A two-stage model for high-risk prediction in insurance ratemaking: Asymptotics and inference

In actuarial practice, modern statistical methodologies are one primary consideration for real actuarial problems, such as premium calculation, insurance preservation, marginal risk analysis, etc. The claim data usually possesses a complex data structure, so direct applications of statistical techniques will result in unstable prediction. For example, insurance losses are semicontinuous variables, where a positive mass on zero is often associated with an otherwise positive continuous outcome. Thus, the prediction of high-risk events of claim data needs additional treatment to avoid significant underestimation. In this article, we propose a new two-stage composite quantile regression model for the prediction of the value-at-risks of the aggregate insurance losses. As we are interested in the statistical properties of our method, the asymptotic results are established corresponding to different types of risk levels. Finally, some simulation studies and a data analysis are implemented for the illustration of our method.