Certainty equivalent measures of risk

Alexander Vinel, Pavlo A. Krokhmal

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We study a framework for constructing coherent and convex measures of risk that is inspired by infimal convolution operator, and which is shown to constitute a new general representation of these classes of risk functions. We then discuss how this scheme may be effectively applied to obtain a class of certainty equivalent measures of risk that can directly incorporate preferences of a rational decision maker as expressed by a utility function. This approach is consequently employed to introduce a new family of measures, the log-exponential convex measures of risk. Conducted numerical experiments show that this family can be a useful tool for modeling of risk-averse preferences in decision making problems with heavy-tailed distributions of uncertain parameters.

Original languageEnglish (US)
Pages (from-to)75-95
Number of pages21
JournalAnnals of Operations Research
Issue number1-2
StatePublished - Feb 1 2017


  • Coherent measures of risk
  • Convex measures of risk
  • Log-exponential convex measures of risk
  • Risk-averse preferences
  • Stochastic optimization
  • Utility theory

ASJC Scopus subject areas

  • General Decision Sciences
  • Management Science and Operations Research


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