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On automatic bias reduction for extreme expectile estimation

Abstract : Expectiles induce a law-invariant risk measure that has recently gained popularity in actuarial and financial risk management applications. Unlike quantiles or the quantile-based Expected Shortfall, the expectile risk measure is coherent and elicitable. The estimation of extreme expectiles in the heavy-tailed framework, which is reasonable for extreme financial or actuarial risk management, is not without difficulties; currently available estimators of extreme expectiles are typically biased and hence may show poor finite-sample performance even in fairly large samples. We focus here on the construction of bias-reduced extreme expectile estimators for heavy-tailed distributions. The rationale for our construction hinges on a careful investigation of the asymptotic proportionality relationship between extreme expectiles and their quantile counterparts, as well as of the extrapolation formula motivated by the heavy-tailed context. We accurately quantify and estimate the bias incurred by the use of these relationships when constructing extreme expectile estimators. This motivates the introduction of a class of bias-reduced estimators whose asymptotic properties are rigorously shown, and whose finite-sample properties are assessed on a simulation study and three samples of real data from economics, insurance and finance.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03086048
Contributor : Gilles Stupfler <>
Submitted on : Tuesday, January 5, 2021 - 11:09:44 AM
Last modification on : Thursday, May 6, 2021 - 5:16:58 PM

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  • HAL Id : hal-03086048, version 2

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Stéphane Girard, Gilles Stupfler, Antoine Usseglio-Carleve. On automatic bias reduction for extreme expectile estimation. 2021. ⟨hal-03086048v2⟩

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