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.

翻译：本文针对聚合索赔金额提出了三种贝叶斯CART（或称BCART）模型，即频率-严重程度模型、序列模型与联合模型。我们提出了适用于多变量响应数据的BCART通用建模框架，该框架特别适用于具有双变量响应（索赔次数与聚合索赔金额）的联合BCART模型。为促进频率-严重程度建模，我们通过多种分布形式研究了适用于右偏且厚尾索赔严重程度数据的BCART模型。研究发现，由于韦伯分布在树模型中能够捕捉不同的尾部特征，其性能优于伽马分布与对数正态分布。此外，我们发现纳入索赔次数与平均严重程度相依关系的序列BCART模型与联合BCART模型具有显著优势，因此优于假设独立性的频率-严重程度BCART模型。通过精心设计的模拟实验与真实保险数据，验证了这些模型的有效性能。