A Sparse Deep Two-part Model for Nonlife Insurance Claims with Dependent Frequency and Severity

Frequency-severity modeling of insurance claims is critical to various actuarial applications in nonlife insurance. In this article, we introduce a sparse deep learning method for handling the joint distribution of claim frequency and severity. The proposed sparse deep learning method allows us to capture nonlinear covariates effect and perform variable selection simultaneously in the existing frequency-severity framework. Specifically, we employ basis functions formed by deep feedforward neural networks in the two-part model and use versions of group lasso regularization to carry out variable selection in the neural networks. The method is investigated in extensive simulation studies where we examine models for both frequency and severity of insurance claims and we discuss regularization for both continuous and categorical rating variables. In predictive applications, we show the favorable performance of the proposed method using a data set in healthcare utilization