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Update rules for convex risk measures

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  • Sina Tutsch
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    Abstract

    In the first part of the paper we investigate the properties that describe the intertemporal structure of dynamic convex risk measures. The usual backward approach to dynamic risk assessment leads to strong and weak versions of time consistency. As an alternative, we introduce a forward approach of consecutivity. In the second part we discuss the problem of how to update a convex risk measure when new information arrives. We analyse to what extent the above properties are appropriate update criteria.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/14697680802055960
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    Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

    Volume (Year): 8 (2008)
    Issue (Month): 8 ()
    Pages: 833-843

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    Handle: RePEc:taf:quantf:v:8:y:2008:i:8:p:833-843
    DOI: 10.1080/14697680802055960
    Contact details of provider: Web page: http://www.tandfonline.com/RQUF20

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    Keywords: Dynamic convex risk measures; Time consistency; Consecutivity; Robust shortfall risk measure; Updating;

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    Cited by:

    1. Beatrice Acciaio & Irina Penner, 2010. "Dynamic risk measures," Papers 1002.3794, arXiv.org.
    2. 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.
    3. Roorda Berend & Schumacher Hans, 2013. "Membership conditions for consistent families of monetary valuations," Statistics & Risk Modeling, De Gruyter, vol. 30(3), pages 255-280, August.
    4. 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.
    5. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2014. "A unified approach to time consistency of dynamic risk measures and dynamic performance measures in discrete time," Papers 1409.7028, arXiv.org, revised Aug 2015.
    6. 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.
    7. Berend Roorda & Johannes M. Schumacher, 2016. "Weakly time consistent concave valuations and their dual representations," Finance and Stochastics, Springer, vol. 20(1), pages 123-151, January.
    8. Daniel Lacker, 2015. "Law invariant risk measures and information divergences," Papers 1510.07030, arXiv.org, revised Jun 2016.
    9. Föllmer Hans, 2014. "Spatial risk measures and their local specification: The locally law-invariant case," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 1-23, March.

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