Stochastic Dispersion Mixed Poisson Spatial-Temporal Regression Models for Climate-Related Claim Counts

We introduce a general family of stochastic dispersion mixed Poisson spatial-temporal regression models for climate-related claim counts. The proposed framework can account for overdispersion caused by unobserved heterogeneity stemming from geographical differences and long-term climate patterns. The model is constructed based on a mixing between alternative base distributions: the Poisson, zero-inflated Poisson, and Hurdle Poisson distributions and unit mean continuous prior, or mixing distributions. Spatial variability is accommodated by linking the mean functions of the base distributions through a spatial adjacency matrix, with covariates also included. The temporal component is defined by an intensity process that quantifies heteroskedasticity over time and controls spatial effects for each region. Four versions of the mean function are presented: the spatial effect is combined with the risk characteristic either additively or multiplicatively, and the spatial adjacency matrix is either known a priori or learned during model training. A lasso regularizer is added when the spatial adjacency matrix is learned to reduce overfitting and remove spurious spatial-temporal associations between regions. The model is calibrated by maximizing the likelihood using a novel regularized Expectation-Maximization algorithm. The model's implementation is demonstrated using climate-related claim data from a Greek property insurance company for the period 2012-2022. Supplemental materials and code are available online.