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Bayesian CART models for insurance claims frequency

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  • Zhang, Yaojun
  • Ji, Lanpeng
  • Aivaliotis, Georgios
  • Taylor, Charles

Abstract

The accuracy and interpretability of a (non-life) insurance pricing model are essential qualities to ensure fair and transparent premiums for policy-holders, that reflect their risk. In recent years, classification and regression trees (CARTs) and their ensembles have gained popularity in the actuarial literature, since they offer good prediction performance and are relatively easy to interpret. In this paper, we introduce Bayesian CART models for insurance pricing, with a particular focus on claims frequency modelling. In addition to the common Poisson and negative binomial (NB) distributions used for claims frequency, we implement Bayesian CART for the zero-inflated Poisson (ZIP) distribution to address the difficulty arising from the imbalanced insurance claims data. To this end, we introduce a general MCMC algorithm using data augmentation methods for posterior tree exploration. We also introduce the deviance information criterion (DIC) for tree model selection. The proposed models are able to identify trees which can better classify the policy-holders into risk groups. Simulations and real insurance data will be used to illustrate the applicability of these models.

Suggested Citation

  • Zhang, Yaojun & Ji, Lanpeng & Aivaliotis, Georgios & Taylor, Charles, 2024. "Bayesian CART models for insurance claims frequency," Insurance: Mathematics and Economics, Elsevier, vol. 114(C), pages 108-131.
    • Handle: RePEc:eee:insuma:v:114:y:2024:i:c:p:108-131
    DOI: 10.1016/j.insmatheco.2023.11.005
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    1. Dong, Panyi & Quan, Zhiyu, 2025. "Automated machine learning in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 120(C), pages 17-41.

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    Keywords

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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