Deterministic solvency thresholds and RL-based premium calibration for life insurance under age-structured epidemics

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 ${\mathcal{R}}_0$, and for any finite horizon $[0,T]$, we derive an explicit solvency threshold in the form of a critical premium $p_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}(T)$ 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.