Bayesian CART models for insurance claims frequency

Yaojun Zhang, Lanpeng Ji, Georgios Aivaliotis and Charles Taylor

Insurance: Mathematics and Economics, 2024, vol. 114, issue C, 108-131

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.

Keywords: Bayesian CART; Claims frequency; DIC; Insurance pricing; MCMC; Negative binomial distribution; Zero-inflated Poisson distribution (search for similar items in EconPapers)
JEL-codes: C11 C14 C51 G22 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:114:y:2024:i:c:p:108-131

DOI: 10.1016/j.insmatheco.2023.11.005

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