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Tree-based censored regression with applications in insurance

Author

Listed:
  • Olivier Lopez

    (LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

  • Xavier Milhaud

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Pierre-Emmanuel Thérond

    (Galea & Associés, SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

Abstract

We propose a regression tree procedure to estimate the conditional distribution of a variable which is not directly observed due to censoring. The model that we consider is motivated by applications in insurance , including the analysis of guarantees that involve durations, and claim reserving. We derive consistency results for our procedure, and for the selection of an optimal subtree using a pruning strategy. These theoretical results are supported by a simulation study, and two applications involving insurance datasets. The first concerns income protection insurance, while the second deals with reserving in third-party liability insurance.

Suggested Citation

  • Olivier Lopez & Xavier Milhaud & Pierre-Emmanuel Thérond, 2016. "Tree-based censored regression with applications in insurance," Post-Print hal-01141228, HAL.
    • Handle: RePEc:hal:journl:hal-01141228
    DOI: 10.1214/16-EJS1189
    Note: View the original document on HAL open archive server: https://hal.science/hal-01141228v2
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    References listed on IDEAS

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    Cited by:

    1. Farkas, Sébastien & Lopez, Olivier & Thomas, Maud, 2021. "Cyber claim analysis using Generalized Pareto regression trees with applications to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 92-105.
    2. Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    3. Guillaume Coqueret & Tony Guida, 2020. "Training trees on tails with applications to portfolio choice," Annals of Operations Research, Springer, vol. 288(1), pages 181-221, May.
    4. Guillaume Coqueret & Tony Guida, 2020. "Training trees on tails with applications to portfolio choice," Post-Print hal-04144665, HAL.
    5. Crevecoeur, Jonas & Robben, Jens & Antonio, Katrien, 2022. "A hierarchical reserving model for reported non-life insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 104(C), pages 158-184.
    6. Marie Michaelides & Mathieu Pigeon & H'el`ene Cossette, 2022. "Individual Claims Reserving using Activation Patterns," Papers 2208.08430, arXiv.org, revised Aug 2023.
    7. Gu, Zheng & Li, Yunxian & Zhang, Minghui & Liu, Yifei, 2023. "Modelling economic losses from earthquakes using regression forests: Application to parametric insurance," Economic Modelling, Elsevier, vol. 125(C).
    8. 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.

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