Loss-Based Risk Measures
AbstractStarting 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.
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Bibliographic InfoPaper provided by HAL in its series Working Papers with number hal-00629929.
Date of creation: 2011
Date of revision:
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risk measure; coherent risk measure; Fenchel-Legendre transform; Choquet capacity;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-15 (All new papers)
- NEP-FMK-2011-10-15 (Financial Markets)
- NEP-MIC-2011-10-15 (Microeconomics)
- NEP-RMG-2011-10-15 (Risk Management)
- NEP-UPT-2011-10-15 (Utility Models & Prospect Theory)
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- 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.
- Elyès Jouini & Walter Schachermayer & Nizar Touzi, 2006. "Law Invariant Risk Measures Have the Fatou Property," Post-Print halshs-00176522, HAL.
- Frittelli, Marco & Rosazza Gianin, Emanuela, 2002. "Putting order in risk measures," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1473-1486, 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.
- Robert Jarrow, 2002. "Put Option Premiums and Coherent Risk Measures," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 135-142.
- 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.
- Carlo Acerbi, 2007. "Coherent measures of risk in everyday market practice," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 359-364.
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