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Multivariate Shortfall Risk Allocation and Systemic Risk


  • Yannick Armenti
  • Stephane Crepey
  • Samuel Drapeau
  • Antonis Papapantoleon


The ongoing concern about systemic risk since the outburst of the global financial crisis has highlighted the need for risk measures at the level of sets of interconnected financial components, such as portfolios, institutions or members of clearing houses. The two main issues in systemic risk measurement are the computation of an overall reserve level and its allocation to the different components according to their systemic relevance. We develop here a pragmatic approach to systemic risk measurement and allocation based on multivariate shortfall risk measures, where acceptable allocations are first computed and then aggregated so as to minimize costs. We analyze the sensitivity of the risk allocations to various factors and highlight its relevance as an indicator of systemic risk. In particular, we study the interplay between the loss function and the dependence structure of the components. Moreover, we address the computational aspects of risk allocation. Finally, we apply this methodology to the allocation of the default fund of a CCP on real data.

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  • Yannick Armenti & Stephane Crepey & Samuel Drapeau & Antonis Papapantoleon, 2015. "Multivariate Shortfall Risk Allocation and Systemic Risk," Papers 1507.05351,, revised Mar 2017.
  • Handle: RePEc:arx:papers:1507.05351

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    References listed on IDEAS

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    2. Zachary Feinstein & Birgit Rudloff & Stefan Weber, 2015. "Measures of Systemic Risk," Papers 1502.07961,, revised Oct 2016.
    3. Francesca Biagini & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2015. "A Unified Approach to Systemic Risk Measures via Acceptance Sets," Papers 1503.06354,, revised Apr 2015.
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    7. Ignacio Cascos & Ilya Molchanov, 2013. "Multivariate risk measures: a constructive approach based on selections," Papers 1301.1496,, revised Jul 2016.
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    9. Patrick Cheridito & Tianhui Li, 2009. "Risk Measures On Orlicz Hearts," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 189-214, April.
    10. Aharon Ben‐Tal & Marc Teboulle, 2007. "An Old‐New Concept Of Convex Risk Measures: The Optimized Certainty Equivalent," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 449-476, July.
    11. Ernst Eberlein & Kathrin Glau & Antonis Papapantoleon, 2010. "Analysis of Fourier Transform Valuation Formulas and Applications," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(3), pages 211-240.
    12. Viral Acharya & Robert Engle & Matthew Richardson, 2012. "Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risks," American Economic Review, American Economic Association, vol. 102(3), pages 59-64, May.
    13. repec:dau:papers:123456789/353 is not listed on IDEAS
    14. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Zachary Feinstein & Birgit Rudloff, 2015. "A Supermartingale Relation for Multivariate Risk Measures," Papers 1510.05561,, revised Jan 2018.
    2. Francesca Biagini & Jean-Pierre Fouque & Marco Frittelli & Thilo Meyer-Brandis, 2018. "On Fairness of Systemic Risk Measures," Papers 1803.09898,, revised Apr 2019.
    3. c{C}au{g}{i}n Ararat & Birgit Rudloff, 2016. "Dual representations for systemic risk measures," Papers 1607.03430,, revised Jul 2019.
    4. Zachary Feinstein, 2017. "Obligations with Physical Delivery in a Multi-Layered Financial Network," Papers 1702.07936,, revised May 2019.
    5. Michel Baes & Pablo Koch-Medina & Cosimo Munari, 2017. "Existence, uniqueness and stability of optimal portfolios of eligible assets," Papers 1702.01936,, revised Dec 2017.

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