Bias-regularised neural-network metamodelling of insurance portfolio risk

Deep learning models have attracted considerable attention in metamodelling of financial risks for large insurance portfolios. Those models, however, are generally trained in disregard of the collective nature of the data in the portfolio under study. Consequently, the training procedure often suffers from slow convergence, and the trained model often has poor accuracy. This is particularly evident in the presence of extreme individual contracts. In this paper, we advocate the view that the training of a meta-model for a portfolio should be guided by portfolio-level metrics. In particular, we propose an intuitive loss regulariser that explicitly accounts for the portfolio-level bias. Further, this training regulariser can be easily implemented with the minibatch stochastic gradient descent commonly used in training deep neural networks. Empirical evaluations on both simulated data and a benchmark dataset show that the regulariser yields more stable training, resulting in faster convergence and more reliable portfolio-level risk estimates.