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

Journal article

Yang Qiao; Jinggong Zhang; Wenjun Zhu; Chou-Wen Wang

Insurance: Mathematics and Economics · 2026-05 · Volume 128 · Article 103235
DOI: 10.1016/j.insmatheco.2026.103235 · Download citation (BibTeX)

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Abstract

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 em- pirical analyses across multiple populations demonstrate that the proposed models consis- tently outperform traditional approaches in predictive accuracy. We further illustrate their practical utility through an application to longevity swap pricing.

Keywords: Interpretable Neural Network, Mortality Prediction, Longevity Risk, Stochastic Mortality Model, Quantile Regression, Monte Carlo Simulation, Longevity Swap

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