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Applications of Gaver-Stehfest method of inverting laplace transforms to ruin theory

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dc.contributor.authorUsábel Rodrigo, Miguel Arturo
dc.date.accessioned2023-06-21T01:36:10Z
dc.date.available2023-06-21T01:36:10Z
dc.date.issued1997
dc.description.abstractThe Stehfest-Gaver method of inverting Laplace transforms is a very useful tool in approximating non-ruin probabilities. An accuracy of 6 to 10 significant digits is obtained in every case studied (Tables 1,2 and 3) except for Log-normal claim size and large initial reserves where the accuracy of the "exact" values (using Product integration ) is not guaranteed to be more than 5 digits. The efficiency in terms of computational time is also outstanding because we onIy need to evaluate 20 times the Laplace transform of the c.dJ. of the claim size as shown in (1.6).
dc.description.departmentDecanato
dc.description.facultyFac. de Ciencias Económicas y Empresariales
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/27016
dc.identifier.issn2255-5471
dc.identifier.relatedurlhttps://economicasyempresariales.ucm.es/working-papers-ccee
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64126
dc.issue.number17
dc.language.isoeng
dc.page.total18
dc.publication.placeMadrid
dc.publisherFacultad de Ciencias Económicas y Empresariales. Decanato
dc.relation.ispartofseriesDocumentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales
dc.rightsAtribución-NoComercial-CompartirIgual 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subject.keywordModelos matemáticos
dc.subject.keywordRiesgo.
dc.subject.ucmProbabilidades (Matemáticas)
dc.subject.ucmTeoría de la decisión
dc.subject.unesco1209.04 Teoría y Proceso de decisión
dc.titleApplications of Gaver-Stehfest method of inverting laplace transforms to ruin theory
dc.typetechnical report
dc.volume.number1997
dcterms.referencesBühlmann, H. (1970). Mathematical methods in Risk Theory. Springer-Verlag, New York. Burden, R. L. and Faires, J. D (1985). Numerical Analysis, P.W.S., Boston. Davies,B and Martin,B. (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. Journal of computational physics,33. Delves, L. M. and Mohamed, J. L. (1985). Computational methods for integral equations. Cambridge, England. Cambridge University Press. Feller, W. (1973). An introduction to probability and its applications. Volume II John Willey. Gaver, D. P. (1966). Operational Research. 14,444-459. Grandell, J. (1990). Aspects of Risk Theory. Springer-Verlag. New York. Haber, S. (1970). Numerical evaluation of multiple integrals, SIAM Rev., 12, 481-526. Panjer, R.H. (1981). Recursive evaluation of a family of compound distributions, ASTIN Bulletin, 12, 22-26. Panjer, R.H. & Willmot, G.E. (1992). Insurance risk Models, Society of Actuaries, Schaumburg. Ramsay, C.M. (1992a). "A Practical Algorithm for Approximating the Probability of Ruin." Transactions of the Society of Actuaries, XLIV, 443-59. Ramsay, C.M. (1992b). "Improving Goovaerts' and De Vylder's Stable Recursive AIgorithm. ASTIN Bulletin, 22, 51-59. Ramsay,C.M. and Usábel,M.A. (1997).Calculating Ruin probabilities via Product integration. Próxima aparición ASTIN BULLETIN Noviembre 1997. cv Stehfest, R. (1970). Numerical inversion of Laplace transform. Communications of the ACM, Vol. 19. No 1.
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