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 particular interesting model was proposed by Mack: Under the assumption of his model, Mack proved that the chain ladder predictors on non-observable aggregate claims are unbiased, and Schmidt and Schnaus 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.

Keywords: Chain ladder method; IBNR claims; Reserving; Prediction