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Epidemic risk and insurance coverage

  • Claude Lefèvre (a1), Philippe Picard (a2) and Matthieu Simon (a1)

Abstract

In this paper we aim to apply simple actuarial methods to build an insurance plan protecting against an epidemic risk in a population. The studied model is an extended SIR epidemic in which the removal and infection rates may depend on the number of registered removals. The costs due to the epidemic are measured through the expected epidemic size and infectivity time. The premiums received during the epidemic outbreak are measured through the expected susceptibility time. Using martingale arguments, a method by recursion is developed to calculate the cost components and the corresponding premium levels in this extended epidemic model. Some numerical examples illustrate the effect of removals and the premium calculation in an insurance plan.

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Corresponding author

* Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium.
** Email address: clefevre@ulb.ac.be Also at the ISFA, Université de Lyon.
*** Postal address: ISFA, Université de Lyon, 50 Avenue Tony Garnier, F-69007 Lyon, France. Email address: philippe.picard69@free.fr
**** Email address: matsimon@ulb.ac.be

References

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Andersson, H. and Britton, T. (2000).Stochastic Epidemic Models and Their Statistical Analysis, (Lecture Notes Statist. 151).Springer,New York.
Ball, F. and O’Neill, P. D. (1993).A modification of the general stochastic epidemic motivated by AIDS modelling.Adv. Appl. Prob. 25,3962.
Ball, F., O’Neill, P. D. and Pike, J. (2007).Stochastic epidemic models in structured populations featuring dynamic vaccination and isolation.J. Appl. Prob. 44,571585.
Ball, F. G. (1986).A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models.Adv. Appl. Prob. 18,289310.
Ball, F. G., Knock, E. S. and O’Neill, P. D. (2008).Control of emerging infectious diseases using responsive imperfect vaccination and isolation.Math. Biosci. 216,100113.
Chen, H. and Cox, S. H. (2009).An option-based operational risk management model for pandemics.N. Amer. Actuarial J. 13,5479.
Daley, D. and Gani, J. (1999).Epidemic Modelling.Cambridge University Press.
Denuit, M. and Robert, C. (2007).Actuariat des Assurances de Personnes.Economica,Paris.
Feng, R. and Garrido, J. (2011).Actuarial applications of epidemiological models.N. Amer. Actuarial J. 15,112136.
Gani, J. and Jerwood, D. (1972).The cost of a general stochastic epidemic.J. Appl. Prob. 9,257269.
Gleissner, W. (1988).The spread of epidemics.Appl. Math. Comput. 27,167171.
Haberman, S. and Pitacco, E. (1999).Actuarial Models for Disability Insurance,Chapman and Hall,Boca Raton.
O’Neill, P. D. (1997).An epidemic model with removal-dependent infection rate.Ann. Appl. Prob. 7,90109.
Picard, P. (1980).Applications of martingale theory to some epidemic models.J. Appl. Prob. 17,583599.
Picard, P. and Lefèvre, C. (1990).A unified analysis of the final size and severity distribution in collective Reed–Frost epidemic processes.Adv. Appl. Prob. 22,269294.
Picard, P. and Lefèvre, C. (1993).Distribution of the final state and severity of epidemics with fatal risk.Stoch. Process. Appl. 48,277294.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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