Convex measures of risk and trading constraints

Hans Föllmer and Alexander Schied
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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

Finance and Stochastics, 2002, vol. 6, issue 4, 429-447

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.

Keywords: Risk measure; convex measure of risk; shortfall; trading constraints; efficient hedging (search for similar items in EconPapers)
JEL-codes: C60 C61 G11 G18 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: December 2000; final version received: January 2002
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Citations: View citations in EconPapers (527)

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