Optimization with Multivariate Conditional Value-at-Risk Constraints

Nilay Noyan () and Gábor Rudolf ()
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Nilay Noyan: Manufacturing Systems and Industrial Engineering Program, Sabancı University, Istanbul 34956, Turkey
Gábor Rudolf: Manufacturing Systems and Industrial Engineering Program, Sabancı University, Istanbul 34956, Turkey

Operations Research, 2013, vol. 61, issue 4, 990-1013

Abstract: For many decision-making problems under uncertainty, it is crucial to develop risk-averse models and specify the decision makers' risk preferences based on multiple stochastic performance measures (or criteria). Incorporating such multivariate preference rules into optimization models is a fairly recent research area. Existing studies focus on extending univariate stochastic dominance rules to the multivariate case. However, enforcing multivariate stochastic dominance constraints can often be overly conservative in practice. As an alternative, we focus on the widely applied risk measure conditional value-at-risk (CVaR), introduce a multivariate CVaR relation, and develop a novel optimization model with multivariate CVaR constraints based on polyhedral scalarization. To solve such problems for finite probability spaces, we develop a cut generation algorithm, where each cut is obtained by solving a mixed-integer problem. We show that a multivariate CVaR constraint reduces to finitely many univariate CVaR constraints, which proves the finite convergence of our algorithm. We also show that our results can be naturally extended to a wider class of coherent risk measures. The proposed approach provides a flexible and computationally tractable way of modeling preferences in stochastic multicriteria decision making. We conduct a computational study for a budget allocation problem to illustrate the effect of enforcing multivariate CVaR constraints and demonstrate the computational performance of the proposed solution methods.

Keywords: multivariate risk aversion; conditional value-at-risk; multiple criteria; cut generation; coherent risk measures; stochastic dominance; Kusuoka representation (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (21)

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