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Convex measures of risk and trading constraints

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  • Föllmer, Hans
  • Schied, Alexander

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 not ion 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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  • Föllmer, Hans & Schied, Alexander, 2001. "Convex measures of risk and trading constraints," SFB 373 Discussion Papers 2001,71, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200171
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    Cited by:

    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. repec:zbw:bofrdp:2008_005 is not listed on IDEAS
    3. Huhtala, Heli, 2008. "Along but beyond mean-variance: Utility maximization in a semimartingale model," Bank of Finland Research Discussion Papers 5/2008, Bank of Finland.
    4. Huhtala, Heli, 2008. "Along but beyond mean-variance : Utility maximization in a semimartingale model," Research Discussion Papers 5/2008, Bank of Finland.

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