A New Expression for the True One-Year Prediction Uncertainty in the Chain-Ladder Model of Mack

Abstract

In this paper we provide a new expression for the true one-year prediction uncertainty within the chain-ladder model of Mack, which can be useful for quantification and sensitivity analysis.
We also show that, in case sufficiently large sized claims trapezoids are considered (which might not be easily available in practice though), classical estimators for the true one-year prediction uncertainty (notably the Merz-Wüthrich and the Gisler formulas) mostly succeed to respectably estimate the true uncertainty. This is highly linked with the fact that in this case the traditional estimator for the sigma squared parameters results to have a sufficiently low variance.
Otherwise, for instance when considering small sized claims triangles, the classical estimators might be particularly prone to materially fail in estimating the true value.

Keywords: Claims reserving, distribution free chain-ladder model, conditional mean square error of prediction, one-year prediction uncertainty

JEL Classification: G22, G28