Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Robust General Multivariate Chain Ladder Method

Version 1 : Received: 27 July 2018 / Approved: 30 July 2018 / Online: 30 July 2018 (04:43:55 CEST)

A peer-reviewed article of this Preprint also exists.

Peremans, K.; Van Aelst, S.; Verdonck, T. A Robust General Multivariate Chain Ladder Method. Risks 2018, 6, 108. Peremans, K.; Van Aelst, S.; Verdonck, T. A Robust General Multivariate Chain Ladder Method. Risks 2018, 6, 108.


The chain ladder method is a popular technique to estimate the future reserves needed to handle claims that are not fully settled. Since the predictions of the aggregate portfolio (consisting of different subportfolios) in general differ from the sum of the predictions of the subportfolios, a general multivariate chain ladder (GMCL) method has already been proposed. However, the GMCL method is based on the seemingly unrelated regression (SUR) technique which makes it very sensitive to outliers. To address this issue a robust alternative is introduced which estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to detect which claims have an abnormally large influence on the reserve estimates. We introduce a simulation design to generate artificial multivariate run-off triangles based on the GMCL model and illustrate the importance of taking into account contemporaneous correlations and structural connections between the run-off triangles. By adding contamination to these artificial datasets, the sensitivity of the traditional GMCL method and the good performance of the robust GMCL method is shown. From the analysis of a portfolio from practice it is clear that the robust GMCL method can provide better insight in the structure of the data.


claims reserving; contemporaneous correlations; outliers; robust MM-estimators; seemingly unrelated regression


Computer Science and Mathematics, Probability and Statistics

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