This paper studies estimation of the conditional mean squared error of prediction, conditional on what is known at the time of prediction. The particular problem considered is the assessment of actuarial reserving methods given data in the form of run-off triangles (trapezoids), where the use of prediction assessment based on out-of-sample performance is not an option. The prediction assessment principle advocated here can be viewed as a generalisation of Akaike’s final prediction error. A direct application of this simple principle in the setting of a data-generating process given in terms of a sequence of general linear models yields an estimator of the conditional mean squared error of prediction that can be computed explicitly for a wide range of models within this model class. Mack’s distribution-free chain ladder model and the corresponding estimator of the prediction error for the ultimate claim amount are shown to be a special case. It is demonstrated that the prediction assessment principle easily applies to quite different data-generating processes and results in estimators that have been studied in the literature.

We consider the Bayesian over-dispersed Poisson (ODP) model for claims reserving in general insurance. We choose two different types of prior distributions for the parameters and then study the different Bayesian predictors. This study leads, on the one hand, to the classical chain ladder predictor and, on the other hand, to Bornhuetter & Ferguson predictors. We highlight (either analytically or numerically) how these predictors are obtained and how their prediction uncertainty can be determined.

The prediction of adequate claims reserves is a major subject in actuarial practice and science. Due to their simplicity, the chain ladder (CL) and Bornhuetter–Ferguson (BF) methods are the most commonly used claims reserving methods in practice. However, in contrast to the CL method, no estimator for the conditional mean square error of prediction (MSEP) of the ultimate claim has been derived in the BF method until now, and as such, this paper aims to fill that gap. This will be done in the framework of generalized linear models (GLM) using the (overdispersed) Poisson model motivation for the use of CL factor estimates in the estimation of the claims development pattern.

We revisit the stochastic model of Alai et al. (2009) for the Bornhuetter-Ferguson claims reserving method, Bornhuetter & Ferguson (1972). We derive an estimator of its conditional mean square error of prediction (MSEP) using an approach that is based on generalized linear models and maximum likelihood estimators for the model parameters. This approach leads to simple formulas, which can easily be implemented in a spreadsheet.

In recent Solvency II considerations much effort has been put into the development of appropriate models for the study of the one-year loss reserving uncertainty in non-life insurance. In this article we derive formulas for the conditional mean square error of prediction of the one-year claims development result in the context of the Bayes chain ladder model studied in Gisler-Wüthrich. The key to these formulas is a recursive representation for the results obtained in Gisler-Wüthrich.