Claim Prediction and Premium Pricing for Telematics Auto-Insurance Data Using Poisson Regression with Lasso Regularisation

We analyse a large telematics data with 65 driving variables (DVs) and insurance claim counts for 14,157 drivers. Our aim is to predict future claims according to driving behaviour measured by the DVs, to identify important DVs that differentiate driving behaviours, classify drivers according to their driving behaviours and calculate the premium that reflects actual driving risk. We use two-stage Poisson, Poisson mixture and zero-inflated Poisson regression models with lasso regularisation to minimise the chance of over-fitting for this noisy data with over 92 percent of zero claims. We consider different lasso regularisation techniques and further robustify the results with 100 repeats. DVs are selected only if they are frequently selected over the repeats. We assess model performances with several criteria, namely Bayesian Information Criterion, Mean Square Error, Pearson correlation and area under receiver operating characteristic curve. Finally, we propose a usage-based experience-rating premium calculation method using the predicted claims