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Risk measures for processes and BSDEs

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  • Irina Penner

    ()
    (Institut für Mathematik - Humboldt Universität zu Berlin)

  • Anthony Reveillac

    ()
    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

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    Abstract

    The paper analyzes risk assessment for cash flows in continuous time using the notion of convex risk measures for processes. By combining a decomposition result for optional measures, and a dual representation of a convex risk measure for bounded \cd processes, we show that this framework provides a systematic approach to the both issues of model ambiguity, and uncertainty about the time value of money. We also establish a link between risk measures for processes and BSDEs.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/81/47/02/PDF/Penner_Reveillac.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00814702.

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    Date of creation: 17 Apr 2013
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    Handle: RePEc:hal:wpaper:hal-00814702

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00814702
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    Related research

    Keywords: Convex risk measures for processes; Discounting ambiguity; Model ambiguity; Cash subadditivity; Decomposition of optional measures; BSDEs;

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    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 9(3), pages 203-228.
    2. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1473-1486, July.
    3. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, Springer, vol. 9(3), pages 369-387, 07.
    4. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, Springer, vol. 6(4), pages 429-447.
    5. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "On the Hedging of Options On Exploding Exchange Rates," Papers 1202.6188, arXiv.org, revised Nov 2013.
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