Bootstrap Estimation of the Predictive Distributions of Reserves Using Paid and Incurred Claims

By Huijuan Liu, Richard Verrall

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Abstract

This paper presents a bootstrap approach to estimate the prediction distributions of reserves produced by the Munich chain ladder (MCL) model. The MCL model was introduced by Quarg and Mack (2004) and takes into account both paid and incurred claims information. In order to produce bootstrap distributions, this paper addresses the application of bootstrapping methods to dependent data, with the consequence that correlations are considered. Numerical examples are provided to illustrate the algorithm and the prediction errors are compared for the new bootstrapping method applied to MCL and a more standard bootstrapping method applied to the chain ladder technique.

KEYWORDS: Bootstrap, Munich chain ladder, correlation, simulation

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Citation

Liu, Huijuan, and Richard Verrall, "Bootstrap Estimation of the Predictive Distributions of Reserves Using Paid and Incurred Claims," Variance 4:2, 2010, pp. 121-135.

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Variance is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.