Reduced-bias estimation of extreme risk measures for heavy-tailed distributions - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Reduced-bias estimation of extreme risk measures for heavy-tailed distributions

Résumé

Conditional tail expectation (CTE) is a coherent risk measure defined as the mean of the loss distribution above a high quantile.The existence of the CTE as well as the asymptotic properties of associated estimators however require integrability conditions that may be violated when dealing with heavy-tailed distributions. We introduce Box-Cox transforms of the CTE that have two benefits. First, they alleviate these theoretical issues. Second, they enable the recovery of a number of risk measures such as conditional tail moments. The construction of dedicated estimators is based on the investigation of the asymptotic relationship between Box-Cox transforms of the CTE and quantiles at extreme probability levels, as well as on an extrapolation formula established in the heavy-tailed context. We quantify and estimate the bias induced by the use of these approximations and then introduce reduced-bias estimators whose asymptotic properties are rigorously shown. Their finite-sample properties are assessed on a simulation study and illustrated on real data, highlighting the practical interest of both the bias reduction and the Box-Cox transform.
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Dates et versions

hal-04683578 , version 1 (02-09-2024)

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  • HAL Id : hal-04683578 , version 1

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Michaël Allouche, Jonathan El Methni, Stéphane Girard. Reduced-bias estimation of extreme risk measures for heavy-tailed distributions. MAS 2024 - Journées de Modélisation Aléatoire et Statistique, Aug 2024, Poitiers, France. ⟨hal-04683578⟩
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