Uncertain minimax mean-variance and mean-semivariance models for portfolio selection

Traditionally, the return on investment has been described as either a random variable or a fuzzy variable, while this paper discusses the uncertain portfolio selection in which each security return is assumed to be an uncertain variable. To better optimize the return and risk of a portfolio, we propose two models: uncertain minimax mean-variance (UM-EV) model and uncertain minimax mean-semivariance (UM-SVE) model. The crisp equivalents of the UM-EV model that regard the security return as a normal and linear uncertain variable are derived, and the optimization problem is solved using linear programming. For the UM-SVE model, the crisp equivalent of a zigzag uncertain variable is introduced, and the optimization solution is calculated using hybrid intelligent algorithm. Finally, the effectiveness of the proposed models is illustrated using numerical examples.