Further Observations on Chain Ladder Bias

Abstract

The chain ladder forecast (CLF) has previously been shown to be biased upward. The present paper calculates the second order approximation to the magnitude of the bias, ie the Taylor series for the bias truncated at terms involving second order moments of observations. Some order relations between data triangles are obtained with respect to this second order bias. While the prediction error of the CLF, as a predictor of loss reserve, does not have zero mean, it does have zero median under certain circumstances. Some numerical consequences are explored.