Abstract
Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that we generalize for panel count data. To correctly observe the relationship between distance driven and claim frequency, we show that a Poisson distribution with fixed effects should be used because it removes residual heterogeneity that was incorrectly captured by previous models based on GAM and GAMLSS theory. We show that an approximately linear relationship between distance driven and claim frequency can be derived. We argue that this approach can be used to compute the premium surcharge for additional kilometers the insured wants to drive, or as the basis to construct Pay-as-you-drive (PAYD) insurance for self-service vehicles. All models are illustrated using data from a major Canadian insurance company.
Highlights
In the past decade, new technologies such as GPS-collected data have emerged, which offer new ways to approach car insurance pricing
We have studied the relationship between claim frequency and the distance driven through different models by observing smooth functions
We first reproduced with our data the model proposed by Boucher et al (2017) and observed what the authors called the “learning effect,” where the expected number of claims seems to decrease as kilometers driven increase
Summary
New technologies such as GPS-collected data have emerged, which offer new ways to approach car insurance pricing. Before GPS and telematics devices, the insurance industry had to rely on proxy variables such as territory, gender and age of the drivers to measure risk Such covariates only describe the general behavior of insured in those groups. The authors argue that a representation in two dimensions is sufficient to preserve most of the driving information, meaning that it is possible to obtain continuous representations with small-dimensional data This representation could be included in a Generalized Additive Model (GAM), as in the study by Gao et al (2019).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
