A Flexible Hierarchical Insurance Claims Model with Gradient Boosting and Copulas

Predicting future claims is an important task for actuaries, and sophisticating the claim modeling process allows insurers to be more competitive and to stay financially sound. We propose a hierarchical claim model that refines traditional methods by considering dependence between payment occurrences with a multinomial distribution and between payment amounts with copulas. We perform prediction with covariates using XGBoost, a scalable gradient boosting algorithm, gaining predictive power over the frequently used generalized linear models. The model construction and fitting is illustrated with a real auto insurance dataset from a large Canadian insurance company. The use of XGBoost is well suited for such big data containing a lot of insureds and covariates. To our knowledge, the validity of the copula inference with gradient boosting margins has not been demonstrated in past literature, so we perform simulation studies to assess the performance of methods based on ranks of residuals. We show some applications of our model and compare the performance with reference models. Results show that the dependence components of our model improve the segmentation quality and better replicate the global stochasticity.