We propose a new approach to solve the multi-objective portfolio selection problem in the presence of skewness. The selection of efficient portfolios requires the optimization of different and conflicting criteria: maximizing expected return and skewness and minimizing risk. Hence, the portfolio selection can be formulated as a tri-objective programming problem to solve the mean-variance-skewness efficient set. Rescaling on the unit variance space leads to a biobjective problem, but adds a nonlinear equality constraint to the model. Through a change in variables, we reformulate it as a lower dimensional bound constrained biobjective problem. The recent algorithm BiMads for biobjective optimization is applied to generate an efficient set of portfolios on a test problem from the literature.
Published November 2007 , 20 pages