Abstract: The problem of constructing an optimal portfolio of securities under uncertainty was considered. The global market crisis of recent years has shown that the existing theory of optimization of investment portfolios and forecasting stock indices exhausted and the revision of the basic theory of portfolio management is strongly needed. Therefore the fuzzy sets theory was used for getting an optimal portfolio. In this paper direct, dual and multicriteria problems with the use of triangular membership functions work were considered. The problem of portfolio optimization during the time period also was described in this article. In direct task we define structure of a portfolio, which will provide the maximum profitableness at the set risk level. In dual task we define structure of a portfolio, which will provide the minimum risk level at the set level of critical profitableness. In multicriteria problem we simultaneously maximize profitability and minimize risk level. The input data for the optimization system were predicted by using the Fuzzy Group Method of Data Handling (FGMDH). The optimal portfolios for assets were determined. The comparative analysis of optimal portfolios obtained by different methods and approaches was fulfilled.

Keywords: membership function, fuzzy sets theory, optimal portfolio, investments, stock securities, fuzzy number, FGMDH

ACM Classification Keywords: G.1.0 Mathematics of Computing– General – Error analysis; G.1.6 Mathematics of Computing – Numerical Analysis – Optimization - Gradient methods, Least squares methods; I.2.3 Computing Methodologies - Artificial Intelligence - Uncertainty, “fuzzy”, and probabilistic reasoning.

Link:

CONSTRUCTING AN OPTIMAL INVESTMENT PORTFOLIO BY USING FUZZY SETS THEORY

Yuri Zaychenko, Inna Sydoruk

http://www.foibg.com/ijima/vol04/ijima04-02-p05.pdf