Insurance ratemaking for climate-related claim counts using mixed Poisson spatio-temporal and temporal Besag regression models

This paper introduces a unified framework of mixed Poisson spatio-temporal regression models for climate-related property insurance claims. Our approach integrates two model specifications which have been studied separately in the literature, a spatio-temporal (SP) model that explicitly accounts for spatial autocorrelation, and a temporal Besag model that leverages spatial random effects to smooth regional variations. For expository purposes, the spatio-temporal Negative Binomial (SP-NB) and temporal Besag Negative Binomial (Besag-NB) regression models are fitted to claim data related to flood and flood–windstorm events from a Greek property insurance company over the period 2012–2022. Parameter estimation is performed using an Expectation–Maximization algorithm for the SP-NB model and Integrated Nested Laplace Approximations for the Besag-NB model. Finally, the a posteriori (bonus–malus) premium rates derived from these models incorporate property-specific characteristics, geographical information, regional trends, individual experiences, and a flood vulnerability index that accurately reflects true exposure in flood-prone areas.