Non-optimal prediction by the chain ladder method

The chain ladder method is one of the most common methods for reserving, and various attempts have been made to justify it in a stochastic model. A particularly interesting model was proposed by Mack (1993, 1994a,b): Under the assumptions of his model, Mack proved that the chain ladder predictors of non-observable aggregate claims are unbiased, and Schmidt and Schnaus (1996) proved that the chain ladder predictor for the first non-observable calendar year is also optimal in the sense that it minimizes expected squared error loss over a wide class of unbiased predictors. In the present paper, it is shown that optimality fails for the chain ladder predictor for the second non-observable calendar year.