Hierarchical random effects model for insurance pricing of vehicles belonging to a fleet

Abstract

We propose a hierarchical random effect model for the posterior insurance ratemaking of vehicles belonging to a fleet by allowing random effects for fleet, vehicle, and time. The model is an alternative to the gamma-Dirichlet model of Angers et al ( 2018), which does not allow for a closed form posterior ratemaking formula. Our theoretical extension derives a simple and tractable closed form ratemaking formula based on a hierarchical random effects specification. We estimate the corresponding econometric model and compute insurance premiums in relation to the past experience of both the vehicle and the fleet. Our econometric model can also be applied to any other dynamic count modeling application with random individual, time, and common effects, such as labor contracting, chirurgical accidents, or any other random event implying principals and many agents.

Road Safety for Fleets of Vehicles

“…There are very few statistical analyses of the road accident risks of owners and operators of heavy vehicles (HVOs) in the insurance literature. Some authors have studied the risks of heavy vehicle drivers, without really assessing the aggregate risk of vehicle fleets (Savage, 2011(Savage, , 2012Lueck & Murray, 2011;Angers et al, 2006Angers et al, , 2018Tay, 2005;Desjardins et al, 2021). These studies of HVOs drivers show that fleet owners can influence driver risk through their road safety management.…”