Quantile-based Interpretable Neural Network Models: Mortality Forecasting and Actuarial Simulations

This paper introduces a class of quantile-based, interpretable neural network (NN) models for mortality prediction: the Lee-Carter neural network (LCNN) model, the Renshaw-Haberman neural network (RHNN) model, and the simple neural network (simpleNN) model that balances simplicity with predictive performance. These models preserve the linear interpretability of classic stochastic mortality models while harnessing the flexibility of NNs to capture complex nonlinear patterns in mortality data, thereby achieving enhanced predictive performance. Leveraging a composite loss function that integrates pinball, median anchoring, and quantile-crossing penalty terms, we estimate mortality quantiles and develop an efficient simulation scheme based on interpolation. This framework provides distributional insights essential for pricing, reserving and risk management. Extensive empirical analyses across multiple populations demonstrate that the proposed models consistently outperform traditional approaches in predictive accuracy. We further illustrate their practical utility through an application to longevity swap pricing.