Annals of Operations Research

, Volume 249, Issue 1–2, pp 75–95 | Cite as

Certainty equivalent measures of risk



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.


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


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.3131 Seamans Center for the Engineering Arts and SciencesIowa CityUSA

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