Coherent Approaches to Risk in Optimization Under Uncertainty

Free AccessAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to SectionFree Access HomeINFORMS TutORials in Operations ResearchOR Tools and Applications: Glimpses of Future Technologies Coherent Approaches to Risk in Optimization Under UncertaintyR. Tyrrell RockafellarR. Tyrrell RockafellarPublished Online:14 Oct 2014https://doi.org/10.1287/educ.1073.0032Abstract Decisions often need to be made before all the facts are in. A facility must be built to withstand storms, floods, or earthquakes of magnitudes that can only be guessed from historical records. A portfolio must be purchased in the face of only statistical knowledge, at best, about how markets will perform. In optimization, this implies that constraints may need to be envisioned in terms of safety margins instead of exact requirements. But what does that really mean in model formulation? What guidelines make sense, and what are the consequences for optimization structure and computation? The idea of a coherent measure of risk in terms of surrogates for potential loss, which has been developed in recent years for applications in financial engineering, holds promise for a far wider range of applications in which the traditional approaches to uncertainty have been subject to criticism. The general ideas and main facts are presented here with the goal of facilitating their transfer to practical work in those areas. This publication has no references to display. Previous Back to Top Next FiguresReferencesRelatedInformationCited ByRisk-Averse Selfish RoutingThanasis Lianeas, Evdokia Nikolova, Nicolas E. Stier-Moses6 September 2018 | Mathematics of Operations Research, Vol. 44, No. 1Risk-Averse Stochastic Modeling and OptimizationNilay Noyan19 October 2018Mitigating Delays and Unfairness in Appointment SystemsJin Qi30 June 2016 | Management Science, Vol. 63, No. 2Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under UncertaintyWeini Zhang, Hamed Rahimian, Güzin Bayraksan10 May 2016 | INFORMS Journal on Computing, Vol. 28, No. 3Data-Driven Stochastic Programming Using Phi-DivergencesGüzin BayraksanDavid K. Love26 October 2015A Mean-Risk Model for the Traffic Assignment Problem with Stochastic Travel TimesE. Nikolova, N. E. Stier-Moses25 April 2014 | Operations Research, Vol. 62, No. 2A Survey of Linear and Mixed-Integer Optimization TutorialsAlexandra M. Newman, Martin Weiss9 October 2013 | INFORMS Transactions on Education, Vol. 14, No. 1Optimization with Multivariate Conditional Value-at-Risk ConstraintsNilay Noyan, Gábor Rudolf22 August 2013 | Operations Research, Vol. 61, No. 4 OR Tools and Applications: Glimpses of Future TechnologiesSeptember 2007 Article Information Metrics Downloaded 891 times in the past 12 months Information Published Online:October 14, 2014 Copyright © 2007, INFORMSCite asR. Tyrrell Rockafellar (2014) Coherent Approaches to Risk in Optimization Under Uncertainty. INFORMS TutORials in Operations Research null(null):38-61. https://doi.org/10.1287/educ.1073.0032Keywordsoptimization under uncertaintysafeguarding against risksafety marginsmeasures of riskmeasures of potential lossmeasures of deviationcoherencyvalue-at-riskconditional value-at-riskprobabilistic constraintsquantilesrisk envelopesdual representationsstochastic programming