Actuarial Analysis of an Infectious Disease Insurance based on an SEIARD Epidemiological Model

2025-08-07

AI Summary

Conventional life insurance models rely on static mortality assumptions, failing to capture dynamic epidemiological risks. Method: This paper develops a novel dynamic framework integrating SEIARD epidemic dynamics with actuarial science, endogenizing latency, infection progression, and disease-induced mortality into survival probability modeling—yielding an epidemic-adaptive survival function. A nonstandard finite-difference (NSFD) scheme ensures numerical stability across multi-parameter scenarios; closed-form expressions for time-varying net premiums and policy reserves are derived. Contribution/Results: The model sensitively captures the nonlinear impacts of varying infection and case-fatality rates on annuity present values, premium pricing, and liability reserves. It significantly enhances the timeliness and robustness of insurance product design and solvency assessment during epidemics.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Accountability, Transparency, and Ethics for personalization

Abstract

The growing number of infectious disease outbreaks, like the one caused by the SARS-CoV-2 virus, underscores the necessity of actuarial models that can adapt to epidemic-driven risks. Traditional life insurance frameworks often rely on static mortality assumptions that fail to capture the temporal and behavioral complexity of disease transmission. In this paper, we propose an integrated actuarial framework based on the SEIARD epidemiological model. This framework enables the explicit modeling of incubation periods and disease-induced mortality. We derive key actuarial quantities, including the present value of annuity benefits, payment streams, and net premiums, based on SEIARD dynamics. We formulate a prospective reserve function and analyze its evolution throughout the course of an epidemic. Additionally, we examine the forces of infection, mortality, and removal to assess their impact on epidemic-adjusted survival probabilities. Numerical simulations implemented via a nonstandard finite difference (NSFD) scheme illustrate the model's applicability under various parameter settings and insurance policy assumptions.

Problem

• Develops actuarial model for infectious disease insurance risks
• Integrates SEIARD model to capture dynamic mortality factors
• Analyzes epidemic impacts on insurance reserves and premiums

Innovation

• SEIARD model for dynamic actuarial analysis
• Nonstandard finite difference numerical simulations
• Epidemic-adjusted survival probabilities assessment