Modelling Claim Frequency with Spatial Effects for Accurate Insurance Premium Cost Calculations

This paper challenges the traditional assumption of independence between claim counts and amounts in non-life insurance. It explores the effectiveness of Generalized Linear Models (GLMs) in analyzing claim frequency data, a key component of accurate premium pricing. The proposed approach utilizes GLMs for both the marginal frequency and conditional severity of claims. Dependence between these factors is introduced by incorporating the number of claims as a covariate in the severity model. This strategy offers ease of implementation and interpretability, particularly when combined with Poisson counts and a log-link function. The resulting pure premium calculation considers the marginal mean frequency, a modified severity, and a dependence correction term. The paper further establishes the importance of spatial factors in claim frequency modelling for insurance businesses. It proposes a novel GLMM with a CAR (Conditional Autoregressive) model to account for these spatial effects. The impact of spatial factors on pure premium calculations is evaluated using simulated claim data.