Multioutput Gaussian Processes for Loss Ratio Development

Gaussian processes are receiving increased attention for their use in loss development. Their flexibility in fitting time series data and reliable estimates of uncertainty can be useful for loss reserving and enterprise risk management. This paper examines a multioutput Gaussian process model to learn incremental paid and case loss ratio patterns simultaneously. Shared learning of these development patterns benefits the projection of both and more accurately identifies uncertainty. Using the NAIC loss development database, we show strong predictive performance for both point and distribution estimates.