Modeling insurance claims using Bayesian nonparametric regression

Predicting future insurance claims using observed covariates is essential for actuaries in setting appropriate insurance premiums. For this purpose, actuaries commonly employ parametric regression models, which assume the same functional form tying the response to the covariates across all data points. However, these models may lack the flexibility required to accurately capture, at the individual level, the relationship between covariates and claims frequency and severity. This limitation is particularly relevant as claims data are often multimodal, highly skewed, and heavy-tailed. In this paper, we explore the use of Bayesian nonparametric (BNP) regression models to predict claims frequency and severity based on covariates. Specifically, we model claims frequency as a mixture of Poisson regression and the logarithm of claims severity as a mixture of normal regression. We then employ Dirichlet process (DP) and Pitman–Yor process (PY) as priors for the mixing distribution over the regression parameters. Unlike parametric regression, such models allow each data point to have its own individual parameters, thereby making them highly flexible and resulting in improved prediction accuracy. We describe model fitting using Markov chain Monte Carlo (MCMC) methods and illustrate their applicability using two independent real-world insurance datasets. The proposed BNP models reduced the mean squared error for the French and Belgian claims frequency data by approximately 52% and 33%, respectively (relative to standard Poisson regression), and for the corresponding claims severity data by nearly 45% and 79%, respectively (relative to standard multiple linear regression).