Estimation of Conditional Mean Squared Error of Prediction for Claims Reserving

39 Pages Posted: 3 Jan 2019

See all articles by Mathias Lindholm

Mathias Lindholm

Stockholm University

Filip Lindskog

Stockholm University

Felix Wahl

Stockholm University

Date Written: December 17, 2018

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.

Keywords: mean squared error of prediction, reserving methods, prediction error, estimation error, ultimate claim amount, claims development result, chain ladder method

JEL Classification: G22

Suggested Citation

Lindholm, Mathias and Lindskog, Filip and Wahl, Felix, Estimation of Conditional Mean Squared Error of Prediction for Claims Reserving (December 17, 2018). Available at SSRN: https://ssrn.com/abstract=3302576 or http://dx.doi.org/10.2139/ssrn.3302576

Mathias Lindholm

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Filip Lindskog (Contact Author)

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

Felix Wahl

Stockholm University ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

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