Bayesian CART models for aggregate claim modeling

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 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 the aggregate claim amount. To facilitate frequency-severity modeling, we investigate BCART models for the right-skewed and heavy-tailed claim severity data 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 can incorporate more complex dependence between the number of claims and severity, are beneficial and thus preferable to the frequency-severity BCART models in which independence is commonly assumed. The effectiveness of these models' performance is illustrated by carefully designed simulations and real insurance data.