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Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time

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Author Info

  • PATRICK CHERIDITO

    ()
    (ORFE, Princeton University, Princeton, NJ 08544, USA)

  • MICHAEL KUPPER

    (Department of Mathematics Humboldt University Berlin 10099 Berlin, Germany)

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    Abstract

    In discrete time, every time-consistent dynamic monetary risk measure can be written as a composition of one-step risk measures. We exploit this structure to give new dual representation results for time-consistent convex monetary risk measures in terms of one-step penalty functions. We first study risk measures for random variables modelling financial positions at a fixed future time. Then we consider the more general case of risk measures that depend on stochastic processes describing the evolution of financial positions or cumulated cash flows. In both cases the new representations allow for a simple composition of one-step risk measures in the dual. We discuss several explicit examples and provide connections to the recently introduced class of dynamic variational preferences.

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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): 14 (2011)
    Issue (Month): 01 ()
    Pages: 137-162

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    Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:p:137-162

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    Related research

    Keywords: Dynamic risk measures; time-consistency; dual representations;

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    Cited by:
    1. Zachary Feinstein & Birgit Rudloff, 2012. "Time consistency of dynamic risk measures in markets with transaction costs," Papers 1201.1483, arXiv.org, revised Dec 2012.
    2. Karl-Theodor Eisele & Michael Kupper, 2013. "Asymptotically Stable Dynamic Risk Assessments," Working Papers of LaRGE Research Center 2013-04, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    3. 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.
    4. Andreas L\"ohne & Birgit Rudloff, 2011. "An algorithm for calculating the set of superhedging portfolios in markets with transaction costs," Papers 1107.5720, arXiv.org, revised Dec 2013.
    5. Beatrice Acciaio & Hans Föllmer & Irina Penner, 2012. "Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles," LSE Research Online Documents on Economics 50118, London School of Economics and Political Science, LSE Library.
    6. Stadje, M.A. & Pelsser, A., 2014. "Time-Consistent and Market-Consistent Evaluations (Revised version of 2012-086)," Discussion Paper 2014-002, Tilburg University, Center for Economic Research.
    7. Mitja Stadje & Antoon Pelsser, 2011. "Time-Consistent and Market-Consistent Evaluations," Papers 1109.1749, arXiv.org, revised Dec 2013.
    8. Dilip Madan & Martijn Pistorius & Mitja Stadje, 2013. "On consistent valuations based on distorted expectations: from multinomial random walks to L\'{e}vy processes," Papers 1301.3531, arXiv.org.
    9. Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
    10. Zachary Feinstein & Birgit Rudloff, 2013. "A comparison of techniques for dynamic multivariate risk measures," Papers 1305.2151, arXiv.org, revised Oct 2013.
    11. Beatrice Acciaio & Hans Föllmer & Irina Penner, 2012. "Risk assessment for uncertain cash flows: model ambiguity, discounting ambiguity, and the role of bubbles," Finance and Stochastics, Springer, vol. 16(4), pages 669-709, October.

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