Hostname: page-component-7b7567c8c-wxvwp Total loading time: 0 Render date: 2026-11-15T03:52:39.153Z Has data issue: false hasContentIssue false
  • English
  • Français

A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities

Published online by Cambridge University Press:  29 August 2014

Marc Goovaerts and
Florian de Vylder
Marc Goovaerts
Affiliation:
K.U. Leuven and U.C. Louvain, Belgium
Florian de Vylder
Affiliation:
K.U. Leuven and U.C. Louvain, Belgium
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Probabilities of ruin are solutions of differential or integrodifferential equations. Solving such equations numerically can be performed by means of approximate quadrature formulae for the convolution part of the equation. In this contribution it is shown how applicable recursion formulae, giving results within a prescribed tolerance level, can be obtained. Some numerical results are displayed.

Keywords

Ruin probabilitynumerical analysisordering of risks

Information

Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 14 , Issue 1 , April 1984, pp. 53 - 59
Copyright
Copyright © International Actuarial Association 1984

References

Gerber, H. U. (1979) An Introduction to Mathematical Risk Theory. Homewood: Richard D. Irwin, Inc.Google Scholar
Gerber, H. U. (1982) On the Numerical Evaluation of the Distribution of Aggregate Claims and its Stop-Loss Premiums. Insurance: Mathematics and Economics. 1, 13–18.Google Scholar
Goovaerts, M. and De Vylder, F. (1983) Upper and Lower Bounds on Infinite Time Ruin Probabilities in Case of Constraints on Claim Size Distributions. Journal of Econometrics. 23, 77–90.CrossRefGoogle Scholar
Panjer, H. H. (1981) Recursive Evaluation of a Family of Compound Distributions. Astin Bulletin. 12, 22–26.CrossRefGoogle Scholar
Sundt, B. and Jewell, W. S. (1981) Further Results on Recursive Evaluation of Compound Distributions. Astin Bulletin. 12, 27–39.CrossRefGoogle Scholar
Wouwe, M. Van, De Vylder, F. and Goovaerts, M. (1982) Numerical Bounds on Infinite Time Ruin Probabilities in Case of Constraints on Claim Size Distributions. (To be presented at the 22nd International Congress of Actuaries, Sydney 1984).Google Scholar