Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-26T19:10:27.305Z Has data issue: false hasContentIssue false
  • English
  • Français

A Heuristic Review of some Ruin Theory Results

Published online by Cambridge University Press:  29 August 2014

G. C. Taylor
G. C. Taylor*
Affiliation:
E. S. Knight & Co., Sydney
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.

The paper deals with the renewal equation governing the infinite-time ruin probability. It is emphasized as intended to be no more than a pleasant ramble through a few scattered results. An interesting connection between ruin probability and a recursion formula for computation of the aggregate claims distribution is noted and discussed. The relation between danger of the claim size distribution and ruin probability is reexamined in the light of some recent results on stochastic dominance. Finally, suggestions are made as to the way in which the formula for ruin probability leads easily to conclusions about the effect on that probability of the long-tailedness of the claim size distribution. Stable distributions, in particular, are examined.

Keywords

Ruin probabilityrecursive computation of aggregate claims distributiondanger of claim size distributionstable claim size distributions
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 15 , Issue 2 , November 1985 , pp. 73 - 88
Copyright
Copyright © International Actuarial Association 1985

References

Bowers, N. L., Gerber, H. U., Hickman, J. C., Jones, D. A. and Nesbitt, C. J. (1982). Society of Actuaries Study Note on Risk Theory. Society of Actuaries: Chicago.Google Scholar
Broeckx, F., Goovaerts, M. and De Vylder, F. (1984). Ordering of Risks and Ruin Probabilities. Paper presented to the Macquarie University General Insurance Seminar, October 1984.Google Scholar
Bühlmann, H. (1970). Mathematical Methods in Risk Theory. Springer-Verlag: Berlin.Google Scholar
Bühlmann, H., Gagliardi, B., Gerber, H. U. and Straub, E. (1977). Some Inequalities for Stop-Loss Premiums. Astin Bulletin 9, 75–83.CrossRefGoogle Scholar
De Vylder, F. (1978). A Practical Solution to the Problem of Infinite Time Ruin Probability. Scandinavian Actuarial Journal.CrossRefGoogle Scholar
Embrechts, P. and Veraverbeke, N. (1982). Estimates for the Probability of Ruin with Special Emphasis on the Possibility of Large Claims. Insurance: Mathematics and Economics 1, 55–72.Google Scholar
Feller, W. (1966). An Introduction to Probability Theory and its Applications, Vol. II. 2nd ed. John Wiley & Sons Inc.: New York.Google Scholar
Gerber, H. U. (1979). An Introduction to Mathematical Risk Theory. Monograph No. 8, S. S. Huebner Foundation for Insurance Education, Wharton School, University of Pennsylvania, Philadelphia. Distributed by Richard D. Irwin, Inc., Homewood, Illinois.Google Scholar
Goovaerts, M. and De Vylder, F. (1984 a). A Stable Recursive Algorithm for Evaluation of Ultimate Ruin Probabilities. Astin Bulletin 14, 53–59.CrossRefGoogle Scholar
Goovaerts, M. and De Vylder, F. (1984 b). Dangerous Distributions and Ruin Probabilities in the Classical Risk Model. Transactions of the 22nd International Congress of Actuaries 3, 111–120.Google Scholar
Goovaerts, M., De Vylder, F. and Haezendonck, J. (1984). Stop-Loss Dominance. Blätter der Deutschen Gesellschaft für Versicherungsmathematik 16, 301–310.Google Scholar
Lundberg, F. (1909). Über die Theorie der Rückversicherung. Ber. VI. Intern. Kong. Versich. Wissens. 1, 877–948.Google Scholar
Lundberg, F. (1926–1928). Forsakringsteknisk Riskutjämning, I, Teori; II, Statistik Englund: Stockholm.Google Scholar
Panjer, H. H. (1981). Recursive Evaluation of a Family of Compound Distributions. Astin Bulletin 12, 22–26.CrossRefGoogle Scholar
Panjer, H. H. (1984). Direct Calculation of Ruin Probabilities. Submitted for publication.Google Scholar
Seal, H. L. (1979). Stochastic Theory of a Risk Business. John Wiley & Sons Inc.: New York.Google Scholar
Sundt, B. and Jewell, W. S. (1981). Further Results on Recursive Evaluation of Compound Distributions. Astin Bulletin 12, 27–39.CrossRefGoogle Scholar
Taylor, G. C. (1974). On the Radius of Convergence of an Inverted Taylor Series with Particular Reference to the Solution of Characteristic Equations. Scandinavian Actuarial Journal 1974, 11–20.Google Scholar
Taylor, G. C. (1976). Use of Differential and Integral Inequalities to Bound Ruin and Queueing Probabilities. Scandinavian Actuarial Journal 1976, 197–208.CrossRefGoogle Scholar