Application of generalized linear Models in Pricing Usage-Based Insurance

Abstract

Technological advancements and big data adaptations are broadly impacting the insurance industry. Usage Based Insurance is a result of the emerging technologies and big data adaptation as it is based on telematics data. Incorporating telematics data in auto insurance pricing models reduces moral hazard and adverse selection phenomena which arise from information asymmetry. Traditional auto insurance does not consider how and when driving is done which is part of telematics data. Thus, there is need for insurers to rede ne their pricing models and risk selection criteria to include telematics data. This study aims to model claim frequency and severity using generalized linear models in order to evaluate the impact of distance driven, speed and time of driving on premium rates which are part of telematics data. Generalized linear models have been applied by insurers in ratemaking, reserving and underwriting general insurance policies for over 50 years. The models allow for response variables with non-gaussian error distributions hence suitable for modelling auto insurance claim frequency and severity. Speci cally, the gamma and Poisson generalized models have been employed in this study. The gamma has been used to model claim severity while claim frequency is modelled by the Poisson model. From the insurance portfolio analyzed, speed and distance variables were found to be signi cant while time was not signi cant in both models. Coe cient estimates for distance categories were positive indicating positive correlation. Speed band categories had negative estimate values indicating negative correlation. We observe that severity and frequency increase with distance and speed. Similarly, the pure premium increases with distance and speed. These ndings are representative of particular auto insurance policies and do not represent a generalized trend. Results of this study can help auto insurance industries to evaluate the risk of driving more precisely and come up with personalized premiums for drivers based on their real time driving factors.