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Convex measures of risk and trading constraints

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Author Info
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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Publisher 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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Find related papers by 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 and Programming - - - General
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

References listed on IDEAS
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  1. Hans FÃllmer & Peter Leukert, 2000. "Efficient hedging: Cost versus shortfall risk," Finance and Stochastics, Springer, vol. 4(2), pages 117-146. [Downloadable!] (restricted)
  2. H. Föllmer & D. Kramkov, . "Optional decompositions under constraints," Sonderforschungsbereich 373 1997-31, Humboldt Universitaet Berlin.
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