@article{Sagidolla2026, 
author = {Bizhigit Sagidolla and Shirali Kadyrov},
title = {Deterministic solvency thresholds and RL-based premium calibration for life insurance under age-structured epidemics},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {7},
pages = {4512-4534},
keywords = {epidemic risk modelling, life insurance solvency, age-structured SEIRD model, reinforcement learning, premium calibration, numerical stress testing, insurance mathematics},
url = {https://www.sciopen.com/article/10.3934/era.2026199},
doi = {10.3934/era.2026199},
abstract = {We develop a deterministic framework that links epidemic propagation, mortality risk, and life-insurance solvency by modeling the population through an age-structured SEIRD system in which disease-induced deaths drive an insurer's surplus process governed by an ordinary differential equation with a continuous premium inflow and death-benefit outflow. We characterize the disease-free equilibrium and show that its local stability depends on the basic reproduction number              R        0  , and for any finite horizon    [  0  ,  T  ], we derive an explicit solvency threshold in the form of a critical premium        p                  c        r        i        t              (  T  ) that guarantees a nonnegative surplus and depends on the age-weighted infection burden. For large horizons, we obtain an analytically tractable approximation of this threshold using multi-group final-size relations and show that it monotonically increases with epidemic severity. To illustrate practical implications, we formulate an age-specific premium selection as a one-shot continuous-action reinforcement-learning problem in which a Proximal Policy Optimization (PPO) agent is trained on simulated age-structured epidemic scenarios to choose premiums that avoid ruin while remaining near actuarially fair levels; out-of-sample tests confirm that the learned premiums satisfy the analytical solvency constraints, deliver low ruin probabilities, and achieve tight fairness calibration. The combined analytical and numerical results provide a transparent basis for epidemic-sensitive premium design and stress testing of life-insurance portfolios.}
}