A Poisson Mixture Model of Claim Counts to Improve Insurance Claim Predictions Using Incomplete Data/ Asymmetric Data: A Case Study with Telematics Insurance

Abstract

In the evolving landscape of insurance analytics, integrating traditional and telematics data is pivotal for enhancing the accuracy of claim predictions. This study introduces a two-fold approach utilizing a Poisson mixture model to merge these distinct data streams effectively. Initially, we apply the Poisson mixture model to traditional insurance features common to both datasets, employing Hamiltonian Monte Carlo (HMC) and Metropolis-Hastings algorithms separately for model fitting. Subsequently,the predicted claim counts derived from the Poisson mixture model are used as an offset to fit a Poisson generalized linear model (GLM) exclusively with telematics-based features. Our focus is on assessing the suitability of HMC and Metropolis-Hastings for addressing data integration challenges within Poisson mixture frameworks. Comparative analysis reveals that while HMC demands more computational time to achieve convergence, it exhibits superior performance in parameter estimation in scenarios with increased model complexity. This study underscores the potential of advanced Monte Carlo methods in refining predictive models by leveraging the synergy between traditional and telematics data sources.