Chain Ladder and Error Propagation

Abstract

We show how estimators for the chain ladder prediction error in Mack's distribution-free stochastic model can be derived using the error propagation formula. The estimators we obtain are identical to Mack's and other previously published formulae, but we present them in a new, more compact form. We also derive new, equally compact formulae for the prediction error of the claims development result between two arbitrary future horizons - of interest in risk margin calculations for solvency purposes. In each case, we give a split into process error and parameter error. Our proofs identify and exploit symmetries of "chain ladder processes" in a novel way. For the sake of wider practical applicability of the formulae derived, we allow for incomplete historical data and the exclusion of outliers in the triangles.