ExpectHill estimation, extreme risk and heavy tails

Abstract : Risk measures of a financial position are traditionally based on quantiles. Replacing quantiles with their least squares analogues, called expectiles, has recently received increasing attention. The novel expectile-based risk measures satisfy all coherence requirements. We revisit their extreme value estimation for heavy-tailed distributions. First, we estimate the underlying tail index via weighted combinations of top order statistics and asymmetric least squares estimates. The resulting expectHill estimators are then used as the basis for estimating tail expectiles and Expected Shortfall. The asymptotic theory of the proposed estimators is provided, along with numerical simulations and applications to actuarial and financial data.
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Pré-publication, Document de travail
2018
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https://hal.inria.fr/hal-01856212
Contributeur : Stephane Girard <>
Soumis le : vendredi 10 août 2018 - 10:08:47
Dernière modification le : vendredi 17 août 2018 - 18:52:19

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  • HAL Id : hal-01856212, version 1

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Abdelaati Daouia, Stéphane Girard, Gilles Stupfler. ExpectHill estimation, extreme risk and heavy tails. 2018. 〈hal-01856212〉

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