Calculating ruin probabilities via product integration

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dc.contributor.authorRamsay, Colin M.
dc.contributor.authorUsábel Rodrigo, Miguel Arturo
dc.date.accessioned2023-06-21T01:36:08Z
dc.date.available2023-06-21T01:36:08Z
dc.date.issued1997
dc.description.abstractWhen claims in the compound Poisson risk model are from a heavy-tailed distribution (such as the Pareto or the lognormal), traditional techniques used to compute the probability of ultimate ruin converge slowly to desired probabilities. Thus, faster and more accurate roethods are needed. Product integration can be used in such situations to yield fast and accurate estimates of ruin probabilities because it uses quadrature weights that are suited to the underlying distribution. Tables of ruin probabilities for the Pareto and lognormal distributions are provided.
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/27013
dc.identifier.isbn2255-5471
dc.identifier.relatedurlhttps://economicasyempresariales.ucm.es/working-papers-ccee
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64124
dc.issue.number15
dc.language.isoeng
dc.page.total13
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.keywordIntegral equation
dc.subject.keywordConvergence
dc.subject.keywordHeavy-tailed distributions
dc.subject.ucmEconomía financiera
dc.subject.ucmFunciones (Matemáticas)
dc.subject.unesco1202 Análisis y Análisis Funcional
dc.titleCalculating ruin probabilities via product integration
dc.typetechnical report
dc.volume.number1997
dcterms.referencesAbramowitz, M. and Stegun, I.A. (1964). Handbook of Mathematical Functions. New York, N.Y.: Dover Publications. Bowers, N.L., Gerber, R.U., Hickman, J.C., Jones, D.A. and Nesbitt, C.J. (1986). Actuarial Mathematics. lthasca, m.: Society of Actuaries. Delves, L.M. and Mohamed, J.L. (1985). Computational Methods for Integral Equations. Cambridge, England: Cambridge University Press. Dickson, D.C.M. (1989). "Recursive Calculation of the Probability and Severity of Ruin." Insurance: Mathematics and Economics, 8, pp. 145-148. Dickson, D.C.M., Egidio dos Reis, A.D. and Waters, H.R. (1995). "Some Stable Algorithms in Ruin Theory aud Their Application." Astin Bulletin 25, pp. 153-175. Dickson, D.C.M. and Waters, R.R. (1991) "Recursive Calculation of Survival Probabilities." Astin Bulletin 21, pp. 199-221. Gerber, R.U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monograph 8. Philadelphia, Pa.: University of Pennsylvania. (Distributed by Irwin, Homewood, IL.) Goovaerts, M. and de Vylder, F. (1984). "A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities." ASTIN Bulletin, 14, pp. 53-59. Grandell, J. (1990). Aspects of Risk Theory. Springer Verlag, New York. Linz, P. (1985). Analytical and Numerical Methods for Volterra Equations. Philadelphia, Pa.: SIAM Studies in Applied Mathematics. Panjer, R.R. (l986). "Direct Calculation of Ruin Probabilities." Journal of Risk and Insurance, 53, pp. 521-529. Ramsay and Usabel: Product Integration. Panjer, H.H. and Wang, S. (1993). "On the Stability of Recursive Formulas." ASTIN Bulletin, 23, pp. 227-258. Ramsay, C.M. (1992a). "A Practical Algorithm for Approsimating the Probability of Ruin." Transactions of the Society of Actuaries, XLIV, 443-459. Ramsay, C.M. (1992b). "Improviug Goovaerts' and De Vylder's Stable Recursive Algorithm. ASTIN Bulletin, 22, pp. 51-59. Thorin, O and Wikstad, N. (1977). "Calculation of Ruin Probabilities When the Claim Distribution is Lognormal." ASTIN bulletin, 9, pp. 231-246. Young, A. (1954). "Approximate Product Integration." Proc. Royal Soc. London, Ser. A, 224, pp. 561-573.
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