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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

4 Issues per year

Cite Score 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.455
Source Normalized Impact per Paper (SNIP) 2017: 0.853

Mathematical Citation Quotient (MCQ) 2017: 0.32

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Volume 30, Issue 2


Loss-based risk measures

Rama Cont / Romain Deguest / Xue Dong He
Published Online: 2013-06-27 | DOI: https://doi.org/10.1524/strm.2013.1132


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

About the article

* Correspondence address: CNRS - Université Pierre et Marie Curie, Laboratoire de Probabilités et Modèles Alèatoires, 4 place Jussieu, 75252 Paris, Frankreich,

Published Online: 2013-06-27

Published in Print: 2013-06-01

Citation Information: Statistics & Risk Modeling with Applications in Finance and Insurance, Volume 30, Issue 2, Pages 133–167, ISSN (Print) 2193-1402, DOI: https://doi.org/10.1524/strm.2013.1132.

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