Chain Ladder Plus: a versatile approach for claims reserving

This paper introduces yet another stochastic model replicating chain ladder estimates and furthermore considers extensions that add flexibility to the modeling. We show that there is a one-to-one correspondence between chain-ladder's individual development factors and averaged hazard rates in reversed development time. By exploiting this relationship, we introduce a new model that is able to replicate chain ladder's development factors. The replicating model is a GLM model with averaged hazard rates 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, the resulting model only has half the number of parameters compared to when modeling the claim amounts; because exposure is not modeled. The 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.