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Dual characterization of properties of risk measures on Orlicz hearts

  • Patrick Cheridito
  • Tianhui Li
Article

Abstract

We extend earlier representation results for monetary risk measures on Orlicz hearts. Then we give general conditions for such risk measures to be Gâteaux-differentiable, strictly monotone with respect to almost sure inequality, strictly convex modulo translation, strictly convex modulo comonotonicity, or monotone with respect to different stochastic orders. The theoretical results are used to analyze various specific examples of risk measures.

Keywords

Risk measures Gâteaux-differentiability Strict monotonicity Strict convexity Stochastic orders Orlicz hearts 

JEL Classification

D81 G32 

Mathematics Subject Classification (2000)

91B28 91B30 46B42 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Cambridge UniversityCambridgeUK

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