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Journal of Applied Mathematics
Volume 2012, Article ID 105616, 25 pages
Research Article

On the Computation of the Efficient Frontier of the Portfolio Selection Problem

Departamento de Matemáticas para la Economía y la Empresa, Universidad de Valencia, P.O. Box 46022, Valencia, Spain

Received 22 December 2011; Revised 17 May 2012; Accepted 18 May 2012

Academic Editor: Yuri Sotskov

Copyright © 2012 Clara Calvo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An easy-to-use procedure is presented for improving the -constraint method for computing the efficient frontier of the portfolio selection problem endowed with additional cardinality and semicontinuous variable constraints. The proposed method provides not only a numerical plotting of the frontier but also an analytical description of it, including the explicit equations of the arcs of parabola it comprises and the change points between them. This information is useful for performing a sensitivity analysis as well as for providing additional criteria to the investor in order to select an efficient portfolio. Computational results are provided to test the efficiency of the algorithm and to illustrate its applications. The procedure has been implemented in Mathematica.