Faculty of Actuarial Science and Insurance Seminar with Mathias Lindholm, Stockholme University.

Speaker:      Dr Mathias Lindholm, Department of Mathematics, Stockholme University.

Title:            Estimation of conditional mean squared error of prediction for claims triangle reserving

Abstract:

The aim of the talk is to present a transparent approach to account for estimation error in the analysis of prediction error of reserving methods and to provide an explicit estimator of the prediction error, in the form of an estimator of the conditional mean squared error of prediction, MSEP. The method of obtaining this estimator relies on using a certain resampling scheme, where the resampling can be carried out either conditionally or unconditionally, together with a single first order Taylor expansion.

The applicability of the approach is illustrated by applying the method to both sequential (conditional) reserving models, e.g. the distribution-free chain ladder model, as well as non-sequential models, e.g. the over-dispersed chain ladder model. In particular, we show that the suggested approach retrieves Mack's famous MSEP formula for the ultimo claim amount and we provide a simple derivation of the MSEP for the claims development result for the distribution-free chain ladder model and discuss why the resulting formula differs from already known similar results. Further, we illustrate the effect of using either conditional or unconditional resampling in the calculation of MSEP for the ultimo claim amount for the distribution-free chain ladder model. The resulting difference turns out to be small - something which can be shown to hold asymptotically for a wider class of sequential linear models to which the distribution-free chain ladder model is a special case.

If time permits we will discuss how the method applies to point process based micro models, distribution-free model selection and Bayesian analyses.

This talk is based on joint work together with Filip Lindskog and Felix Wahl.