Loss Reserving Prediction Error with Special Reference to a Tweedie Sub-Family

Abstract

The paper is concerned with model distribution error in loss reserving, i.e. the error in the loss reserve that arises from the wrong choice of distribution of observations. This is considered within the Tweedie family of distributions, examining the prediction error that occurs when one value of the Tweedie dispersion parameter p is correct, but a different one assumed in the modelling a claim array. The study is carried out under the condition that the ratio of mean to variance is constant across all cells of the array, a condition that is found commonly compatible with real data sets. The main result of the paper is that, when cells have largish coefficients of variation under the constant mean-to-variance condition, and the array can be modelled with a GLM, the MSEP of the loss reserve is relatively insensitive to the value of p. This implies that model distribution error can often be dismissed as small in many situations where MSEP of loss reserve is the measure of interest.