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Extreme value estimation of the conditional risk premium in reinsurance

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  • Goegebeur, Yuri
  • Guillou, Armelle
  • Qin, Jing

Abstract

In the paper we study the estimation of reinsurance premiums when the claim size is observed together with additional information in the form of random covariates. Using extreme value arguments, we propose an estimator for the risk premium conditional on a value for the covariate, and derive its asymptotic properties, after suitable normalization. The finite sample behavior is evaluated with a simulation experiment, and we apply the methodology to a dataset of automobile insurance claims from Australia.

Suggested Citation

  • Goegebeur, Yuri & Guillou, Armelle & Qin, Jing, 2021. "Extreme value estimation of the conditional risk premium in reinsurance," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 68-80.
    • Handle: RePEc:eee:insuma:v:96:y:2021:i:c:p:68-80
    DOI: 10.1016/j.insmatheco.2020.10.010
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    References listed on IDEAS

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    1. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    2. Gardes, Laurent & Girard, Stéphane, 2016. "On the estimation of the functional Weibull tail-coefficient," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 29-45.
    3. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Vandewalle, B. & Beirlant, J., 2006. "On univariate extreme value statistics and the estimation of reinsurance premiums," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 441-459, June.
    5. Beirlant, J. & Matthys, G. & Dierckx, G., 2001. "Heavy-Tailed Distributions and Rating," ASTIN Bulletin, Cambridge University Press, vol. 31(1), pages 37-58, May.
    6. Mikael Escobar‐Bach & Yuri Goegebeur & Armelle Guillou, 2018. "Local Estimation of the Conditional Stable Tail Dependence Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 590-617, September.
    7. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.
    8. Jonathan El Methni & Laurent Gardes & Stéphane Girard, 2014. "Non-parametric Estimation of Extreme Risk Measures from Conditional Heavy-tailed Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 988-1012, December.
    Full references (including those not matched with items on IDEAS)

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