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A Robust General Multivariate Chain Ladder Method

Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2018, 6(4), 108;
Received: 27 July 2018 / Revised: 19 September 2018 / Accepted: 21 September 2018 / Published: 30 September 2018
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) do not need to be equal to 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, we propose a robust alternative that estimates the SUR parameters in a more outlier resistant way. With the robust methodology it is possible to automatically flag the claims with a significantly 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. View Full-Text
Keywords: claims reserving; contemporaneous correlations; outliers; robust MM-estimators; seemingly unrelated regression claims reserving; contemporaneous correlations; outliers; robust MM-estimators; seemingly unrelated regression
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Peremans, K.; Van Aelst, S.; Verdonck, T. A Robust General Multivariate Chain Ladder Method. Risks 2018, 6, 108.

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