2008-07-02Buch DOI: 10.18452/3019
Processing Second-Order Stochastic Dominance models using cutting-plane representations
Fabian, Csaba I.
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
Second-order stochastic dominance (SSD) is widely recognised as an important decision criteria in portfolio selection. Unfortunately, stochastic dominance models can be very demanding from a computational point of view. In this paper we consider two types of models which use SSD as a choice criterion. The ﬁrst, proposed by Dentcheva and Ruszczyski (2006), uses a SSD constraint, which can be written as a set of integrated chance constraints (ICCs). The second, proposed by Roman, Darby-Dowman, and Mitra (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 (2006) for ICCs, and by Künzi-Bay and Mayer (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 give 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, Darby-Dowman, and Mitra (2006).
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