Entropy Coherent and Entropy Convex Measures of Risk

R.J.A. Laeven, M.A. Stadje

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Abstract

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. We prove that convex, entropy convex and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic and multiple priors preferences, respectively, upon requiring the certainty equivalents to be translation invariant. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and prove their distribution invariant representation. Some financial applications and examples of entropy coherent and entropy convex measures of risk are also investigated.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Volume2011-031
Publication statusPublished - 2011

Publication series

NameCentER Discussion Paper
Volume2011-031

Keywords

  • Multiple priors
  • Variational and homothetic preferences
  • Robustness
  • Convex risk measures
  • Exponential utility
  • Relative entropy
  • Translation invariance
  • Convexity
  • Indifference valuation

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  • Cite this

    Laeven, R. J. A., & Stadje, M. A. (2011). Entropy Coherent and Entropy Convex Measures of Risk. (CentER Discussion Paper; Vol. 2011-031). Econometrics.