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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
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    More about this item

    Keywords

    Risk measure; convex measure of risk; shortfall; trading constraints; efficient hedging;
    All these keywords.

    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

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