Penalising unexplainability in neural networks for predicting payments per claim incurred

In actuarial modelling of risk pricing and loss reserving in general insurance, also known as P&C or non-life insurance, there is business value in the predictive power and automation through machine learning. However, interpretability can be critical, especially in explaining to key stakeholders and regulators. We present a granular machine learning model framework to jointly predict loss development and segment risk pricing. Generalising the Payments per Claim Incurred (PPCI) loss reserving method with risk variables and residual neural networks, this combines interpretable linear and sophisticated neural network components so that the "unexplainable" component can be identified and regularised with a separate penalty. The model is tested for a real-life insurance dataset, and generally outperformed PPCI on predicting ultimate loss for sufficient sample size.