Replicating and extending chain-ladder via an age-period-cohort structure on the claim development in a run-off triangle

TL;DR

This paper presents a new stochastic model for claim development that replicates chain-ladder estimates using a GLM framework focused on hazard rates, offering greater flexibility and simplicity, with an accompanying R package for practical application.

Contribution

The paper introduces a novel GLM-based model that replicates chain-ladder estimates through hazard rates, reducing complexity and enabling flexible extensions, along with a new R package for implementation.

Findings

Model closely aligns with chain-ladder estimates

Reduced parameter count simplifies extensions

Empirical study on 30 datasets demonstrates effectiveness

Abstract

This paper introduces yet another stochastic model replicating chain-ladder estimates and furthermore considers extensions that add flexibility to the modeling. In its simplest form, the proposed model replicates the chain-ladder's development factors using a GLM model with averaged hazard rates running in reversed development time as response. This is in contrast to the existing reserving literature within the GLM framework where claim amounts are modeled as response. Modeling the averaged hazard rate corresponds to modeling the claim development and is arguably closer to the actual chain-ladder algorithm. Furthermore, since exposure does not need to be modeled, the model only has half the number of parameters compared to when modeling the claim amounts. This lesser complexity can be used to easily introduce model extensions that may better fit the data. We provide a new R-package, $\texttt{clmplus}$, where the models are implemented and can be fed with run-off triangles. We conduct an empirical study on 30 publicly available run-off triangles making a case for the benefit of having $\texttt{clmplus}$ in the actuary's toolbox.