加权极大-极小随机模糊投资组合模型及实证研究

A Portfolio Selection Model with Random Fuzzy Returns and Weighted Max-Min Operator and its Empirical Study

考虑投资者面临证券市场随机和模糊的双重不确定性,将证券收益率视为随机模糊变量,根据前景理论建立符合投资者心理特征的期望收益和目标概率隶属度函数。利用加权极大-极小算子考虑投资者对期望收益和目标概率的差异要求,构建目标权重不等的加权极大-极小随机模糊投资组合模型,进一步推导模型的最优解。采用实证的方法,研究模型的表型。结果表明:加权极大-极小随机模糊投资组合模型有效边界与均值-方差投资组合模型不一致;加权极大-极小随机模糊投资组合模型可以根据期望收益和目标概率的权重变化,构建符合不同投资者心理需求的投资组合;加权极大-极小随机模糊投资组合模型的投资收益优于均值-方差投资组合模型。

For the uncertainty in the stock market, we model the security returns as random fuzzy variables, and built the expected return and target probability membership functions according to investors＇ psychological trait and based on the prospect theory. Considering investors＇ diversified requirements of expected return and target probability, we construct a weighted max-min random fuzzy portfolio model by using weighted max-rain operator and obtain the optimal solution. We also empirically study the performance of the proposed model. The result shows that： the efficient frontier of the model is inconsistent with mean-variance model by changing the target weights of expected return and target probability, the model can be used to construct portfolios to meet different investors＇ psychological requirement the investment return of the model outperforms mean-variance model.