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Vector-Valued Coherent Risk Measure Processes

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  • IMEN BEN TAHAR

    ()
    (CEREMADE, CNRS UMR 7534, Paris Dauphine University, France)

  • EMMANUEL LÉPINETTE

    ()
    (CEREMADE, CNRS UMR 7534, Paris Dauphine University, France; International Laboratory of Quantitative Finance, National Research University, Higher school of Economics, Myasnitskaya 20, Moscow 101000, Russia)

Abstract

Introduced by Artzner et al. (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini et al. (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 17 (2014)
Issue (Month): 02 ()
Pages: 1450011-1-1450011-28

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Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:p:1450011-1-1450011-28

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Keywords: Vector-valued risk measure; coherent risk measure; dynamic risk measure; dual representation; transaction costs; partial order;

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Cited by:
  1. Zachary Feinstein & Birgit Rudloff, 2012. "Multi-portfolio time consistency for set-valued convex and coherent risk measures," Papers 1212.5563, arXiv.org, revised May 2014.
  2. \c{C}a\u{g}\in Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org.
  3. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Oct 2013.

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