Approximations for multivariate characteristics of classical risk ruin processes
| dc.contributor.author | Usábel Rodrigo, Miguel Arturo | |
| dc.date.accessioned | 2023-06-21T01:36:15Z | |
| dc.date.available | 2023-06-21T01:36:15Z | |
| dc.date.issued | 1998 | |
| dc.description.abstract | Multivariate characteristic of risk processes are of high interest to academic actuaries. In such modele the probability of ruin ie obtained not only considering initial reserves u but the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using Gaver-Stehfest method of invertig Laplace transforms. | |
| 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/27082 | |
| dc.identifier.issn | 2255-5471 | |
| dc.identifier.relatedurl | https://economicasyempresariales.ucm.es/working-papers-ccee | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/64131 | |
| dc.issue.number | 01 | |
| dc.language.iso | eng | |
| dc.page.total | 8 | |
| 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 | Multivariate ultimate ruin probability | |
| dc.subject.keyword | Laplace transform | |
| dc.subject.keyword | Integral equations | |
| dc.subject.keyword | Numerical methods. | |
| dc.subject.ucm | Probabilidades (Matemáticas) | |
| dc.subject.ucm | Teoría de la decisión | |
| dc.subject.unesco | 1209.04 Teoría y Proceso de decisión | |
| dc.title | Approximations for multivariate characteristics of classical risk ruin processes | |
| dc.type | technical report | |
| dc.volume.number | 1998 | |
| dcterms.references | Boas, R. (1987) Invitation to complex analysis. The Random House/Birkhiiuser mathematics series. New York. r-convolution- a new proof. Sean. Act. Journal. 117-119. Burden, R.L. and Faires, J.D.(1985). Numerical Analysis, P.W.S., Boston. Conway, J. (1978) Functions of one complex variable I. Second edition. Springer-Verlag. New York. Cramer, R. (1955) Collective Risk Theory. Jubille Volume of F. Skandia. 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. Dickson, C. (1989) Recursive calculation of tite probability and severity of ruin. Insurance: Mathematics and Economics, 8. Dickson, C. and Waters, R. (1992) The probability and severity of ruin infinite and infinite time. ASTIN Bulletin, Vol 22, 2. Dickson, C. (1993) On the distribution of the claim causing ruin. Insutance: Mathematics and Economics, 12. Dufresne, F. and Gerber, R. (1988) The surpluses immediately before and at ruin, and the amount of the claim causing ruin. Insurance: Mathematies and Economics, 7. Feller, W. (1973). An introduction to probability and its applications. Volume II. John Willey. Frey, A. and Schmidt, V,. (1996) Taylor Series expansion for multivariate characteristics of classical risk processes. Insurance: Mathematics and Economics, 18. Gaver, D. P. (1966). Operational Research. 14,444-459. Gerber, R., Goovaerts, M., Kaas, R. (1987) On the probability and severity of ruin. ASTIN Bulletin, Vol. 17,2. Piessens, R. (1969) New quadrature formulas for the numerical inversion of Laplace transforms. BIT 9, 351-361. Ramsay, C.M. (1992a). "A Practical Algorithm for Approximating the Probability of Ruin." Transactions of tite Society of Actuaries, XLIV, 443-59. Ramsay, C.M. (1992b). Improving Goovaerts and De Vylder's Stable Recursive Algorithm. ASTIN Bulletin, 22, 51-59. Rarnsay,C.M. and Usábel,M.A. (1997).Calculating Ruin probabilities via Product integration. ASTIN Bulletin. Vo1.27, 2. Seal, H. (1971) Numerical calculation of the Bohman-Esscher family of convolution-mixed negative binomial distribution junctions. Mitt. Verein. schweiz. Versich.-M.atbr. 71, 71-94. Seal, H. (1974) The numerical calculation of U(w,t), the probability of non-ruin in an interval (O,t). Sean. Act. Journal, 121-139. Seal, H. (1977) Numerical inversion of characteristic functions. Sean. Act. Journa1, 48-53. Stehfest, H. (1970). Numerical inversion of Laplace transform. Communications of the ACM, Vol. 19. No 1. Thorin, O. (1970). Some remarks on the ruin problem in case the epochs of claims form a renewal process. Skandinavisk Aktuarietidskrift. 29-50. Thorin, O. (1971). Purther 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 Aktuarietidskrift. 100-119. Thorin, O. (1977). Ruinprobabilities prepared for numerical calculation. Seandinavian Actuarial Journal. Thorin, O. and Wikstad, N. (1973). Numerical evaluation of ruin probabilities for a finite periodo ASTIN Bul1etin VII:2, 138-153. Wikstad,N. (1971) Exemplifications of ruin probabilities. ASTIN Bulletin, vol. VI, part 2. Wlkstad, N. (1977). How to calculate Ruin probabilities according to the classical Risk Theory. Seand. Actuarial Journal. | |
| dspace.entity.type | Publication |
Download
Original bundle
1 - 1 of 1
