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Loss-based risk measures

Author

Listed:
  • Cont Rama
  • Deguest Romain

    (EDHEC Business School, Nice, Frankreich)

  • He Xue Dong

    (Columbia University, IEOR Dept, New York, NY 10027, U.S.A.)

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

    as
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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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