Encyclopedia of Operations Research and Management Science

2013 Edition
| Editors: Saul I. Gass, Michael C. Fu

Conditional Value-at-Risk (CVaR)

  • Gaia Serraino
  • Stanislav UryasevEmail author
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-1153-7_1232


Conditional Value-at-Risk (CVaR), introduced by Rockafellar and Uryasev (2000), is a popular tool for managing risk. CVaR approximately (or exactly, under certain conditions) equals the average of some percentage of the worst case loss scenarios. CVaR risk measure is similar to the Value-at-Risk (VaR) risk measure which is a percentile of a loss distribution. VaR is heavily used in various engineering applications, including financial ones. VaR risk constraints are equivalent to the so called chance constraints on probabilities of losses. Some risk communities prefer VaR, others prefer chance (or probabilistic) functions. There is a close correspondence between CVaR and VaR: with the same confidence level, VaR is a lower bound for CVaR. Rockafellar and Uryasev (2000, 2002) showed that CVaR is superior to VaR in optimization applications. The problem of choice between VaR and CVaR, especially in financial risk management, has been quite popular in academic literature....

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.American Optimal DecisionsGainesvilleUSA
  2. 2.Risk Management and Financial Engineering Lab, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA