Processing Second-Order Stochastic Dominance Models using Cutting Plane Representations

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 Ruszczy4nski (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 K|nzi-Bay and Mayer (Comput Manage Sci 3:3-27, 2006) for CVaRminimization. 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).