A premium structure for a pandemic insurance policy

This paper aims to establish an actuarial model tailored for insurance companies offering contracts covering pandemic events. The corresponding premium is determined based on both the probability of contagion and subsequent outcomes for insured individuals. We assume a one-year insurance coverage period, during which policyholders are exposed to the risk of contracting the virus. A random variable for contagion is defined, following a theoretical geometric distribution. Variable benefits are provided depending on the insured individual's "status" resulting from infection outcomes, with a lump sum payment offered in case of death. The duration of each "status" is modeled by a Gamma distribution. Utilizing these assumptions, a fair premium for the policy is estimated. The risk analysis of the proposed policy involves quantifying benefit volatility, establishing a specified confidence level, and conducting threshold analysis using Markov's Inequality to determine the probability that benefits exceed a certain value. Additionally, we discuss the insurer's decision to customize the policy "prior" by applying a uniform premium to the entire population before applying a safety loading. Numerical applications are explored using weekly reports on the COVID-19 epidemic from the Istituto Superiore della Sanità (ISS).