Estimating loss reserves using hierarchical Bayesian Gaussian process regression with input warping

In this paper, we visualize the loss reserve runoff triangle as a spatially-organized data set. We apply Gaussian Process (GP) regression with input warping and several covariance functions to estimate future claims. We then compare our results over a range of product lines, including workers' comp, medical malpractice, and personal auto. Even though the claims development of the lines are very different, the GP method is very flexible and can be applied to each without much customization. We find that our model generally outperforms the classical chain ladder model as well as the recently proposed hierarchical growth curve models of Guszcza (2008) in terms of point-wise predictive accuracy and produces dramatically better estimates of outstanding claims liabilities.