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

Author

Listed:
  • PATRICK CHERIDITO

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

  • MICHAEL KUPPER

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

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.

Suggested Citation

  • Patrick Cheridito & Michael Kupper, 2011. "Composition Of Time-Consistent Dynamic Monetary Risk Measures In Discrete Time," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 137-162.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:01:n:s0219024911006292
    DOI: 10.1142/S0219024911006292
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    References listed on IDEAS

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    1. Beatrice Acciaio & Hans Foellmer & Irina Penner, 2010. "Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles," Papers 1002.3627, arXiv.org.
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    1. Beatrice Acciaio & Irina Penner, 2010. "Dynamic risk measures," Papers 1002.3794, arXiv.org.

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