Spatial Tweedie exponential dispersion models: an application to insurance rate-making

In this paper we propose a statistical modeling framework that contributes to advancing methods for modeling insurance policy premium in the actuarial literature. Specification of separate frequency and severity models, accounting for territorial risk and performing accurate inference, are some of the challenges an actuary faces while modeling policy premium. Policy premiums are characterized to follow a semi-continuous probability distribution, featuring a non-zero probability at zero along with a positive continuous support. Interpretability is a concern when quantifying unobserved risks premiums face from spatial variation. Commonly used strategies in the literature are known to successfully quantify this risk, but do not necessarily produce interpretable estimates. Resorting to frequency-severity models leaves the actuary indecisive about the specification of covariates and spatial effects. The novelty of our proposed approach lies in the development of a parsimonious and interpretable zero-adjusted modeling framework that allows for joint estimation of the effect of policy and individual characteristics on the mean premium and dispersion, while quantifying spatial variability in the mean model. The developed methods are applied to a database featuring premiums arising from the collision coverage in insurance policies for motor vehicles within the state of Connecticut, USA, for the year 2008.