Loss-Based Risk Measures
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.
|Date of creation:||Oct 2011|
|Date of revision:||Apr 2013|
|Publication status:||Published in Statistics and Risk Modeling, Vol 30, Issue 2, pages 133-167 (2013)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, July.
- 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.
- 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.
- Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
- Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142.
- Carlo Acerbi, 2007. "Coherent measures of risk in everyday market practice," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 359-364.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- 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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