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Dual characterization of properties of risk measures on Orlicz hearts

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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.

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Authors and Affiliations

  1. Princeton University, Princeton, NJ, 08544, USA

    Patrick Cheridito

  2. Cambridge University, Cambridge, CB3 0DS, UK

    Tianhui Li

Authors
  1. Patrick Cheridito
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  2. Tianhui Li
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Corresponding author

Correspondence to Patrick Cheridito.

Additional information

We thank Andreas Hamel and Michael Kupper for fruitful discussions and helpful comments. P. Cheridito has been supported by NSF Grant DMS-0642361, a Rheinstein Award and a Peek Fellowship. T. Li has been supported by a Marshall Scholarship and a Merage Fellowship.

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Cheridito, P., Li, T. Dual characterization of properties of risk measures on Orlicz hearts. Math Finan Econ 2, 29–55 (2008). https://doi.org/10.1007/s11579-008-0013-7

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  • DOI: https://doi.org/10.1007/s11579-008-0013-7

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