Bayesian Neural Networks for Robust Reserve Decisions under Lévy Mortality Shocks

This paper addresses the critical decision-making problem of valuing life insurance reserves under extreme demographic uncertainty, such as pandemics, climate-induced shifts, and economic crises. We introduce a novel framework that integrates Bayesian deep learning with measure-theoretic actuarial science to overcome the limitations of classical models. By modeling financial and demographic risks through product measures (μ ⊗ ν) and incorporating Lévy processes for mortality shocks, our approach captures the complex interaction between stochastic discounting and discontinuous demographic dynamics. The neural architecture, a stochastic multilayer perceptron with Bayesian Bernoulli dropout and Lévy-distributed noise injection (εₗ ∼ Levy(1.7)), ensures Radon-Nikodym compatibility via a measure-preserving neural operator, guaranteeing actuarial interpretability and decision robustness under Solvency II regulatory standards.

We validate the framework empirically using EIOPA mortality data across multiple stress scenarios, including a simulated COVID-19-style pandemic shock with tripled arrival rates. Results demonstrate significant improvements: a 63% reduction in mean absolute error (MAE) and a 77% decrease in Kullback–Leibler (KL) divergence compared to classical models. Under pandemic stress, our model achieves a 64% error reduction, requiring 22% less economic capital under the 99.5% Value-at-Risk (VaR) Solvency II requirement. Additionally, we integrate fairness metrics via Pearl's do-calculus, achieving a fairness score of ε = 0.0031—well below the EIOPA regulatory threshold (<0.005)—with an adjusted average treatment effect (ATE) for gender of -0.0031 ± 0.0004, eliminating demographic bias.

The framework offers a scalable, transparent, and ethically-aware solution for reserve modeling and decision-making in volatile demographic environments, with projected quantum-inspired complexity of O(√N) for large portfolios.