Computing the Nondominated Surface in Tri-Criterion Portfolio Selection

Authors:
Markus Hirschberger;Ralph E. Steuer;Sebastian Utz;Maximilian Wimmer;Yue Qi
Affiliations:
Department of Mathematics, University of Eichstätt-Ingolstadt, 85072 Eichstätt, Germany;Department of Finance, University of Georgia, Athens, Georgia 30602;Department of Finance, University of Regensburg, 93040 Regensburg, Germany;Department of Finance, University of Regensburg, 93040 Regensburg, Germany;Department of Financial Management, Nankai University, Tianjin, China
Venue:
Operations Research
Year:
2013

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Abstract

Computing the nondominated set of a multiple objective mathematical program has long been a topic in multiple criteria decision making. In this paper, motivated by the desire to extend Markowitz portfolio selection to an additional linear criterion dividends, liquidity, sustainability, etc., we demonstrate an exact method for computing the nondominated set of a tri-criterion program that is all linear except for the fact that one of its objectives is to minimize a convex quadratic function. With the nondominated set of the resulting quad-lin-lin program being a surface composed of curved platelets, a multiparametric algorithm is devised for computing the platelets so that they can be graphed precisely. In this way, graphs of the tri-criterion nondominated surface can be displayed so that, as in traditional portfolio selection, a most preferred portfolio can be selected while in full view of all other contenders for optimality. Finally, by giving an example for socially responsible investors, we demonstrate that our algorithm can outperform standard portfolio strategies for multicriterial decision makers.