Bivariate Poisson Credibility Model and Bonus–Malus Scale for Claim and Near-Claim Events

Abstract

With the emergence of telematics, huge amounts of data have become available to insurers, raising the question of their integration into motor insurance pricing. Near-claim events are dangerous events that could have triggered a claim. Typically, they correspond to harsh deceleration, acceleration, or cornering. Based on the motor third-party liability insurance portfolio of an insurance company operating in Belgium, we highlight that deceleration events are the best candidates for characterizing near-claim events. Then, we propose to integrate these events in the pricing structure in addition to a policyholder’s claim history with the help of a bivariate Poisson-Lognormal credibility model. Finally, we design an original bonus–malus scale based on both claim and near-claim events.