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Vector-valued Coherent Risk Measures

Author

Listed:
  • Elyès Jouini

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

  • Moncef Meddeb

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Nizar Touzi

    (CMAP - Centre de Mathématiques Appliquées - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines - Polytechnique - X - CNRS - Centre National de la Recherche Scientifique)

Abstract

We define a coherent risk measures as set-valued maps satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner, Delbaen, Eber and Heath (1998). We then discuss the aggregation issue, i.e. the passage from valued random portofolio to valued measure of Risk. Necessary and sufficient conditions of coherent aggregation are provided

Suggested Citation

  • Elyès Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued Coherent Risk Measures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00167154, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00167154 Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00167154
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    References listed on IDEAS

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    1. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, April.
    2. Detemple, Jerome B & Selden, Larry, 1991. "A General Equilibrium Analysis of Option and Stock Market Interactions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 32(2), pages 279-303, May.
    3. Benveniste, L M & Scheinkman, J A, 1979. "On the Differentiability of the Value Function in Dynamic Models of Economics," Econometrica, Econometric Society, vol. 47(3), pages 727-732, May.
    4. A, Bizid & Elyès Jouini & Pf. Koehl, 1997. "Pricing in Incomplete Markets : An Equilibrium Approach," Working Papers 97-41, Center for Research in Economics and Statistics.
    5. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Keywords

    risk; measures;

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