Generic framework for a coherent integration of experience and exposure rating in reinsurance

This article introduces a comprehensive framework that effectively combines experience rating and exposure rating approaches in reinsurance for both short-tail and long-tail businesses. The generic framework applies to all nonlife lines of business and products emphasizing nonproportional treaty business. The approach is based on three pillars that enable a coherent usage of all available information. The first pillar comprises an exposure-based generative model that emulates the generative process leading to the observed claims experience. The second pillar encompasses a standardized reduction procedure that maps each high-dimensional claim object to a few weakly coupled reduced random variables. The third pillar comprises calibrating the generative model with retrospective Bayesian inference. The derived calibration parameters are fed back into the generative model, and the reinsurance contracts covering future cover periods are rated by projecting the calibrated generative model to the cover period and applying the future contract terms.