IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v9y2005i4p597-608.html
   My bibliography  Save this article

Robust representation of convex risk measures by probability measures

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00780-005-0160-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00780-005-0160-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    3. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    4. 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.
    5. 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.
    6. repec:dau:papers:123456789/342 is not listed on IDEAS

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:finsto:v:9:y:2005:i:4:p:597-608. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.