IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v6y2002i4p429-447.html
   My bibliography  Save this article

Convex measures of risk and trading constraints

Author

Listed:
  • Hans Föllmer

    (Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

  • Alexander Schied

    (Institut für Mathematik, Humboldt-Universität, Unter den Linden 6, 10099 Berlin, Germany Manuscript)

Abstract

We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust notion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints.

Suggested Citation

  • Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
  • Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:429-447
    Note: received: December 2000; final version received: January 2002
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00780/papers/2006004/20060429.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted

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

    More about this item

    Keywords

    Risk measure; convex measure of risk; shortfall; trading constraints; efficient hedging;

    JEL classification:

    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

    Statistics

    Access and download statistics

    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:6:y:2002:i:4:p:429-447. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.