Hierarchical Growth Curve Models for Loss Reserving

Hierarchical or multilevel modeling extends traditional GLM or non-linear models by giving certain of the model parameters their own probability sub-models. Hierarchical modeling can be viewed as an extension of Bayesian credibility theory that allows one to build models for data that are grouped along a dimension containing multiple levels. In particular, hierarchical modeling can be used to analyze longitudinal datasets containing multiple observations for each of several subjects. A contention of this paper is that traditional loss reserving triangles are most naturally regarded as longitudinal datasets. Non-linear hierarchical models – known also as non-linear mixed effects models – therefore provide a natural and flexible framework in which to model loss development across multiple accident years. The use of non-linear growth curves together with multilevel modeling techniques allows one to build models that are at once parsimonious and easy to interpret. Finally, because they incorporate growth curves, such models obviate the need to specify tail factors.

Keywords: Stochastic loss reserving, hierarchical models, multilevel models, nonlinear mixed effects models, growth models, repeated measurements, longitudinal data, Bayesian credibility, shrinkage, R.