A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets

Abstract

Since security return cannot be accurately estimated using past data, in this paper it is assumed to take values in a given ellipsoidal uncertainty set. This paper aims to discuss a robust multi-objective portfolio selection problem based on the minimax regret criterion under an ellipsoidal uncertainty sets, in which the two objective functions are the portfolio return to be maximized and the mean absolute deviation as a risk measure to be minimized. The robust counterpart formulation for the proposed model is firstly presented, then an algorithm based on the relaxation procedure is designed to solve the robust counterpart formulation with second-order cone constraints and infinite constraints. Finally, a practical example based on real market data is presented to illustrate the effectiveness of the proposed model and the algorithm. Compared with the traditional robust portfolio model based on minimax robustness, the robust minimax regret optimal solutions proposed in this paper have better performance on several evaluation criteria.