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Vector-Valued Coherent Risk Measure Processes

Author

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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.

Suggested Citation

  • Imen Ben Tahar & Emmanuel Lépinette, 2014. "Vector-Valued Coherent Risk Measure Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-28.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:02:n:s0219024914500113
    DOI: 10.1142/S0219024914500113
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    References listed on IDEAS

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    1. Yuri Kabanov, 2009. "Markets with Transaction Costs. Mathematical Theory," Post-Print hal-00488168, HAL.
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    Cited by:

    1. Çağın Ararat & Zachary Feinstein, 2021. "Set-valued risk measures as backward stochastic difference inclusions and equations," Finance and Stochastics, Springer, vol. 25(1), pages 43-76, January.
    2. c{C}au{g}{i}n Ararat & Andreas H. Hamel & Birgit Rudloff, 2014. "Set-valued shortfall and divergence risk measures," Papers 1405.4905, arXiv.org, revised Sep 2017.
    3. Yanhong Chen & Zachary Feinstein, 2022. "Set-valued dynamic risk measures for processes and for vectors," Finance and Stochastics, Springer, vol. 26(3), pages 505-533, July.
    4. Emmanuel Lepinette & Duc Thinh Vu, 2024. "Coherent Risk Measure on $L^0$: NA Condition, Pricing and Dual Representation," Papers 2405.06764, arXiv.org.
    5. Çağin Ararat & Andreas H. Hamel & Birgit Rudloff, 2017. "Set-Valued Shortfall And Divergence Risk Measures," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(05), pages 1-48, August.

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