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Update rules for convex risk measures

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  • Sina Tutsch

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.

Suggested Citation

  • Sina Tutsch, 2008. "Update rules for convex risk measures," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 833-843.
    • Handle: RePEc:taf:quantf:v:8:y:2008:i:8:p:833-843
    DOI: 10.1080/14697680802055960
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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 Sep 2017.
    3. Acciaio, Beatrice & Föllmer, Hans & Penner, Irina, 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.
    4. 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.
    5. 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.
    6. Daniel Lacker, 2015. "Law invariant risk measures and information divergences," Papers 1510.07030, arXiv.org, revised Jun 2016.
    7. Jun Zhao & Emmanuel Lépinette & Peibiao Zhao, 2019. "Pricing under dynamic risk measures," Post-Print hal-02135232, HAL.
    8. Aloisio Araujo & Alain Chateauneuf & José Heleno Faro & Bruno Holanda, 2019. "Updating pricing rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(2), pages 335-361, September.
    9. Beatrice Acciaio & Irina Penner, 2010. "Dynamic risk measures," Papers 1002.3794, arXiv.org.
    10. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2018. "A Unified Approach to Time Consistency of Dynamic Risk Measures and Dynamic Performance Measures in Discrete Time," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 204-221, February.
    11. Yi-Ting Chen & Edward W. Sun & Min-Teh Yu, 2018. "Risk Assessment with Wavelet Feature Engineering for High-Frequency Portfolio Trading," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 653-684, August.
    12. 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.
    13. Lacker Daniel, 2018. "Law invariant risk measures and information divergences," Dependence Modeling, De Gruyter, vol. 6(1), pages 228-258, November.
    14. Marlon Moresco & M'elina Mailhot & Silvana M. Pesenti, 2023. "Uncertainty Propagation and Dynamic Robust Risk Measures," Papers 2308.12856, arXiv.org, revised Feb 2024.
    15. Tomasz Kosmala & Randall Martyr & John Moriarty, 2020. "Markov risk mappings and risk-sensitive optimal prediction," Papers 2001.06895, arXiv.org, revised Sep 2022.
    16. D. Madan & M. Pistorius & M. Stadje, 2017. "On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation," Finance and Stochastics, Springer, vol. 21(4), pages 1073-1102, October.
    17. Föllmer Hans, 2014. "Spatial risk measures and their local specification: The locally law-invariant case," Statistics & Risk Modeling, De Gruyter, vol. 31(1), pages 79-101, March.

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