Bayesian CART models for aggregate claim modeling

TL;DR

This paper introduces Bayesian CART models for aggregate insurance claims, including frequency-severity, sequential, and joint models, demonstrating their effectiveness through simulations and real data analysis.

Contribution

It develops a general BCART framework for multivariate responses and shows the advantages of sequential and joint models over traditional frequency-severity models.

Findings

Weibull distribution outperforms gamma and lognormal for claim severity.

Sequential and joint BCART models better capture dependence between claim frequency and severity.

Models show improved performance on simulated and real insurance data.

Abstract

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.