108
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Coupling and Explicit Rate of Convergence in Cramér–Lundberg Approximation for Reinsurance Risk Processes

&
Pages 3524-3539 | Received 22 Nov 2010, Accepted 12 Apr 2011, Published online: 30 Aug 2011

References

  • Asmussen , S. ( 2000 ). Ruin Probabilities . Singapore : World Scientific .
  • Cramér , H. ( 1930 ). On the Mathematical Theory of Risk . Stockholm : Skandia Jubilee Volume .
  • Cramér , H. ( 1955 ). Collective Risk Theory . Stockholm : Skandia Jubilee Volume .
  • Embrechts , P. , Klüppelberg , C. , Mikosch , T. ( 1997 ). Modelling Extremal Events for Insurance and Finance . Applications of Mathematics , Vol. 33 . Berlin : Springer .
  • Feller , W. (1971). An Introduction to Probability Theory and Its Applications , Vol. II . New York : Wiley.
  • Gerber , H. U. ( 1979 ). An Introduction to Mathematical Risk Theory . Philadelphia : Huebner Foundation Monographs .
  • Grandell , J. ( 1991 ). Aspects of Risk Theory . New York : Springer .
  • Gyllenberg , M. , Silvestrov , D. S. ( 2000 ). Cramer–Lundberg approximation for non-linearly perturbed risk processes . Insur. Math. Econom. 26 : 75 – 90 .
  • Gyllenberg , M. , Silvestrov , D. ( 2008 ). Quasi-Stationary Phenomena in Nonlinearly Perturbed Stochastic Systems . De Gruyter Expositions in Mathematics , Vol. 44 . Berlin : Walter de Gruyter .
  • Kalashnikov , V. ( 1997 ). Geometric Sums: Bounds for Rare Events with Applications . Mathematics and Its Applications , Vol. 413 . Dordrecht : Kluwer .
  • Lundberg , F. ( 1903 ). I. Approximerad Framställning av Sannolikhetsfunktionen. II. Återför-säkring av Kollektivrisker . Uppsala : Almqvist & Wiksell .
  • Lundberg , F. ( 1909 ). Über die der Theorie Rückversicherung . In: VI Internationaler Kongress für Versicherungswissenschaft. Bd. 1, Vien , pp. 877 – 955 .
  • Lundberg , F. ( 1926 ). Försäkringsteknisk Riskutjämning . Stockholm : F. Englunds boktryckeri AB .
  • Rolski , T. , Schmidli , H. , Schmidt , V. , Teugels , J. ( 1999 ). Stochastic Processes for Insurance and Finance . Wiley Series in Probability and Statistics . New York : Wiley .
  • Schmidli , H. ( 1997 ). An extension to the renewal theorem and an application to risk theory . Ann. Appl. Probab. 7 : 121 – 133 .
  • Silvestrov , D. S. ( 1983 ). Method of a single probability space in ergodic theorems for regenerative processes. I . Math. Operationsforsch. Statist., Ser. Optim. 14 : 285 – 299 .
  • Silvestrov , D. S. ( 1984a ). Method of a single probability space in ergodic theorems for regenerative processes. II . Math. Operationsforsch. Statist., Ser. Optim. 15 : 601 – 612 .
  • Silvestrov , D. S. ( 1984b ). Method of a single probability space in ergodic theorems for regenerative processes. III . Math. Operationsforsch. Statist., Ser. Optim. 15 : 613 – 622 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.