Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function
| dc.contributor.author | Usábel Rodrigo, Miguel Arturo | |
| dc.date.accessioned | 2023-06-21T01:36:16Z | |
| dc.date.available | 2023-06-21T01:36:16Z | |
| dc.date.issued | 1998 | |
| dc.description.abstract | The non-ruin probability, for initial reserves u, in the classical can be calculated using the so-called Bromwich-Mellin inversion formula, an outstanding result from Residues Theory first introduced for these purposes by Seal(1977) for exponential claim size. We will use this technique when claim sizes follow a generalized r-convolution function distribution. Some of the most frequently used heavy-tailed distributions in actuarial science belongs to this family. Thorin(1977) or Berg(1981) proved that Pareto distributions are members of this family; so Thorin(1977) did with Log-normal distributions. | |
| dc.description.department | Decanato | |
| dc.description.faculty | Fac. de Ciencias Económicas y Empresariales | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/27083 | |
| dc.identifier.issn | 2255-5471 | |
| dc.identifier.relatedurl | https://economicasyempresariales.ucm.es/working-papers-ccee | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64132 | |
| dc.issue.number | 02 | |
| dc.language.iso | eng | |
| dc.page.total | 10 | |
| dc.publication.place | Madrid | |
| dc.publisher | Facultad de Ciencias Económicas y Empresariales. Decanato | |
| dc.relation.ispartofseries | Documentos de Trabajo de la Facultad de Ciencias Económicas y Empresariales | |
| dc.rights | Atribución-NoComercial-CompartirIgual 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-sa/3.0/es/ | |
| dc.subject.keyword | Ultimate non-ruin probability | |
| dc.subject.keyword | Laplace transforms | |
| dc.subject.keyword | Bromwich-Mellin inversion formula | |
| dc.subject.keyword | Gerenalized r-convolution functions. | |
| dc.subject.ucm | Probabilidades (Matemáticas) | |
| dc.title | Calculating ultimate non-ruin probabilities when claim sizes follow a generalized r-convolution distribution function | |
| dc.type | technical report | |
| dc.volume.number | 1998 | |
| dcterms.references | Boas, R. (1987) Invitation to complex analysis. The Random House/Birkhauser mathematics series. New York. Bohman, H. (1971) Ruin probabilities. Skandinavisk Aktuarietidskrift. 159-163. Bohman, H. (1974) Fouricr Invcrsion-Distribution functions-Long tails. Scand. Actuarial Journal 43-45. Bohman, H. (1975) Numerical inversion of characteristic functions. Sean. Act. JournaL 121-124. Berg, C. (1981). The Pareto distribution is a generalized r-convolution-a new proof. Sean. Act. Journal. 117-119. Conway, J. (1978) Punctions of one complex variable I. Second edition. Springer-Verlag. New York. Cramer, H. (1955) Collective Risk Theory. Jubille Volume of F. Skandia. Goovaerts, M., D'Hooge, L., De Pril, N. (1977). On a class of generalized r-convolutions. Sean. Act. Journal. 21-30. Piessens, R. (1969) New quadrature formulas for the numerical inversion of Laplace tmnsforms. BIT 9, 351-361. Seal, H. (1971) Numerical calculation of the Bohman-Esscher family of convolution-mixed negative binomial distribution functions. Mitt. Verein. schweiz. Versich.-Mathr. 71, 71-94. Seal, H. (1974) The numerical calculation of U(w,t), the probability of non-ruin in an interual (a,t). Sean. Aet. Journal, 121-139. Seal, H. (1977) Numerical inversion of chamcteristic functions. Sean. Aet. Journal,48-53. Thorin, O. (1970). Some remarks on the ruinproblem in case the epochs of claims form a renewal process. Skanclinavisk Aktuarietidslrrift. 29-50. Thorin, O. (1971). Further remarks on the ruin problem in case the epochs of claims form a renewal process. Skandinavisk Aktuarietidskrift. 14-38, 121-142. Thorin, O. (1973). The ruin problem in case the tail of a distribution is completely monotone. Skandinavisk Aktuarietidslrrift. 100-119. Thorin, O. (1977). Ruin probabilities prepared for numerical calculation. Seandinavian Actuarial Journal. Thorin, O. (1977). On the infinite divisibility of the Pareto distribution. Sean. Act. Jomnal. 31-40. Thorin, O. (1977). On the infinite divisibility of the Lognormal distribution. Sean. Act. Jomnal. 121-148. Thorin, O. (1978). An extension of the notion of a generalized r-convolution. Sean. Act. Journal. 141-149. Thorin, O. and Wikstad, N. (1973). Numerical evaluation of ruin probabilities for a finite periodo ASTIN Bulletin VII:2, 138-153. Wikstad,N. (1971) Exemplifications of ruin probabilities. ASTIN Bulletín, vol. VI, part 2. Wikstad, N. (1977). How to calculate Ruin probabilities according to the classical Risk Theory. Scand. Actuarial Journal. | |
| dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1
