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Bayesian CART models for aggregate claim modeling

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  • Yaojun Zhang
  • Lanpeng Ji
  • Georgios Aivaliotis
  • Charles C. Taylor

Abstract

This paper proposes three types of Bayesian CART (or BCART) models for aggregate claim amount, namely, frequency-severity models, sequential models and joint models. We propose a general framework for the BCART models applicable to data with multivariate responses, which is particularly useful for the joint BCART models with a bivariate response: the number of claims and aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data by using various distributions. We discover that the Weibull distribution is superior to gamma and lognormal distributions, due to its ability to capture different tail characteristics in tree models. Additionally, we find that sequential BCART models and joint BCART models, which incorporate dependence between the number of claims and average severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.

Suggested Citation

  • Yaojun Zhang & Lanpeng Ji & Georgios Aivaliotis & Charles C. Taylor, 2024. "Bayesian CART models for aggregate claim modeling," Papers 2409.01908, arXiv.org.
  • Handle: RePEc:arx:papers:2409.01908
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    References listed on IDEAS

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    1. Michel Denuit & Arthur Charpentier & Julien Trufin, 2021. "Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning," Papers 2103.03635, arXiv.org, revised Jul 2021.
    2. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Discussion Papers ISBA 2021013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Lee, Gee Y. & Shi, Peng, 2019. "A dependent frequency–severity approach to modeling longitudinal insurance claims," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 115-129.
    4. Denuit, Michel & Charpentier, Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 485-497.
    5. Claudia Czado & Rainer Kastenmeier & Eike Brechmann & Aleksey Min, 2012. "A mixed copula model for insurance claims and claim sizes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2012(4), pages 278-305.
    6. Roel Henckaerts & Marie-Pier Côté & Katrien Antonio & Roel Verbelen, 2021. "Boosting Insights in Insurance Tariff Plans with Tree-Based Machine Learning Methods," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(2), pages 255-285, April.
    7. Denuit, Michel & Charpentier , Arthur & Trufin, Julien, 2021. "Autocalibration and Tweedie-dominance for insurance pricing with machine learning," LIDAM Reprints ISBA 2021049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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