Fuzzy Portfolio Optimization with Application of Forecasting Methods

The problem of constructing an optimal portfolio of securities under uncertainty is considered. The main objective of portfolio investment is to improve the investment environment, giving securities such investment characteristics that are only possible in their combination. The global market crisis of recent years has shown that the existing theory of investment portfolios optimization exhausted and revision of the basic theory of portfolio management is needed. Therefore in this work the novel theory of investment portfolio optimization under uncertainty is presented based on fuzzy set theory and efficient forecasting methods. The direct and dual problem of fuzzy portfolio optimization are considered. In the direct problem we determine structure of a portfolio which will provide the maximum profitableness at the given risk level. In dual problem we define structure of a portfolio which provides the minimum risk level at the set level of profitableness. The input data for the portfolio optimization are predicted by the Fuzzy Group Method of Data Handling (FGMDH).The experimental investigations of the suggested theory and comparison with classical methods are performed.