Hierarchical Compartmental Reserving Models

Abstract

Hierarchical compartmental reserving models provide a parametric framework for describing aggregate insurance claims processes using differential equations. We discuss how these models can be specified in a fully Bayesian modelling framework to jointly fit paid and outstanding claims development data, taking into account the random nature of claims and underlying latent process parameters. We demonstrate how modellers can utilise their expertise to describe specific development features and incorporate prior knowledge into parameter estimation. We also explore the subtle, yet important difference between modelling incremental and cumulative claims payments. Finally, we discuss parameter variation across multiple dimensions and introduce an approach to incorporate market cycle data such as rate changes into the modelling process. Examples and case studies are shown using the probabilistic programming language Stan via the ‘brms’ package in R.

Publication
CAS Research Report