Claims Run-Off Uncertainty: The Full Picture

Abstract

The aim of this contribution is to revisit, clarify and complete the picture of uncertainty estimates in the chain-ladder (CL) claims reserving method. Therefore, we consider the conditional mean square error of prediction (MSEP) of the total prediction uncertainty (using Mack’s formula) and the one of the one-year prediction uncertainty (using the Merz-Wüthrich formula). We discuss and compare these two formulas and we derive the missing pieces that close the gap between the one-year and total run-off uncertainty view.

Keywords: Claims reserving, chain-ladder method, gamma-gamma Bayesian chain-ladder model, conditional mean square error of prediction, claims development result, one-year uncertainty, run-off uncertainty, Mack’s formula, Merz- Wüthrich formula, risk margin, R package ChainLadder

JEL Classification: G22, G28, D46