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

• 成果类型: Article
• 署名作者: Fabian, Csaba I.; Mitra, Gautam; Roman, Diana
• 署名单位: Brunel University; Eotvos Lorand University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0326-1
• 发表日期: 2011
• 页码: 33-57
• 关键词: MEAN-RISK MODELS; programming-models; conditional value; constraints; optimization; utility

摘要

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 RuszczyAski (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 Kunzi-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).