Entropy coherent and entropy convex measures of risk

Roger Laeven, M.A. Stadje

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Abstract

We introduce entropy coherent and entropy convex measures of risk and prove a collection of axiomatic characterization and duality results. We show in particular that entropy coherent and entropy convex measures of risk emerge as negative certainty equivalents in (the regular and a generalized version, respectively, of) the popular maxmin expected utility theory of Gilboa and Schmeidler [12] whenever the negative certainty equivalents are translation invariant. In addition, we derive the dual conjugate function for entropy coherent and entropy convex measures of risk, and prove their distribution invariant representation. Keywords: Robust preferences; Convex risk measures; Exponential utility; Relative entropy; Translation invariance; Convexity.
Original languageEnglish
Place of PublicationEindhoven
PublisherEurandom
Number of pages34
Publication statusPublished - 2010

Publication series

NameReport Eurandom
Volume2010020
ISSN (Print)1389-2355

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    Laeven, R., & Stadje, M. A. (2010). Entropy coherent and entropy convex measures of risk. (Report Eurandom; Vol. 2010020). Eurandom.