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Loss-based risk measures

Author

Listed:
  • Cont Rama
  • Deguest Romain
  • He Xue Dong

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.

Suggested Citation

  • Cont Rama & Deguest Romain & He Xue Dong, 2013. "Loss-based risk measures," Statistics & Risk Modeling, De Gruyter, vol. 30(2), pages 133-167, June.
    • Handle: RePEc:bpj:strimo:v:30:y:2013:i:2:p:133-167:n:3
    DOI: 10.1524/strm.2013.1132
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    References listed on IDEAS

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    Cited by:

    1. Pablo Koch-Medina & Santiago Moreno-Bromberg & Cosimo Munari, 2014. "Capital adequacy tests and limited liability of financial institutions," Papers 1401.3133, arXiv.org, revised Feb 2014.

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