Insurance loss modeling with gradient tree-boosted mixture models

In actuarial practice, finite mixture model is one widely applied statistical method to model the insurance loss. Although the Expectation-Maximization (EM) algorithm usually plays an essential tool for the parameter estimation of mixture models, it suffers from other issues which cause unstable predictions. For example, feature engineering and variable selection are two crucial modeling issues that are challenging for mixture models as they involve several component models. Avoiding overfitting is another technical concern of the modeling method for the prediction of future losses. To address those issues, we propose an Expectation-Boosting (EB) algorithm, which implements the gradient boosting decision trees to adaptively increase the likelihood in the second step. Our proposed EB algorithm can estimate both the mixing probabilities and the component parameters non-parametrically and overfitting-sensitively, and further perform automated feature engineering, model fitting, and variable selection simultaneously, which fully explores the predictive power of feature space. Moreover, the proposed algorithm can be combined with parallel computation methods to improve computation efficiency. Finally, we conduct two simulation studies to show the good performance of the proposed algorithm and an empirical analysis of the claim amounts for illustration.