Gaussian Process Models for Incremental Loss Ratios

We develop Gaussian process (GP) models for incremental loss ratios in loss development triangles. Our approach brings a machine learning, spatial-based perspective to stochastic loss modeling. GP regression offers a nonparametric probabilistic distribution regarding future losses, capturing uncertainty quantification across three distinct layers—model risk, correlation risk, and extrinsic uncertainty due to randomness in observed losses. To handle statistical features of loss development analysis—namely, spatial nonstationarity, convergence to ultimate claims, and heteroskedasticity—we develop several novel implementations of fully Bayesian GP models. We perform extensive empirical analyses over the NAIC loss development database across six business lines, comparing and demonstrating the strong performance of our models. Our computational work is performed using the R and Stan programming environments and is publicly shareable.