Spatial copula-based modeling of claim frequency and claim size in third-party car insurance: A Poisson-mixed approach for predictive analysis

The number and amount of claims, referred to as the sum of claims or the total claim/loss amounts in insurance literature, are crucial pieces of information for insurance companies. The analysis of these numerical values can provide essential insights for targeted planning. This study explores a spatial approach for jointly modeling claim frequency and claim size. We assume that the number of accidents follows a Poisson distribution with a variable mean, and this mean, in turn, has a distribution commonly known as a mixed distribution. The spatial dependence structure within the observations is then modeled using an appropriate copula. By estimating the parameters of the proposed model, we draw prediction maps for both claim frequencies and total claim size. These maps will contribute to the prediction of future claim dynamics, offering insurers the opportunity to refine their market strategies and enhance their overall risk management approach based on evolving spatial patterns.