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Processing second-order stochastic dominance models using cutting-plane representations

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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).

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Authors and Affiliations

  1. Institute of Informatics, Kecskemét College, 10 Izsáki út, 6000, Kecskemét, Hungary

    Csaba I. Fábián

  2. Department of OR, Loránd Eötvös University, Budapest, Hungary

    Csaba I. Fábián

  3. CARISMA: The Centre for the Analysis of Risk and Optimisation Modelling Applications, School of Information Systems, Computing and Mathematics, Brunel University, Uxbridge (Middlesex), UB8 3PH, UK

    Gautam Mitra & Diana Roman

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  1. Csaba I. Fábián
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  2. Gautam Mitra
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  3. Diana Roman
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Correspondence to Gautam Mitra.

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Fábián, C.I., Mitra, G. & Roman, D. Processing second-order stochastic dominance models using cutting-plane representations. Math. Program. 130, 33–57 (2011). https://doi.org/10.1007/s10107-009-0326-1

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