Gauss-Markov Loss Prediction in a Linear Model

In a linear model for loss reserving, Gauss-Markov prediction is the natural principle of prediction: It minimizes the mean squared error of prediction over the class of all unbiased linear predictors, and it provides exact formulas for predictors and their mean squared error of prediction. Another advantage of Gauss-Markov prediction is in the fact that the Gauss-Markov predictor of a sum is just the sum of the Gauss-Markov predictors of the single terms of that sum such that essentially only the most elementary quantities have to be predicted.

The use of Gauss-Markov prediction in loss reserving is not new. For example, the additive (or incremental loss ratio) method and the Panning method are based on Gauss-Markov prediction in an appropriate linear model. Here we propose a systematic study of Gauss-Markov prediction in these and several related models. This leads to a variety of new methods of loss reserving, and for each of these models and methods we obtain straightforward estimators of the mean squared error of prediction. To complete the discussion, we also explain certain limitations of the Gauss-Markov principle in connection with the chain-ladder method.

Keywords: loss reserving, linear models