Development Of Robust Random Variable For Portfolio Selection Problem

In this paper, mathematical modeling is developed for portfolio selection problem under uncertainty circumstances with regard to a robust stochastic variable. Two popular and common approaches in the area of modeling uncertainty are robust optimization and stochastic programming These two methods are used with different considerations in mathematical modeling, but each one has a limitation Stochastic programming assumes a static distribution function with static parameters over time for non-deterministic data, and robust optimization considers an indeterminate parameter in a uniform interval around nominal values. Using combination of these two methods can help us to eliminate their drawbacks. For this purpose, the concept of a robust stochastic variable has been developed in this research. This variable enables distribution of the uncertainty parameter to vary over time, and its mean, varies from one period to another; in fact, the parameter of the mean of uncertain probable distribution. The risk measure of CVaR, which allows changes in mean of uncertainty from time to time, is used to implement the proposed approach. As a numerical example, the actual data of Tehran Stock Exchange is used for a year as one-month periods. The practical results of this research show that the developed method can properly overcome the shortcomings of the previous methods.