A Comparison of Resampling Methods for Bootstrapping Triangle GLMs

By Thomas Hartl

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Bootstrapping is often employed for quantifying the inherent variability of development triangle GLMs. While easy to implement, bootstrapping approaches frequently break down when dealing with actual data sets. Often this happens because linear rescaling leads to negative values in the resampled incremental develop­ment data. We introduce two computationally efficient methods for avoiding this pitfall: split­linear rescaling and parametric resampling using a limited Pareto distribution. After describ­ing the essential mathematical properties of the techniques, we present a performance comparison based on a VBA for Excel bootstrapping application. The VBA application is available on request from the author.

Keywords: Bootstrapping and resampling methods, generalized linear modeling, efficient simulation, stochastic reserving, regression


Hartl, Thomas, "A Comparison of Resampling Methods for Bootstrapping Triangle GLMs," Variance 11:1, 2018, pp. 60-73.

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Variance (ISSN 1940-6452) 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.