Bootstrap Methods for Loss Reserve Uncertainty

The Bootstrap Approach

Bootstrap methods for loss reserving generate a full predictive distribution of reserve estimates, going beyond the point estimates and standard errors provided by Mack's model. The over-dispersed Poisson (ODP) bootstrap, popularized by England and Verrall, involves fitting the chain ladder model as a GLM, extracting standardized residuals, resampling those residuals with replacement, and reconstructing pseudo-triangles from which new reserve estimates are computed. Repeating this process thousands of times produces a distribution of possible reserve outcomes, enabling actuaries to compute percentiles, Value at Risk, and Tail Value at Risk for the reserve.

Implementation Details

Practical bootstrap implementation requires attention to several technical issues. Negative incremental values in the triangle must be handled carefully, as they violate the Poisson assumption. Common approaches include adjusting the model or shifting incremental values. The inclusion of process variance (simulating new observations from the fitted distribution) in addition to estimation variance (from resampling residuals) is essential for capturing the full predictive uncertainty. Results should be validated by comparing the mean and standard deviation of the bootstrap distribution with Mack's analytical estimates. Software implementations are available in R (ChainLadder package) and Python.