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Epidemic risk and insurance coverage

Part of: Mathematical economics Markov processes

Published online by Cambridge University Press:  04 April 2017

Claude Lefèvre ,
Philippe Picard  and
Matthieu Simon
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Philippe Picard*
Affiliation:
Université de Lyon
Matthieu Simon*
Affiliation:
Université Libre de Bruxelles
*
* Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium.
*** Postal address: ISFA, Université de Lyon, 50 Avenue Tony Garnier, F-69007 Lyon, France. Email address: philippe.picard69@free.fr
* Postal address: Département de Mathématique, Université Libre de Bruxelles, Campus de la Plaine C.P. 210, B-1050 Bruxelles, Belgium.
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Abstract

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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.

Keywords

SIR epidemicremoval-dependent rateepidemic sizeinfectivity timesusceptibility timeinsurance premiummartingale

MSC classification

Primary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 91B30: Risk theory, insurance 92D30: Epidemiology
Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 1 , March 2017 , pp. 286 - 303
Copyright
Copyright © Applied Probability Trust 2017 

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