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An Actuarial Approach for Modeling Pandemic Risk

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  • Donatien Hainaut

    (LIDAM Institute of Statistics, Biostatistics and Actuarial Sciences, Université Catholique de Louvain, 5032 Isnes, Belgium
    Current address: 20 voie du Roman Pays, 1348 Louvain-La-Neuve, Belgium.)

Abstract

In this article, a model for pandemic risk and two stochastic extensions is proposed. It is designed for actuarial valuation of insurance plans providing healthcare and death benefits. The core of our approach relies on a deterministic model that is an efficient alternative to the susceptible-infected-recovered (SIR) method. This model explains the evolution of the first waves of COVID-19 in Belgium, Germany, Italy and Spain. Furthermore, it is analytically tractable for fair pure premium calculation. In a first extension, we replace the time by a gamma stochastic clock. This approach randomizes the timing of the epidemic peak. A second extension consists of adding a Brownian noise and a jump process to explain the erratic evolution of the population of confirmed cases. The jump component allows for local resurgences of the epidemic.

Suggested Citation

  • Donatien Hainaut, 2020. "An Actuarial Approach for Modeling Pandemic Risk," Risks, MDPI, vol. 9(1), pages 1-28, December.
    • Handle: RePEc:gam:jrisks:v:9:y:2020:i:1:p:3-:d:466966
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    References listed on IDEAS

    as
    1. Na Jia & Lawrence Tsui, 2005. "Epidemic Modelling using Sars as a Case Study," North American Actuarial Journal, Taylor & Francis Journals, vol. 9(4), pages 28-42.
    2. Runhuan Feng & Jose Garrido, 2011. "Actuarial Applications of Epidemiological Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(1), pages 112-136.
    3. Hua Chen & Samuel Cox, 2009. "An Option-Based Operational Risk Management Model for Pandemics," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 54-76.
    4. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    5. Claude Lefe`vre & Sergey Utev, 1999. "Branching Approximation for the Collective Epidemic Model," Methodology and Computing in Applied Probability, Springer, vol. 1(2), pages 211-228, September.
    Full references (including those not matched with items on IDEAS)

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