Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T18:58:37.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimating the Probability of Ruin for Variable Premiums by Simulation

Published online by Cambridge University Press:  29 August 2014

Frédéric Michaud
Frédéric Michaud*
Affiliation:
University of Lausanne, Switzerland
*
École des HEC, Université de Lausanne, CH-1015 Lausanne. Switzerland
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.

There is a duality between the surplus process of classical risk theory and the single-server queue. It follows that the probability of ruin can be retrieved from a single sample path of the waiting time process of the single-server queue. In this paper, premiums are allowed to vary. It has been shown that the stationary distribution of a corresponding storage process is equal to the survival probability (with variable premiums). Thus by simulation of the corresponding storage process, the probability of ruin can be obtained. The special cases where the surplus earns interest and the premiums are charged by layers are considered and illustrated numerically.

Keywords

Risk theoryProbability of ruinVariable premiumsInterestPremiums by layersSimulation
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 1 , May 1996 , pp. 93 - 105
Copyright
Copyright © International Actuarial Association 1996

References

REFERENCES

Asmussen, S. and Petersen, S.S. (1988) Ruin probabilities expressed in terms of storage processes. Advances in Applied Probability, 913–916.Google Scholar
Dufresne, F. and Gerber, H. U. (1989) Three methods to calculate the probability of ruin. ASTIN Bulletin, 19, 71–90.CrossRefGoogle Scholar
Feller, W. (1971) An introduction to probability theory and its applications. Volume 2, Wiley, New York.Google Scholar
Gerber, H. U. (1971) Der Einfluss von Zins auf die Ruinwahrscheinlichkeit. Bulletin of the Swiss Association of Actuaries, 63–70.Google Scholar
Gerber, H.U. (1975) The surplus process as a fair game-utility wise. ASTIN Bulletin, 8, 307–322.CrossRefGoogle Scholar
Gerber, H.U. (1979) An introduction to mathematical risk theory. S.S. Huebner Foundation, University of Pennsylvania. Philadelphia.Google Scholar
Harrison, J.M. and Resnick, S.I. (1978) The recurrence classification of risk and storage processes. Mathematics of Operations Research, 3, 57–66.CrossRefGoogle Scholar
Hoel, P.G., Port, S.C. and Stone, C.J. (1972) Introduction to stochastic processes. Houghton Mifflin, Boston.Google Scholar
Petersen, S. S. (1989) Calculation of ruin probabilities when the premium depends on the current reserve. Scandinavian Actuarial Journal, 147–159.CrossRefGoogle Scholar
Ross, S.M. (1983) Stochastic processes. Wiley, New York.Google Scholar
Rudin, W. (1976) Introduction to mathematical analysis. Third edition, McGraw-Hill, New York.Google Scholar
Schmidli, H. (1994) Risk theory in an economic environment and Markov processes. Bulletin of the Swiss Association of Actuaries, 51–70.Google Scholar
Seal, H. L. (1972) Risk theory and the single server queue. Bulletin of the Swiss Association of Actuaries, 171–178.Google Scholar
Segerdahl, C. O. (1942) Über einige risikotheoretische Fragestellungen. Scandinavian Actuarial Journal, 25, 43–83.CrossRefGoogle Scholar
Siegmund, D. (1976) The equivalence of absorbing and reflecting barrier problems for stochastically monotone Markov processes. The Annals of Applied Probability, 4, 914–924.Google Scholar
Taylor, G. C. (1980) Probability of ruin with variable premium rate. Scandinavian Actuarial Journal, 57–76.CrossRefGoogle Scholar