High-dimensional claim severity modeling with misrepresentation adjustment via deep learning

In insurance underwriting, applicants may deliberately misrepresent certain risk factors to secure lower premiums. However, from the insurer’s perspective, verifying the true status of these risk factors is both time-consuming and resource-intensive. To address this challenge, we propose a novel deep learning framework for claim severity modeling that explicitly accounts for potential misrepresentation of a binary risk factor. To mitigate the identifiability issues arising from the unobservable nature of misrepresentation in neural networks, we introduce a regularization term based on Kullback–Leibler (KL) divergence. This term serves as a conservative anchor by penalizing deviations from a baseline assumption of honesty, unless such deviations are strongly supported by empirical evidence. Additionally, we introduce an innovative regularization term, the upper L 1L1$L_1$ group minimax concave penalty (upper L 1L1$L_1$-gMCP), within the neural network’s loss function. This term facilitates effective variable selection in high-dimensional settings. Through comprehensive simulation studies, we demonstrate that our method maintains robust performance regardless of whether misrepresentation is present in the data. The proposed model excels in both prediction accuracy and the identification of relevant risk factors. We further validate our approach using real-world data from the 2014 Medical Expenditure Panel Survey, treating reported insurance status as a potentially misrepresented variable.