An observation-driven state-space model for claims size modelling

State-space models are popular in econometrics. Recently, these models have gained some popularity in the actuarial literature. The best known state-space models are of the Kalman-filter type. These are called parameter-driven because the observations do not impact the state-space dynamics. A second less well-known class of state-space models comprises the so-called observation-driven state-space models where the state-space dynamics is also impacted by the actual observations. A typical example is the Poisson-gamma observation-driven state-space model for count data, which is fully analytically tractable. The goal of this article is to develop a gamma-gamma observation-driven state-space model for claim size modelling. We provide fully tractable versions of gamma-gamma observation-driven state-space models; these versions extend the work of the Smith–Miller model by allowing for a fully flexible variance behaviour. Additionally, we demonstrate that the proposed model aligns with evolutionary credibility, a methodology in insurance that dynamically adjusts premium rates over time using evolving data.