Fuzzy portfolio optimization problem under uncertainty conditions with application of computational intelligence methods

Abstract

The problem of constructing an optimal securities portfolio under uncertainty is considered along with the direct and dual problems of fuzzy portfolio optimization. The modified fuzzy portfolio optimization problem is also suggested under a constraint on portfolio volatility. In the dual problem, the portfolio structure is determined, which provides the minimum risk level at the specified profitability level. The use of forecasting share prices for the portfolio model was suggested to support the validity of decisions on the portfolio structure and to reduce the risks. The share price data for the portfolio optimization system are forecasted using Fuzzy Group Method of Data Handling (FGMDH). The experimental studies of the suggested fuzzy models were carried out, and a comparison with the Markowitz model was performed on a stock market. As the result of this work, the foundations of the theory of fuzzy portfolio optimization are built on the basis of the theory of fuzzy sets and an effective forecasting method.

Keywords

• fuzzy portfolio
• modified fuzzy portfolio optimization model
• forecasting
• share prices
• fuzzy GMDH