Bayesian CART models for aggregate claim modeling
This work addresses incremental improvements in actuarial science for insurance risk modeling by enhancing predictive accuracy in claim data analysis.
The paper tackled modeling aggregate insurance claims by proposing Bayesian CART models, finding that Weibull distributions best capture tail characteristics and that models incorporating dependence between claim frequency and severity outperform independent ones, as validated through simulations and real data.
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.