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Strongly Consistent Multivariate Conditional Risk Measures

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  • Hannes Hoffmann
  • Thilo Meyer-Brandis
  • Gregor Svindland

Abstract

We consider families of strongly consistent multivariate conditional risk measures. We show that under strong consistency these families admit a decomposition into a conditional aggregation function and a univariate conditional risk measure as introduced Hoffmann et al. (2016). Further, in analogy to the univariate case in F\"ollmer (2014), we prove that under law-invariance strong consistency implies that multivariate conditional risk measures are necessarily multivariate conditional certainty equivalents.

Suggested Citation

  • Hannes Hoffmann & Thilo Meyer-Brandis & Gregor Svindland, 2016. "Strongly Consistent Multivariate Conditional Risk Measures," Papers 1609.07903, arXiv.org.
    • Handle: RePEc:arx:papers:1609.07903
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    References listed on IDEAS

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    1. Hoffmann, Hannes & Meyer-Brandis, Thilo & Svindland, Gregor, 2016. "Risk-consistent conditional systemic risk measures," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2014-2037.
    2. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and dynamic convex risk measures," Finance and Stochastics, Springer, vol. 9(4), pages 539-561, October.
    3. Chen Chen & Garud Iyengar & Ciamac C. Moallemi, 2013. "An Axiomatic Approach to Systemic Risk," Management Science, INFORMS, vol. 59(6), pages 1373-1388, June.
    4. 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.
    5. Kai Detlefsen & Giacomo Scandolo, 2005. "Conditional and Dynamic Convex Risk Measures," SFB 649 Discussion Papers SFB649DP2005-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    6. E. Kromer & L. Overbeck & K. Zilch, 2016. "Systemic risk measures on general measurable spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 323-357, October.
    7. Marco Frittelli & Marco Maggis, 2011. "Conditional Certainty Equivalent," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 41-59.
    8. Hannes Hoffmann & Thilo Meyer-Brandis & Gregor Svindland, 2016. "Risk-Consistent Conditional Systemic Risk Measures," Papers 1609.07897, arXiv.org.
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