Multivariate credibility modelling 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 other driving habits. These data are collected while the contract is in force with the help of 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 incorporated in the score as ordinary a priori observable features. This paper proposes 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 different seniority and drivers using their vehicle to different extent, generating varied volumes of telematics data.

Poisson Models With Dynamic Random Effects and Nonnegative Credibilities Per Period

“…Cars could be connected to the internet of things in the near future. Then, the incumbent insurer could have access to the driver's behavior in continuous time (see Wüthrich (2017), Denuit et al (2019) and Gao et al (2019) for an analysis of this type of data). Data will then be organized as risk exposure spells (car trips).…”

From pool to profile: Social consequences of algorithmic prediction in insurance

“…Predictors extrapolated from telematics data integrate traditional statistical predictors, such as age and sex of the driver or vehicle engine power, in view of the possibility of finding strong correlations between past and future (Baecke and Bocca, 2017;Guillen et al, 2019a;Wu¨thrich, 2017). Unlike traditional statistical factors, signals based on telematics data are obtained directly from the behaviour of the insured, while classic statistical data only offers proxy variables with respect to the prediction of future events (Ayuso et al, 2016;Baecke and Bocca, 2017;Denuit et al, 2019;Gao et al, 2019;Guillen et al, 2019a;Ma et al, 2018). Taking this difference into account, some research (Verbelen, 2018Wu¨thrich, 2017: 1ff) has hypothesised that telematic predictors not only work better but could even replace statistical variables in the near future offering, among other things, an effective strategy to circumvent the European legislation which prohibits the use of gender as variable in the pricing of motor insurance policies as a discriminatory practice.…”

A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents

“…Without going into details, given that our objective for this paper is to measure the impact of distance driven, it means that a rating structure based on MVNB with telematics information reduces the unexplained variance of the model, while offering smaller penalties/discounts for drivers who claim/do not claim. We refer to Denuit et al (2019) for predictive rating models with telematics information.…”

“…More recently, Ayuso et al (2019) propose to improve the traditional ratemaking methods by including information related to risk exposure and driving behavior of insured. Denuit et al (2019) use predictive rating with past telematics information in a credibility model. Weidner et al (2016) study driving behavior and vehicle use on different scales of analysis (maneuver, trip or insurance period) by means of form recognition and Fourier analysis methods.…”