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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Jonathan El Methni,
  • Stéphane Girard

摘要

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.