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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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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