Abstract
This paper studies estimation of 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 runoff 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 generalization 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 conditional mean square 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 is 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.
Highlights
Actuarial reserving amounts to forecasting future claim costs from incurred claims that the insurer is unaware of and from claims known to the insurer that may lead to future claim costs
The predictor commonly used is an expectation of future claim costs computed with respect to a parametric model, conditional on the currently observed data, where the unknown parameter vector is replaced by a parameter estimator
A natural question is how to calculate an estimate of the conditional mean squared error of prediction, MSEP, given the observed data, so that this estimate is a fair assessment of the accuracy of the predictor
Summary
Actuarial reserving amounts to forecasting future claim costs from incurred claims that the insurer is unaware of and from claims known to the insurer that may lead to future claim costs. The approaches considered in Buchwalder et al (2006) are compatible with the general approach of the present paper for the special case of the distribution-free chain ladder model when assessing the prediction error of the ultimate claim amount. The use of this kind of linear approximation is very common in the literature analysing prediction error It appears naturally in the error propagation argument used for assessing prediction error in the setting of the distribution-free chain ladder model in Röhr (2016), the general approach taken in Röhr (2016) is different from the one presented here. For the overdispersed Poisson chain ladder model we derive a (semi-) analytical MSEP-approximation which turns out to coincide with the well-known estimator from Renshaw (1994)
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