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.

（非寿险）保险定价模型的准确性和可解释性是确保投保人获得公平、透明的保费并反映其风险的基本品质。近年来，分类和回归树（CART）及其集成在精算文献中越来越受欢迎，因为它们提供了良好的预测性能并且相对容易解释。在本文中，我们介绍了用于保险定价的贝叶斯 CART 模型，特别关注索赔频率建模。除了用于理赔频率的常见泊松分布和负二项式（NB）分布外，我们还采用贝叶斯 CART 进行零膨胀泊松（ZIP）分布，以解决保险理赔数据不平衡带来的困难。为此，我们引入了一种使用数据增强方法进行后树探索的通用 MCMC 算法。我们还引入了用于树模型选择的偏差信息准则（DIC）。所提出的模型能够识别能够更好地将保单持有人分类为风险组的树。将使用模拟和真实保险数据来说明这些模型的适用性。