An Observation-Driven State-Space Model for Claims Size Modeling

TL;DR

This paper introduces a new Gamma-Gamma observation-driven state-space model for claim size modeling, offering full analytical tractability and flexible variance behavior, with applications in dynamic insurance premium adjustment.

Contribution

It develops a fully tractable Gamma-Gamma state-space model that extends previous work by enabling flexible variance behavior and aligns with evolutionary credibility in insurance.

Findings

Model is fully analytically tractable.

Allows for flexible variance behavior.

Aligns with evolutionary credibility methodology.

Abstract

State-space models are popular models in econometrics. Recently, these models have gained some popularity in the actuarial literature. The best known state-space models are of Kalman-filter type. These models are so-called parameter-driven because the observations do not impact the state-space dynamics. A second less well-known class of state-space models are 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 counts data. This Poisson-Gamma model is fully analytically tractable. The goal of this paper is to develop a Gamma- Gamma observation-driven state-space model for claim size modeling. We provide fully tractable versions of Gamma-Gamma observation-driven state-space models, and these versions extend the work of Smith and Miller (1986) by allowing for a fully flexible variance behavior. 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.