Nonparametric intercept regularization for insurance claim frequency regression models

In a subgroup analysis for an actuarial problem, the goal is for the investigator to classify the policyholders into unique groups, where the claims experience within each group are made as homogenous as possible. In this paper, we illustrate how the alternating direction method of multipliers (ADMM) approach for subgroup analysis can be modified so that it can be more easily incorporated into an insurance claims analysis. We present an approach to penalize adjacent coefficients only and show how the algorithm can be implemented for fast estimation of the parameters. We present three different cases of the model, depending on the level of dependence among the different coverage groups within the data. In addition, we provide an interpretation of the credibility problem using both random effects and fixed effects, where the fixed effects approach corresponds to the ADMM approach to subgroup analysis, while the random effects approach represents the classic Bayesian approach. In an empirical study, we demonstrate how these approaches can be applied to real data using the Wisconsin Local Government Property Insurance Fund data. Our results show that the presented approach to subgroup analysis could provide a classification of the policyholders that improves the prediction accuracy of the claim frequencies in case other classifying variables are unavailable in the data.