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

TL;DR

This paper develops an actuarial framework using the SEIARD epidemiological model to better assess infectious disease risks in insurance, incorporating disease dynamics into financial calculations and reserves.

Contribution

It introduces a novel integration of the SEIARD model into actuarial analysis, enabling dynamic risk assessment during epidemics.

Findings

Derived actuarial quantities based on SEIARD dynamics.

Analyzed the impact of epidemic parameters on reserves.

Numerical simulations demonstrate model applicability.

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.