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Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions

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  • El Methni, Jonathan
  • Stupfler, Gilles

Abstract

A general way to study the extremes of a random variable is to consider the family of its Wang distortion risk measures. This class of risk measures encompasses several indicators such as the classical quantile/Value-at-Risk, the Tail-Value-at-Risk and Conditional Tail Moments. Trimmed and winsorised versions of the empirical counterparts of extreme analogues of Wang distortion risk measures are considered. Their asymptotic properties are analysed, and it is shown that it is possible to construct corrected versions of trimmed or winsorised estimators of extreme Wang distortion risk measures who appear to perform overall better than their standard empirical counterparts in difficult finite-sample situations when the underlying distribution has a very heavy right tail. This technique is showcased on a set of real fire insurance data.

Suggested Citation

  • El Methni, Jonathan & Stupfler, Gilles, 2018. "Improved estimators of extreme Wang distortion risk measures for very heavy-tailed distributions," Econometrics and Statistics, Elsevier, vol. 6(C), pages 129-148.
    • Handle: RePEc:eee:ecosta:v:6:y:2018:i:c:p:129-148
    DOI: 10.1016/j.ecosta.2017.03.002
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    1. Laurent Gardes & Stéphane Girard, 2021. "On the estimation of the variability in the distribution tail," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 884-907, December.
    2. Girard, Stéphane & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Functional estimation of extreme conditional expectiles," Econometrics and Statistics, Elsevier, vol. 21(C), pages 131-158.
    3. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    4. Laurent Gardes & Stéphane Girard & Gilles Stupfler, 2020. "Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp‐optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 922-949, September.
    5. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2021. "ExpectHill estimation, extreme risk and heavy tails," Journal of Econometrics, Elsevier, vol. 221(1), pages 97-117.
    6. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "Tail expectile process and risk assessment," TSE Working Papers 18-944, Toulouse School of Economics (TSE).

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