Standard errors of prediction in claims reserving: a comparison of methods. Analytic and bootstrap estimates of prediction errors in claims reserving

Document description

Renshaw and Verrall (1994) have suggested a stochastic claims reserving model which reproduces the reserve estimates provided by the standard chain ladder model (subject to constraints on the pattern of negative incremental claims). Their model falls within the generalised linear modelling (GLM) framework and can be fitted easily using standard statistical software packages. Having fitted the model, it is possible to obtain analytic prediction errors of the reserves. The GLM framework suggests appropriate goodness-of-fit measures, and also gives a choice of appropriate residual definitions which can be used for informal diagnostic checks of the fitted model. Residuals can also be used in a bootstrap exercise providing a computationally simple method of obtaining estimates of the reserve prediction errors. In this paper, we consider an appropriate residual definition for this purpose, and show how the bootstrap prediction errors can be computed easily in a spreadsheet, without the need for statistical software packages. The bootstrap prediction errors are compared with their analytic equivalent, and also compared with other methods commonly used, including MackUOTEs distribution free approach (Mack 1993) and methods based on log-linear models.