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

We propose a count-data model with hierarchical random effects for the posterior insurance ratemaking of vehicles belonging to a fleet, by allowing random effects for the fleet, the vehicles, and time. We derive a simple closed-form ratemaking formula based on a hierarchical random-effects specification. We estimate the corresponding econometric model and compute insurance premiums according to the past experience of both the vehicle and the fleet. Our model can be used in other count-data applications with random individual and common effects on events involving many agents having activities with a principal in a hierarchical principal–agent environment, such as in education, health care management, finance, and business firms.