| Abstract: |
| This work establishes a formal mathematical bridge between the
Next-Generation Matrix (NGM) method, the celebrated cornerstone of
mathematical epidemiology (ME), and the stochastic ruin theory of the
Cramer-Lundberg process. Drawing on recent developments that prove the
NGM is a structural outcome of the siphon property fundamental in
Chemical Reaction Networks (CRN), we demonstrate how epidemiological
thresholds R_0 can be mapped directly onto insurance solvency metrics.
By treating the epidemic as a balanced bilinear model, we prove that
the stoichiometric dwell times of the infectious compartments, a
concept derived from CRN and ME, determine the asymptotic claim
intensity and the adjustment coefficient of the insurer's surplus.
This synthesis allows for a "stoichiometric stress test" of insurance
portfolios, where financial stability is explicitly linked to the
biological reaction kinetics of a pathogen. |
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