Auto Insurance Net Premium Calculation Using Ensemble Methods of Machine Learning in Comparison with Generalized Linear Models

This study is devoted to the calculation of a net premium in auto insurance using different classes of models and different approaches to data pre-processing. All calculations are performed in the framework of a separate modeling of the loss frequency and severity. We study generalized linear models, that are the conventional for auto insurance, in comparison with the ensemble methods of machine learning, specifically gradient boosting over decision trees (XGBoost). Special attention is paid to the distribution of target variables, especially when gradient boosting is employed. Traditional for auto insurance categorization of features and target encoding are considered as methods of feature processing. The results of net premium calculation within different methods are compared using the ordered Lorenz curve and the Gini index. In addition, the fairness criterion (equality of the average premium and the average loss) with respect to different subgroups of objects is checked. From the qualitative comparison of the calculated premiums it follows that the use of gradient boosting and target encoding give an advantage in the formation of a more profitable risk portfolio from the point of view of the ordered Lorenz curve, as well as an advantage in a greater differentiation of objects depending on the risks they carry. This is an important result, since the proposed method, besides for better calculated premiums, requires less data pre-processing and at the same time can be easily interpreted.