Loss-based risk measures
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Rama Cont
Abstract
Starting from the requirement that risk of financial portfolios should be measured in terms of 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 convex loss-based risk measures by a representation theorem and give examples of such risk measures. We then discuss the statistical robustness of the risk estimators associated with the family of loss-based risk measures: we provide a general criterion for the qualitative robustness of the risk estimators and compare this criterion with a sensitivity analysis of estimators based on influence functions. We find that the risk estimators associated with convex loss-based risk measures are not robust.
© by Oldenbourg Wissenschaftsverlag, München, Germany
Articles in the same Issue
- Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin
- Comments on the review of Statistical Inference
- Loss-based risk measures
- A harmonic function approach to Nash-equilibria of Kifer-type stopping games
- A note on the biasedness and unbiasedness of two-sample Kolmogorov–Smirnov test
Articles in the same Issue
- Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin
- Comments on the review of Statistical Inference
- Loss-based risk measures
- A harmonic function approach to Nash-equilibria of Kifer-type stopping games
- A note on the biasedness and unbiasedness of two-sample Kolmogorov–Smirnov test
