A Measure-Theoretic Approach to Actuarial Reserves via Stieltjes Integration and Deep Learning

AbstractThis paper introduces a novel actuarial framework for life insurance reserve valuation,integrating Stieltjes integration with Bayesian deep learning techniques. Theproposed model employs measure-theoretic formalism and L´evy processes to captureboth financial and demographic uncertainties, particularly under systemic shocks suchas pandemics. A dual-measure compatibility condition, supported by Radon-Nikodymderivatives, ensures a coherent probabilistic structure across heterogeneous data sources.Additionally, the framework incorporates a Jensen-Shannon divergence-based optimizationscheme to enhance calibration and robustness. Empirical validation usingEIOPA datasets demonstrates improved predictive accuracy and full compliance withSolvency II regulations. Beyond technical contributions, the paper explores the societalimplications of the model, emphasizing its potential to foster fairness and resiliencewithin insurance systems. Author affiliation: Independent Researcher; REPRISE – Register of Expert Peer Reviewers for Italian Scientific Evaluation, Ministry of University and Research (MUR), Italy