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Reduced-biased estimators of the Conditional Tail Expectation for heavy-tailed distributions

El Hadji Deme 1, 2 Stephane Girard 2 Armelle Guillou 3
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
Abstract : Several risk measures have been proposed in the literature. In this talk, we focus on the estimation of the Conditional Tail Expectation (CTE). The asymptotic normality of estimators of the CTE has been established in the literature under a finite second moment condition. If this condition is not satisfi ed, no result is available. This talk deals with the estimation problem of the CTE within the class of heavy-tailed distributions, which are quite common in practice, in particular in an actuarial context. More precisely, we introduce a reduced-biased estimator and establish its asymptotic normality under very general assumptions. Our proofs are mainly based on empirical processes arguments combined with some extreme value results. Finally, we illustrate the efficiency of our estimators on a small simulation study.
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Contributor : Stephane Girard <>
Submitted on : Monday, June 24, 2013 - 10:08:10 AM
Last modification on : Tuesday, November 24, 2020 - 4:38:03 PM


  • HAL Id : hal-00837681, version 1



El Hadji Deme, Stephane Girard, Armelle Guillou. Reduced-biased estimators of the Conditional Tail Expectation for heavy-tailed distributions. Mathematical Statistics and Limit Theorems, Conference in honor of Prof. Paul Deheuvels, Jun 2013, Paris, France. ⟨hal-00837681⟩



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