Bootstrap mean squared error of prediction in loss reserving. The prediction of total loss reserve in non-life insurance company is considered. One of the methods currently used in practice applies the generalized linear model (GLM). In the literature one can find the justified extension of the GLM to the hierarchical generalized linear model (HGLM) for loss reserving. A limitation in the use of the HGLM is the fact that the mean squared error of prediction (MSEP) is expressed by a complex analytical formula. An alternative to the analytical formula is to use the bootstrap procedure approximating the sampling distribution of the MSEP. This paper study two ways of bootstrap. The first one is the parametric bootstrap in which one simulates from fitted values of the HGLM. This approach is sensitive to incorrect fit of the model. Therefore the alternative is the simulation by resampling residuals and adding them back to the fitted values. The paper contains the comparison of this two approaches applying the loss triangle investigated by several authors. Bootstrap procedures are implemented in R software and the code is available to download (see url{}).

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  1. Wolny-Dominiak, Alicja: Bootstrap mean squared error of prediction in loss reserving (2017)