A New Multi-objective Approach for the Portfolio Selection Problem with Skewness

The main purpose of this paper is to 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 such as maximizing expected return, 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.

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