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Conditional tail moment and reinsurance premium estimation under random right censoring

Author

Listed:
  • Yuri Goegebeur

    (University of Southern Denmark)

  • Armelle Guillou

    (Université de Strasbourg et CNRS)

  • Jing Qin

    (University of Southern Denmark)

Abstract

We propose an estimator of the conditional tail moment (CTM) when the data are subject to random censorship. The variable of main interest and the censoring variable both follow a Pareto-type distribution. We establish the asymptotic properties of our estimator and discuss bias-reduction. Then, the CTM is used to estimate, in case of censorship, the premium principle for excess-of-loss reinsurance. The finite sample properties of the proposed estimators are investigated with a simulation study and we illustrate their practical applicability on a dataset of motor third party liability insurance.

Suggested Citation

  • Yuri Goegebeur & Armelle Guillou & Jing Qin, 2024. "Conditional tail moment and reinsurance premium estimation under random right censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(1), pages 230-250, March.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:1:d:10.1007_s11749-023-00890-x
    DOI: 10.1007/s11749-023-00890-x
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    References listed on IDEAS

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    1. Worms, J. & Worms, R., 2016. "A Lynden-Bell integral estimator for extremes of randomly truncated data," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 106-117.
    2. Goegebeur, Yuri & Guillou, Armelle & Pedersen, Tine & Qin, Jing, 2022. "Extreme-value based estimation of the conditional tail moment with application to reinsurance rating," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 102-122.
    3. Martin Bladt & Hansjörg Albrecher & Jan Beirlant, 2020. "Combined tail estimation using censored data and expert information," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2020(6), pages 503-525, July.
    4. Julien Worms & Rym Worms, 2018. "Extreme value statistics for censored data with heavy tails under competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 849-889, October.
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