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Convex measures of risk and trading constraints

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  • 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)

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    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.

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    Bibliographic Info

    Article provided by Springer in its journal Finance and Stochastics.

    Volume (Year): 6 (2002)
    Issue (Month): 4 ()
    Pages: 429-447

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    Handle: RePEc:spr:finsto:v:6:y:2002:i:4:p:429-447

    Note: received: December 2000; final version received: January 2002
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    Related research

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

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