A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process

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dc.contributor.author Diko, Peter
dc.contributor.author Usabel Rodrigo, Miguel Arturo
dc.date.accessioned 2011-12-14T19:20:32Z
dc.date.available 2011-12-14T19:20:32Z
dc.date.issued 2011-07
dc.identifier.bibliographicCitation Insurance, Mathematics & Economics, 2011, v. 49, n. 1, pp. 126-132
dc.identifier.issn 0167-6687
dc.identifier.uri http://hdl.handle.net/10016/12757
dc.description.abstract A generalization of the Cramér–Lundberg risk model perturbed by a diffusion is proposed. Aggregate claims of an insurer follow a compound Poisson process and premiums are collected at a constant rate with additional random fluctuation. The insurer is allowed to invest the surplus into a risky asset with volatility dependent on the level of the investment, which permits the incorporation of rational investment strategies as proposed by Berk and Green (2004). The return on investment is modulated by a Markov process which generalizes previously studied settings for the evolution of the interest rate in time. The Gerber–Shiu expected penalty–reward function is studied in this context, including ruin probabilities (a first-passage problem) as a special case. The second order integro-differential system of equations that characterizes the function of interest is obtained. As a closed-form solution does not exist, a numerical procedure based on the Chebyshev polynomial approximation through a collocation method is proposed. Finally, some examples illustrating the procedure are presented
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights ©Elsevier
dc.subject.other Expected penalty–reward function
dc.subject.other Markov-modulated process
dc.subject.other Jump–diffusion process
dc.subject.other Volterra integro-differential system of equations
dc.title A numerical method for the expected penalty–reward function in a Markov-modulated jump–diffusion process
dc.type article
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.insmatheco.2011.03.001
dc.subject.jel G22
dc.subject.eciencia Empresa
dc.identifier.doi 10.1016/j.insmatheco.2011.03.001
dc.rights.accessRights openAccess
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 126
dc.identifier.publicationissue 1
dc.identifier.publicationlastpage 132
dc.identifier.publicationtitle Insurance, Mathematics & Economics
dc.identifier.publicationvolume 49
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