Esfandiaryfard M. Fuzzy Portfolio Optimization Under Uncertainty Using Forecasting

The dissertation is dedicated to the problems of portfolio optimization under uncertainty.In the dissertation new approach for the solution of the portfolio problem is suggested in which the stock prices are considered as fuzzy numbers given in some intervals. In this case the portfolio profitableness will be also a fuzzy number distributed in the corresponding interval and the risk is considered as possibility of events when real profitableness would be less than some criterion value. The corresponding model of fuzzy portfolio optimization problem was constructed and special algorithm of its solution suggested. This model was extended for different membership functions of portfolio profitableness, namely Gaussian and bell-wise form. The dependence "optimal profitableness- risk" for fuzzy portfolio was investigated and the sufficient conditions of its monotonous decreasing form were found. The experimental investigations of fuzzy portfolio problem at the Russian stock exchange were carried out.