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Loss-Based Risk Measures

Author

Listed:
  • Rama Cont
  • Romain Deguest
  • Xuedong He

Abstract

Starting from the requirement that risk measures of financial portfolios should be based on their losses, not their gains, we define the notion of loss-based risk measure and study the properties of this class of risk measures. We characterize loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of estimators of loss-based risk measures: we provide a general criterion for qualitative robustness of risk estimators and compare this criterion with sensitivity analysis of estimators based on influence functions. Finally, we provide examples of statistically robust estimators for loss-based risk measures.

Suggested Citation

  • Rama Cont & Romain Deguest & Xuedong He, 2011. "Loss-Based Risk Measures," Papers 1110.1436, arXiv.org, revised Apr 2013.
  • Handle: RePEc:arx:papers:1110.1436
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    File URL: http://arxiv.org/pdf/1110.1436
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    References listed on IDEAS

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    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. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    3. Carlo Acerbi, 2007. "Coherent measures of risk in everyday market practice," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 359-364.
    4. Rama Cont & Romain Deguest & Giacomo Scandolo, 2010. "Robustness and sensitivity analysis of risk measurement procedures," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 593-606.
    5. Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
    6. Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142.
    7. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    8. Song, Yongsheng & Yan, Jia-An, 2009. "Risk measures with comonotonic subadditivity or convexity and respecting stochastic orders," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 459-465, December.
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    Cited by:

    1. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Munari, Cosimo, 2015. "Capital adequacy tests and limited liability of financial institutions," Journal of Banking & Finance, Elsevier, vol. 51(C), pages 93-102.
    2. Rüdiger Kiesel & Robin Rühlicke & Gerhard Stahl & Jinsong Zheng, 2016. "The Wasserstein Metric and Robustness in Risk Management," Risks, MDPI, Open Access Journal, vol. 4(3), pages 1-14, August.
    3. Niushan Gao & Cosimo Munari, 2017. "Surplus-invariant risk measures," Papers 1707.04949, arXiv.org.
    4. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
    5. Xue Dong He & Xianhua Peng, 2017. "Surplus-Invariant, Law-Invariant, and Conic Acceptance Sets Must be the Sets Induced by Value-at-Risk," Papers 1707.05596, arXiv.org, revised Jan 2018.
    6. Pablo Koch-Medina & Santiago Moreno-Bromberg & Cosimo Munari, 2014. "Capital adequacy tests and limited liability of financial institutions," Papers 1401.3133, arXiv.org, revised Feb 2014.

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