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The Actuary The magazine of the Institute & Faculty of Actuaries


We were interested in the articleon general insurance reservesuncertainty that appeared in theJune issue of The Actuary – it isgood to see this being discussed bythe actuarial profession. Readersmight have been left with the mistakenimpression that the ‘bootstrapping’and Mack approachesare mutually exclusive. In fact,bootstrapping is simply a processthat can be applied to wellspecifiedmodels, and should notbe confused with the underlyingmodel itself.

For example, it is possible to bootstrap Mack’s model, as described in the forthcoming paper, ‘Predictive distributions of outstanding liabilities in general insurance’, to appear in the Annals of Actuarial Science. Presumably, when the authors refer to bootstrapping, they are referring to bootstrapping a special case of the over-dispersed Poisson model, although this is not stated. One advantage of bootstrapping is that it provides a predictive distribution, in addition to the first two moments (mean and variance). Mack’s model, as published in 1993, only considers analytic estimators of the first two moments, and additional distributional assumptions are required to provide percentiles. The assumptions used in this respect in the example are not stated. Furthermore, it is not clear what measure was used to provide the percentiles (in the figure) that is appropriate for all origin years.

We agree with the authors that estimating variability is, and will continue to be, an important part of the forecasting process.