An Interpretable Neural Generalized Linear Model for Insurance Pricing

This article proposes a modeling framework, termed the Actuarial Neural Generalized Linear Model (AN–GLM), which integrates a traditional generalized linear model (GLM) with a deep neural network (DNN). The goal of the proposed algorithm is to increase modeling flexibility while maintaining interpretability, and to offer a practical, implementable alternative to the relatively simple pricing models commonly employed by insurance practitioners, whose predictive accuracy is often limited. The proposed framework consists of two components: a knowledge-based component and a data-driven component. The model is designed to automatically discover a well-performing model specification without sacrificing interpretability, allowing both expert-driven structure and data patterns to jointly determine the Poisson claim frequency. We provide theoretical support for the proposed architecture, establishing conditions under which the proposed model is statistically sound. Furthermore, we assess its empirical performance through extensive simulation experiments and a real world insurance application using policy level data. The results demonstrate that the proposed framework provides both theoretical and practical contributions to the actuarial science field by offering an interpretable, robust, and empirically validated alternative for modern insurance pricing.