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Reduced-Bias Estimator of the Conditional Tail Expectation of Heavy-Tailed Distributions

  • El Hadji Deme
  • Stéphane Girard
  • Armelle Guillou
Chapter

Abstract

Several risk measures have been proposed in the literature. In this paper, we focus on the estimation of the Conditional Tail Expectation (CTE). Its asymptotic normality has been first established in the literature under the classical assumption that the second moment of the loss variable is finite, this condition being very restrictive in practical applications. Such a result has been extended by Necir et al., (Journal of Probability and Statistics 596839:17 2010) in the case of infinite second moment. In this framework, we propose a reduced-bias estimator of the CTE. We illustrate the efficiency of our approach on a small simulation study and a real data analysis.

Notes

Acknowledgments

The authors thank the referee for the comments concerning the previous version. The first author acknowledges support from AIRES-Sud (AIRES-Sud is a program from the French Ministry of Foreign and European Affairs, implemented by the “Institut de Recherche pour le Développement”, IRD-DSF) and from the “Ministère de la Recherche Scientifique” of Sénégal.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • El Hadji Deme
    • 1
  • Stéphane Girard
    • 2
  • Armelle Guillou
    • 3
  1. 1.LERSTADUniversité Gaston Berger de Saint-LouisSaint-LouisSénégal
  2. 2.Team MistisInria Grenoble Rhône-Alpes & Laboratoire Jean KuntzmannMontbonnotFrance
  3. 3.Université de Strasbourg & CNRS, IRMA, UMR 7501StrasbourgFrance

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