Abstract: The problem of forming an optimal portfolio of securities under uncertainty was 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. Careful processing and accounting of investment risks have become an integral and important part of the success of each company. However, the global market crisis of recent years has shown that the existing theory of optimization of investment portfolios and forecasting stock indices themselves exhausted and needed overhaul of the basic theory of portfolio management. Therefore the fuzzy sets theory was used for getting an optimal portfolio. The direct problem with the use of triangular, bell-shaped and Gaussian membership functions and dual problem by using the fuzzy sets theory were considered in this work. 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. The input data for the optimization system were predicted by using the Fuzzy Group Method of Data Handling (FGMDH). The optimal portfolios for asset were determined. The comparative analysis of optimal portfolio obtained by using of different membership functions was fulfilled. Investment portfolio optimization system is an effective tool for the operational management of portfolio investments. This is an opportunity to carry out scientific and reasonable management of their investment portfolio with the ability to reject the planned loss of possession or overvalued risky assets, which increases business efficiency and maximize gain on the stock market.

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:

DIRECT AND DUAL PROBLEM OF INVESTMENT PORTFOLIO OPTIMIZATION UNDER UNCERTAINTY

Yuri Zaychenko, Inna Sydoruk

http://www.foibg.com/ijitk/ijitk-vol08/ijitk08-03-p03.pdf