Pré-Publication, Document De Travail Année : 2025

Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions

Résumé

Most of extrapolation methods dedicated to the estimation of extreme risk measures rely on the approximation of the excesses distribution above a high threshold by a Generalized Pareto Distribution (GPD). We propose an alternative to the GPD, called the Refined Pareto Distribution (RPD), which allows for a second-order approximation of the excesses distribution. The parameters of the RPD are estimated using an Approximate Bayesian Computation (ABC) method, and reduced-bias estimators of extreme risk measures are then derived together with the associated credible intervals. The ABC estimator demonstrates good performance over a wide range of heavy-tailed distributions. Its usefulness is also illustrated on two data sets of insurance claims.

Fichier principal
Vignette du fichier
Second_Order_Bayes_ABC-HAL.pdf (1.02 Mo) Télécharger le fichier

Dates et versions

hal-04965629 , version 1 (25-02-2025)
hal-04965629 , version 2 (06-10-2025)
hal-04965629 , version 3 (28-04-2026)

Licence

Identifiants

  • HAL Id : hal-04965629 , version 3

Citer

Jonathan El Methni, Stéphane Girard. Approximate Bayesian Computation of reduced-bias extreme risk measures from heavy-tailed distributions. 2025. ⟨hal-04965629v3⟩
1052 Consultations
457 Téléchargements

Partager

  • More