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Vector-valued Coherent Risk Measures

Author

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  • Elyès Jouini

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

  • Moncef Meddeb

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Nizar Touzi

    (CMAP - Centre de Mathématiques Appliquées - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines - X - École polytechnique - 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://shs.hal.science/halshs-00167154
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    Keywords

    risk; measures;

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