Fuzzy portfolio optimization model with estimation of results

Journal of Internet Banking and Commerce. 2016. Vol. 21. No. S6: Special Issue: Territory and Industry: The Search for Innovative Ways of Developing.

Nikulin E. E., Perepelitsa D. G., Zhdanova O. A., Smetanin S., Nazarova E. V.

 

​In this paper, we propose two fuzzy portfolio optimization models based on the Markowitz mean-variance approach. Uncertainty is an inherent property of the securities market, there turns of different types of securities can rarely be described statistically. Dealing with uncertainty, portfolio optimization theory began to move toward application of fuzzy mathematic. Besides presenting fuzzy models, this paper reveals the problem of reliability of the fuzzy model results. Solving this problem depends on the investor’s attitude to the model results. The first model involves fuzzy numbers to extend statistical data, the model returns the portfolio expected return and variance as fuzzy numbers. In addition to the problem formulated in the first model, the second model works on improvement of the indicators reliability. Finally, we provide a numerical example to illustrate the work of the proposed methods, as well as to compare the methods with each other and with the classical mean-variance method.​

​In this paper, we propose two fuzzy portfolio optimization models based on the Markowitz mean-variance approach. Uncertainty is an inherent property of the securities market, there turns of different types of securities can rarely be described statistically. Dealing with uncertainty, portfolio optimization theory began to move toward application of fuzzy mathematic. Besides presenting fuzzy models, this paper reveals the problem of reliability of the fuzzy model results. Solving this problem depends on the investor’s attitude to the model results. The first model involves fuzzy numbers to extend statistical data, the model returns the portfolio expected return and variance as fuzzy numbers. In addition to the problem formulated in the first model, the second model works on improvement of the indicators reliability. Finally, we provide a numerical example to illustrate the work of the proposed methods, as well as to compare the methods with each other and with the classical mean-variance method.​

Keywords: Estimation of results, Fuzzy optimization, Markowitz model, Mean-variance model, Portfolio optimization