Robustness in Mean-Variance Portfolio Optimization

In this paper, we discuss some of the concepts of robustness for uncertain multi-objective optimization problem. An important factor involved with multi-objective optimization problems is uncertainty. The uncertainty may arise from estimation of parameters in the model, error of computation, structure of problem and so on. Indeed, some parameters are often unknown at the beginning of solving a multi-objective optimization problem. One of the most important 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.‎‏