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 cho...

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Bibliographic Details
Published in:Mathematical programming 2011-11, Vol.130 (1), p.33-57
Main Authors: Fábián, Csaba I., Mitra, Gautam, Roman, Diana
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Calculus of Variations and Optimal Control
Optimization
Combinatorics
Criteria
Cutting
Decision theory. Utility theory
Dominance
Exact sciences and technology
Expected utility
Full Length Paper
Linear programming
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Operational research and scientific management
Operational research. Management science
Optimization
Portfolio theory
Preferences
Probability and statistics
Random variables
Representations
Roman
Sciences and techniques of general use
Statistics
Stochastic models
Stochasticity
Studies
Theoretical
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Summary: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).
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-009-0326-1