数来刻画投资者对于各种自然状态的主观认知概率,并在模糊概率的基础上构建了行为投资组合优化模型。具体的数值算例表明,本文所提出的模型能够充分反映投资者的认知形态,具有很强的操作性和实用性。

In the optimization model of behavioral portfolio developed by Shefrin and Statman, investors＇ subjective probabilities of various natural states are determined according to SP/A theory developed by Lopes. But the formula presented by Lopes only offers a framework for theoretical analysis and it＇s very difficult to put it into practice. The cognition of people appears fuzzy, so fuzzy sets theory has become a powerful tool in cognition research field. In this paper, investors＇ subjective probabilities of various natural states are expressed by fuzzy numbers and the optimization model of behavioral portfolio is established on the basis of fuzzy probabilities. The concrete numerical example indicates that the model presented in this paper can sufficiently reflect the cognitive states of investors and is very practicable.