Entropy Coherent and Entropy Convex Measures of Risk

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

Research output: Working paperDiscussion paperOther research output

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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

Fingerprint

Entropy
Conjugate functions
Invariant Distribution
Invariant

Keywords

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

Cite this

Laeven, R. J. A., & Stadje, M. A. (2011). Entropy Coherent and Entropy Convex Measures of Risk. (CentER Discussion Paper; Vol. 2011-031). Tilburg: Econometrics.
Laeven, R.J.A. ; Stadje, M.A. / Entropy Coherent and Entropy Convex Measures of Risk. Tilburg : Econometrics, 2011. (CentER Discussion Paper).
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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.",
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Laeven, RJA & Stadje, MA 2011 'Entropy Coherent and Entropy Convex Measures of Risk' CentER Discussion Paper, vol. 2011-031, Econometrics, Tilburg.

Entropy Coherent and Entropy Convex Measures of Risk. / Laeven, R.J.A.; Stadje, M.A.

Tilburg : Econometrics, 2011. (CentER Discussion Paper; Vol. 2011-031).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Entropy Coherent and Entropy Convex Measures of Risk

AU - Laeven, R.J.A.

AU - Stadje, M.A.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Multiple priors

KW - Variational and homothetic preferences

KW - Robustness

KW - Convex risk measures

KW - Exponential utility

KW - Relative entropy

KW - Translation invariance

KW - Convexity

KW - Indifference valuation

M3 - Discussion paper

VL - 2011-031

T3 - CentER Discussion Paper

BT - Entropy Coherent and Entropy Convex Measures of Risk

PB - Econometrics

CY - Tilburg

ER -

Laeven RJA, Stadje MA. Entropy Coherent and Entropy Convex Measures of Risk. Tilburg: Econometrics. 2011. (CentER Discussion Paper).