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Risk measures for processes and BSDEs

Author

Listed:
  • Irina Penner

    () (Institut für Mathematik [Berlin] - TUB - Technische Universität Berlin)

  • Anthony Reveillac

    () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique)

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.

Suggested Citation

  • Irina Penner & Anthony Reveillac, 2013. "Risk measures for processes and BSDEs," Working Papers hal-00814702, HAL.
  • Handle: RePEc:hal:wpaper:hal-00814702
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00814702
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    File URL: https://hal.archives-ouvertes.fr/hal-00814702/document
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    References listed on IDEAS

    as
    1. Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
    2. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2010. "Valuation equations for stochastic volatility models," Papers 1004.3299, arXiv.org, revised Dec 2011.
    3. Patrick Cheridito & Freddy Delbaen & Michael Kupper, 2005. "Coherent and convex monetary risk measures for unbounded càdlàg processes," Finance and Stochastics, Springer, vol. 9(3), pages 369-387, July.
    4. Erhan Bayraktar & Ioannis Karatzas & Song Yao, 2009. "Optimal Stopping for Dynamic Convex Risk Measures," Papers 0909.4948, arXiv.org, revised Nov 2009.
    5. Erhan Bayraktar & Song Yao, 2009. "Optimal Stopping for Non-linear Expectations," Papers 0905.3601, arXiv.org, revised Jan 2011.
    6. Peter Carr & Travis Fisher & Johannes Ruf, 2012. "On the Hedging of Options On Exploding Exchange Rates," Papers 1202.6188, arXiv.org, revised Nov 2013.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

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

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