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Risk assessment for uncertain cash flows: Model ambiguity, discounting ambiguity, and the role of bubbles

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  • Beatrice Acciaio
  • Hans Foellmer
  • Irina Penner

Abstract

We study the risk assessment of uncertain cash flows in terms of dynamic convex risk measures for processes as introduced in Cheridito, Delbaen, and Kupper (2006). These risk measures take into account not only the amounts but also the timing of a cash flow. We discuss their robust representation in terms of suitably penalized probability measures on the optional sigma-field. This yields an explicit analysis both of model and discounting ambiguity. We focus on supermartingale criteria for different notions of time consistency. In particular we show how bubbles may appear in the dynamic penalization, and how they cause a breakdown of asymptotic safety of the risk assessment procedure.

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  • 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.
    • Handle: RePEc:arx:papers:1002.3627
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    References listed on IDEAS

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    Cited by:

    1. Beatrice Acciaio & Irina Penner, 2010. "Dynamic risk measures," Papers 1002.3794, arXiv.org.
    2. 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.

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