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A censored copula model for micro-level claim reserving

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  • Lopez, Olivier

Abstract

In this paper, we consider the question of predicting the final amount of a claim and its distribution from micro-level data. A copula model is used to describe the dependence between the amount of a claim and its duration (that is the time between its occurrence and its closure). Due to the presence of censoring, we adapt classical methodologies using a weighting scheme that corrects the bias caused by this incompleteness in the data. Theoretical results and simulation support the validity of the procedure. A real case coming from medical malpractice claims is presented.

Suggested Citation

  • Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    • Handle: RePEc:eee:insuma:v:87:y:2019:i:c:p:1-14
    DOI: 10.1016/j.insmatheco.2019.04.001
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    References listed on IDEAS

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    1. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
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    4. Svetlana Gribkova & Olivier Lopez, 2015. "Non-parametric Copula Estimation Under Bivariate Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 925-946, December.
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    Cited by:

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    2. Denuit, Michel & Lu, Yang, 2020. "Wishart-Gamma mixtures for multiperil experience ratemaking, frequency-severity experience rating and micro-loss reserving," LIDAM Discussion Papers ISBA 2020016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. van Staden, Heletjé E. & Deprez, Laurens & Boute, Robert N., 2022. "A dynamic “predict, then optimize” preventive maintenance approach using operational intervention data," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1079-1096.
    4. Jackson P. Lautier & Vladimir Pozdnyakov & Jun Yan, 2022. "Pricing Time-to-Event Contingent Cash Flows: A Discrete-Time Survival Analysis Approach," Papers 2201.04981, arXiv.org, revised Jan 2023.
    5. Yanez, Juan Sebastian & Pigeon, Mathieu, 2021. "Micro-level parametric duration-frequency-severity modeling for outstanding claim payments," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 106-119.
    6. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.

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