Fuzzy Mean-Variance Portfolio Selection Based on Machine Learning

In this paper, the Machine Learning methods are applied to the fuzzy portfolio optimization research to deal with the uncertainties in financial markets. First, the trapezoidal fuzzy numbers are employed to model the prices of risky assets. The attribute parameters of these fuzzy numbers are estimated by predicting the stock’s opening, closing, highest, and lowest prices using Machine Learning methods, including eXtreme Gradient Boosting, Elastic Net, and Random Forest. Second, based on the mathematical properties of possibility measures, the possibilistic mean and variance of the portfolio are calculated to assess return and risk. Third, considering the transaction costs, threshold constraints, and borrowing constraints, a new fuzzy mean-variance portfolio selection based on Machine Learning is proposed. Utilizing the measures of possibility, this model can be transformed into a quadratic programming problem. A pivoting algorithm can be employed to solve it. Finally, both in-sample and out-of-sample analyses are performed to assess model performance. The in-sample analysis examines how different constraints affect the efficient frontier. The out-of-sample analysis compares the performance of the predictive fuzzy mean-variance model with the predictive fuzzy equal-weight model, while also evaluating how variations in constraints influence the proposed model’s effectiveness.