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Title: Processing second-order stochastic dominance models using cutting-plane representations
Authors: Fabian, CI
Mitra, G
Roman, D
Keywords: Stochastic programming;Convex programming;Portfolio theory;Numerical methods;Statistical methods
Issue Date: 2011
Publisher: Springer-Verlag
Citation: Mathematical Programming, 130(1): 33 - 57, Nov 2011
Abstract: Second-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).
Description: This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-Verlag
ISSN: 0025-5610
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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