نمونه کارها با اهداف بلند مدت

Markowitz portfolio optimization problem is heavily dependent on the input parameters. To this end, the uncertainties are considered in the portfolio problem. Furthermore, in order to relax the normality assumption of Markowitz portfolio problem, higher moments (skewness and kurtosis) are also incorporated. Introducing the concepts of set ordered relations and the idea of robust counterpart from Ben-Tal and Nemirovski (1998, 1999), robust multiobjective portfolio models with higher moments are analytically built. Meanwhile, multiobjective particle swarm optimization is employed to obtain various (robustly) efficient solutions. Finally, using the data from the real stock market, various robustly efficient frontiers are characterized as well as the portfolio performances compared. The empirical results indicate that the robustly efficient solutions obtained by the combination of uncertainties and higher moments in the portfolio problem would be immensely helpful for investors and portfolio managers.