Statistical models for improved insurance risk assessment using telematics

This paper uses a two-step approach to modelling the probability of a policyholder making an auto insurance claim. We perform clustering via Gaussian mixture models and cluster-specific binary regression models. We use telematics information along with traditional auto insurance information and find that the best model incorporates telematics, without the need for dimension reduction via principal components. We also utilise the probabilistic estimates from the mixture model to account for the uncertainty in the cluster assignments. The clustering process allows for the creation of driving profiles and offers a fairer method for policyholder segmentation than when clustering is not used. By fitting separate regression models to the observations from the respective clusters, we are able to offer differential pricing, which recognises that policyholders have different exposures to risk despite having similar covariate information, such as total miles driven. The approach outlined in this paper offers an explainable and interpretable model that can compete with black box models. Our comparisons are based on a synthesised telematics data set that was emulated from a real insurance data set.