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Ruin problems for epidemic insurance

Part of: Mathematical economics Markov processes

Published online by Cambridge University Press:  01 July 2021

Claude Lefèvre  and
Matthieu Simon Open the ORCID record for Matthieu Simon [Opens in a new window]
Claude Lefèvre*
Affiliation:
Université Libre de Bruxelles
Matthieu Simon*
Affiliation:
University of Melbourne
*
*Postal address: Département de Mathématique, Campus de la Plaine, CP 210, B-1050 Bruxelles, Belgium. Email: claude.lefevre@ulb.be
**Postal address: School of Mathematics and Statistics, Parkville, VIC 3010, Australia. Email: matthieus@unimelb.edu.au
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Abstract

The paper discusses the risk of ruin in insurance coverage of an epidemic in a closed population. The model studied is an extended susceptible–infective–removed (SIR) epidemic model built by Lefèvre and Simon (Methodology Comput. Appl. Prob.22, 2020) as a block-structured Markov process. A fluid component is then introduced to describe the premium amounts received and the care costs reimbursed by the insurance. Our interest is in the risk of collapse of the corresponding reserves of the company. The use of matrix-analytic methods allows us to determine the distribution of ruin time, the probability of ruin, and the final amount of reserves. The case where the reserves are subjected to a Brownian noise is also studied. Finally, some of the results obtained are illustrated for two particular standard SIR epidemic models.

Keywords

SIR-type epidemicsinsurance reservesrisk of ruinblock-structured Markov processesMarkov-modulated fluid flowsmatrix-analytic methodsBrownian noise

MSC classification

Primary: 91B30: Risk theory, insurance 92D30: Epidemiology
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 2 , June 2021 , pp. 484 - 509
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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