Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-24T15:03:55.676Z Has data issue: false hasContentIssue false
  • English
  • Français

The Distribution of the time to Ruin in the Classical Risk Model

Published online by Cambridge University Press:  29 August 2014

David C.M. Dickson  and
Howard R. Waters
David C.M. Dickson
Affiliation:
Centre for Actuarial Studies, The University of Melbourne, Victoria, 3010, Australia
Howard R. Waters
Affiliation:
Department of Actuarial Mathematics & Statistics, Heriot-Watt University, Edinburgh EH14 4AS, Great Britain
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.

We study the distribution of the time to ruin in the classical risk model. We consider some methods of calculating this distribution, in particular by using algorithms to calculate finite time ruin probabilities. We also discuss calculation of the moments of this distribution.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 32 , Issue 2 , November 2002 , pp. 299 - 313
Copyright
Copyright © International Actuarial Association 2002

References

Asmussen, S. (1984) Approximations for the probability of ruin within finite time. Scandinavian Actuarial Journal, 31–57.CrossRefGoogle Scholar
Asmussen, S. (2000) Ruin probabilities. World Scientific Publishing, Singapore.Google Scholar
Cardoso, R.M.R. and Egídio dos Reis, A.D. (2002) Recursive calculation of time to ruin distributions. Insurance: Mathematics & Economics 30, 219–230.Google Scholar
Cheng, S., Gerber, H.U. and Shiu, E.S.W. (2000) Discounted probabilities and ruin theory in the compound binomial model. Insurance: Mathematics & Economics 26, 239–250.Google Scholar
Delbaen, F. (1988) A remark on the moments of ruin time in classic risk theory. Insurance: Mathematics & Economics 9, 121–126.Google Scholar
Dickson, D.C.M. and Waters, H.R. (1991) Recursive calculation of survival probabilities. ASTIN Bulletin 21, 199–221.CrossRefGoogle Scholar
Dickson, D.C.M. and Waters, H.R. (1993) Gamma processes and finite time survival probabilities. ASTIN Bulletin 23, 259–272.CrossRefGoogle Scholar
Dickson, D.C.M. and Egidio dos Reis, A.D. (1996) On the distribution of the duration of negative surplus. Scandinavian Actuarial Journal, 148–164.CrossRefGoogle Scholar
Dickson, D.C.M., Egidio dos Reis, A.D. and Waters, H.R. (1995) Some stable algorithms in ruin theory and their applications. ASTIN Bulletin 25, 153–175.CrossRefGoogle Scholar
Dufresne, F., Gerber, H.U. and Shiu, E.S.W. (1991) Risk theory and the gamma process. ASTIN Bulletin 21, 177–192.CrossRefGoogle Scholar
Egidio dos Reis, A.D. (2000) On the moments of ruin and recovery times. Insurance: Mathematics & Economics 27, 331–344.Google Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. S.S. Huebner Foundation, Philadelphia, PA.Google Scholar
Gerber, H.U. and Shiu, E.S.W. (1998) On the time value of ruin. North American Actuarial Journal, 2, 48–78.CrossRefGoogle Scholar
Klugman, S.A., Panjer, H.H. and Willmot, G.E. (1998) Loss Models – From Data to Decisions. John Wiley and Sons, New York.Google Scholar
Lin, X.S. and Willmot, G.E. (1999) Analysis of a defective renewal equation arising in ruin theory. Insurance: Mathematics & Economics 25, 63–84.Google Scholar
Lin, X.S. and Willmot, G.E. (2000) The moments of the time of ruin, the surplus before ruin, and the deficit at ruin. Insurance: Mathematics & Economics 27, 19–44.Google Scholar
Picard, P. and Lefevre, C. (1998). The moments of ruin time in the classical risk model with discrete claim size distribution. Insurance: Mathematics & Economics 23, 157–172.Google Scholar
Seal, H.L. (1978) Survival probabilities. John Wiley & Sons, New York.Google Scholar
Segerdahl, C-O. (1955) When does ruin occur in the collective theory of risk? Skandinavisk Aktuarietidskrift XXXVIII, 22–36.Google Scholar