Loss-based risk measures

Cont Rama, Deguest Romain and He Xue Dong

Statistics & Risk Modeling, 2013, vol. 30, issue 2, 133-167

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.

Keywords: risk measures; robustness; loss-based risk measures; quantile estimation; convex risk measure (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1524/strm.2013.1132

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