Optimal portfolio selection under minimax criterion with short-selling

The paper mainly considers an extend version of Mean-Maximum Absolute Deviation model, which adds the transaction cost and the limitation of the amount of capital invested (sold short from) in each security when short-selling is permitted in security market. It was proposed that a minimax portfolio selection model using absolute deviation function l (infinity) as the risk measure. The model is bi-objective nonlinear programming problem. Then it was reformulated into a single-objective non-convex programming problem by introduction a risk tolerance factor. Furthermore, attempting to solve the problem by using Difference of Convex function (DC) programming and DC algorithms. Here, a numerical example was given to show the validity of the method.