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

Abstract

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.