Multivariate credibility modeling for usage-based motor insurance pricing with behavioural data

Abstract

Pay-How-You-Drive (PHYD) or Usage-Based (UB) systems for automobile insurance provide actuaries with behavioural risk factors, such as the time of the day, average speeds and driving habits. These data are collected while the contract is in force thanks to telematic devices installed in the vehicle. They thus fall in the category of a posteriori information that becomes available after contract initiation. For this reason, they must be included in the actuarial pricing by means of credibility updating mechanisms instead of being included in the score as ordinary a priori observable features. We propose the use of multivariate mixed models to describe the joint dynamics of telematics data and claim frequencies. Future premiums, incorporating past experience can then be determined using the predictive distribution of claim characteristics given past history. This approach allows the actuary to deal with the variety of situations encountered in insurance practice, ranging from new drivers without telematics record to contracts with di erent seniority and drivers using their vehicle to di erent extent, generating varied volumes of telematics data.