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Simplified bounds on the tails of compound distributions

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

G. E. Willmot  and
Xiaodong Lin
G. E. Willmot*
Affiliation:
University of Waterloo
Xiaodong Lin*
Affiliation:
University of Toronto
*
∗ Postal address: Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
∗∗ Postal address: Department of Statistics, University of Toronto, Toronto, Ontario, Canada M5S 1A1.
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Abstract

Upper and lower bounds are derived for the tail probabilities of compound distributions using simple properties of the claim size distribution. General bounds are then obtained for various classes of claim size distributions. Some examples are given.

Keywords

FAILURE RATELUNDBERG INEQUALITYRUIN PROBABILITY

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 127 - 133
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This work was supported by the Natural Sciences and Engineering Research Council of Canada.

References

Barlow, R. and Proschan, F. (1975) Statistical Theory of Reliability and Life Testing: Probability Models. Holt, Rinehart and Winston, New York.Google Scholar
Lin, X. (1996) Tail of compound distributions and excess time. J. Appl. Prob. 33, 184–195.CrossRefGoogle Scholar
Willmot, G. (1994) Refinements and distributional generalizations of Lundberg's inequality. Insurance: Math. Econ. 15, 49–63.Google Scholar
Willmot, G. and Lin, X. (1994) Lundberg bounds on the tails of compound distributions. J. Appl. Prob. 31, 743–756.Google Scholar