Chain-Ladder as Maximum Likelihood Revisited

It has long been known that maximum likelihood estimation in a Poisson model reproduces the chain-ladder technique.  We revisit this model.  A new canonical parametrisation is proposed to circumvent the inherent identification problem in the parametrisation.  The maximum likelihood estimators for the canonical parameter are simple, interpretable and easy to derive.  The boundary problem where all observations in one particular development year or on particular underwriting year is zero is also analysed.