Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T08:33:00.408Z Has data issue: false hasContentIssue false
  • English
  • Français

Recursive Calculation of Survival Probabilities

Published online by Cambridge University Press:  29 August 2014

David C. M. Dickson  and
Howard R. Waters
David C. M. Dickson*
Affiliation:
Heriot-Watt University, Edinburgh, United Kingdom
Howard R. Waters*
Affiliation:
Heriot-Watt University, Edinburgh, United Kingdom
*
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.
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.

In this paper we present an algorithm for the approximate calculation of finite time survival probabilities for the classical risk model. We also show how this algorithm can be applied to the calculation of infinite time survival probabilities. Numerical examples are given and the stability of the algorithms is discussed.

Keywords

Survival probabilityfinite timeinfinite timerecursive calculationsnumerical stability
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 21 , Issue 2 , November 1991 , pp. 199 - 221
Copyright
Copyright © International Actuarial Association 1991

References

Conte, S. D. and De Boor, C. (1980) Elementary Numerical Analysis. McGraw Hill-Kogakusha, London.Google Scholar
De Vylder, F. and Goovaerts, M.J. (1988) Recursive calculation of finite-time ruin probabilities. Insurance: Mathematics and Economics 7, 1–8.Google Scholar
Dufresne, F. (1988) Distributions stationnaires d'un système bonus-malus et probabilité de ruine. ASTIN Bulletin 18, 31–46.CrossRefGoogle Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation Monograph Series No. 8. Distributed by R. Irwin, Homewood, IL.Google Scholar
Giezendanner, E., Straub, E. and Wettenschwiler, K. (1972) Zur Berechnung von Ruinwahrscheinlichkeiten. Transactions of the 19th International Congress of Actuaries, Oslo, 4, 645–651.Google Scholar
Panjer, H.H. (1981) Recursive evaluation of a family of compound distributions. ASTIN Bulletin 12, 22–26.CrossRefGoogle Scholar
Seal, H.L. (1978) Survival Probablities. John Wiley and Sons, New York.Google Scholar
Wikstad, N. (1971) Exemplification of ruin probabilities. ASTIN Bulletin 6, 147–152.CrossRefGoogle Scholar