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Robust representation of convex risk measures by probability measures

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  • Volker Krätschmer

Abstract

Artzner et al. [1] initiated a new direction to assess risks of financial positions by an axiomatic approach. It relies fundamentally on the concept of risk measures, which are functionals defined on sets of financial positions and satisfying some basic properties. The convex risk measures are exactly those which guarantee that diversification does not increase risk. From the standpoint of individual investors risk measures may be interpreted as loss functions expressing the preferences on the respective sets of financial positions. Starting from this point of view, Föllmer and Schied succeeded in finding a kind of robust Savage representation for convex risk measures by probability contents [3]. They also gave a sufficient condition to achieve a representation by probability measures. One aim of the paper is to show the reverse direction of their result. Another subject of the paper is to weaken the criterion within the setting when the sets of scenarios are endowed with a metrizable topology, restoring an earlier attempt by Föllmer and Schied. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Volker Krätschmer, 2005. "Robust representation of convex risk measures by probability measures," Finance and Stochastics, Springer, vol. 9(4), pages 597-608, October.
    • Handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:597-608
    DOI: 10.1007/s00780-005-0160-0
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    Citations

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    Cited by:

    1. Daniel Hern'andez-Hern'andez & Leonel P'erez-Hern'andez, 2012. "Robust utility maximization for L\'evy processes: Penalization and solvability," Papers 1206.0715, arXiv.org.
    2. Nicole EL KAROUI & Claudia RAVANELLI, 2008. "Cash Sub-additive Risk Measures and Interest Rate Ambiguity," Swiss Finance Institute Research Paper Series 08-09, Swiss Finance Institute.
    3. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    4. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    5. repec:dau:papers:123456789/342 is not listed on IDEAS
    6. Alexander Schied, 2007. "Optimal investments for risk- and ambiguity-averse preferences: a duality approach," Finance and Stochastics, Springer, vol. 11(1), pages 107-129, January.

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