Hierarchical Compartmental Reserving Models
07 August 2023, commit 750d536
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 modeling 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 modelers can utilize their expertise to describe specific development features and incorporate prior knowledge into parameter estimation. We also explore the subtle yet important difference between modeling 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 modeling process. Examples and case studies are shown using the probabilistic programming language Stan via the brms package in R.Preface
For the published article please visit the Casualty Actuarial Society website. This on-line version has been updated to use cmdstan instead of rstan as a backend for brms.
To cite this document, please us:
Gesmann, M., and Morris, J. “Hierarchical Compartmental Reserving Models.” Casualty Actuarial Society, CAS Research Papers, 19 Aug. 2020, https://www.casact.org/sites/default/files/2021-02/compartmental-reserving-models-gesmannmorris0820.pdf