Hierarchical Bayesian Gaussian process regression model for loss reserving using combinations of squared exponential kernels

Abstract

This paper extends the work of Lally and Hartman (2018) on the Gaussian Process (GP) regression with input warping to model claims development and to estimate loss reserves. In an attempt to provide more structure to the loss reserving GP model in improving predictive accuracy and reducing predictive uncertainties, the effects of applying combinations of additive and multiplicative squared exponential kernels into the GP model are being studied. There are evidences of improvements in the estimates of loss reserves when any form of additive kernel is applied in the GP model compared to the multiplicative squared exponential kernel that was proposed in the earlier work.