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Development of Robust Random Variable for Portfolio Selection Problem
Alireza Ghahtarani,Majid Sheikhmohammady,Amir Abbas Najafi 대한산업공학회 2018 Industrial Engineeering & Management Systems Vol.17 No.4
In this paper, mathematical modeling is developed for portfolio selection problem under uncertainty circumstanceswith regard to a robust stochastic variable. Two popular and common approaches in the area of modeling uncertaintyare robust optimization and stochastic programming. These two methods are used with different considerations in mathematicalmodeling, but each one has a limitation. Stochastic programming assumes a static distribution functionwith static parameters over time for non-deterministic data, and robust optimization considers an indeterminate parameterin a uniform interval around nominal values. Using combination of these two methods can help us to eliminatetheir drawbacks. For this purpose, the concept of a robust stochastic variable has been developed in this research. Thisvariable enables distribution of the uncertainty parameter to vary over time, and its mean, varies from one period toanother; in fact, the parameter of the mean of uncertain probable distribution. The risk measure of CVaR, which allowschanges in mean of uncertainty from time to time, is used to implement the proposed approach. As a numericalexample, the actual data of Tehran Stock Exchange is used for a year as one-month periods. The practical results ofthis research show that the developed method can properly overcome the shortcomings of the previous methods.
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