Computing the Nondominated Surface in Tri-Criterion Portfolio Selection

Markus Hirschberger (), Ralph E. Steuer (), Sebastian Utz, Maximilian Wimmer () and Yue Qi ()
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Markus Hirschberger: Department of Mathematics, University of Eichstätt-Ingolstadt, 85072 Eichstätt, Germany
Ralph E. Steuer: Department of Finance, University of Georgia, Athens, Georgia 30602
Maximilian Wimmer: Department of Finance, University of Regensburg, 93040 Regensburg, Germany
Yue Qi: Department of Financial Management, Nankai University, Tianjin, China

Operations Research, 2013, vol. 61, issue 1, 169-183

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.

Keywords: multiple criteria decision making; multicriteria optimization; nondominated surfaces; portfolio selection; multiparametric quadratic programming (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (36)

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