Robustness in Mean-Variance Portfolio Optimization

In this paper, we discuss some of the concepts of robustness for uncertain multi-objective optimization problems. An important factor involved with multi objective optimization problems is uncertainty. The uncertainty may arise fromthe estimation of parameters in the model, error of computation, the structure of a problem, and so on. Indeed, some parameters are often unknown at the beginning of solving a multi-objective optimization problem. One of the mostimportant and popular approaches for dealing with uncertainty is robust optimization. Markowitz’s portfolio optimization problem is strongly sensitive to the perturbations of input parameters. We consider Markowitz’s portfolio optimization problem with ellipsoid uncertainty set and apply set-based minmax and lower robust efficiency to this problem. The concepts of robust efficiency are used in the real stock market and compared to each other. Finally, the increase and decrease effects of uncertainty set parameters on these robust efficient solutions are verified.