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On s-additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model

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  • Volker Krätschmer
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    Abstract

    Recently, Frittelli and Scandolo ([9]) extend the notion of risk measures, originally introduced by Artzner, Delbaen, Eber and Heath ([1]), to the risk assessment of abstract financial positions, including pay offs spread over different dates, where liquid derivatives are admitted to serve as financial instruments. The paper deals with s-additive robust representations of convex risk measures in the extended sense, dropping the assumption of an existing market model, and allowing also unbounded financial positions. The results may be applied for the case that a market model is available, and they encompass as well as improve criteria obtained for robust representations of the original convex risk measures for bounded positions ([4], [7], [16]).

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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2007-010.

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    Length: 29 pages
    Date of creation: Mar 2007
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    Handle: RePEc:hum:wpaper:sfb649dp2007-010

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    Keywords: Convex risk measures; model uncertainty; s-additive robust representation; Fatou property; nonsequential Fatou property; strong s-additive robust representation; Krein-Smulian theorem; Greco theorem; inner Daniell stone theorem; general Dini theorem; Simons’ lemma.;

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    1. Volker Krätschmer, 2006. "Compactness in Spaces of Inner Regular Measures and a General Portmanteau Lemma," SFB 649 Discussion Papers SFB649DP2006-081, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics.
    3. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612.
    4. Touzi, Nizar & Schachermayer, Walter & Jouini, Elyès, 2006. "Law Invariant Risk Measures Have the Fatou Property," Economics Papers from University Paris Dauphine 123456789/342, Paris Dauphine University.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    6. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005.
    7. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
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