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Gamma Processes and Finite Time 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
Howard R. Waters*
Affiliation:
Heriot-Watt University, Edinburgh
*
Centre for Actuarial Studies, University of Melbourne, Parkville, Victoria 3052, Australia
Department of Actuarial Mathematics and Statistics, Heriot-Watt University, Edinburgh EH 14 4AS, Scotland
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Abstract

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In this paper we derive formulae for finite time survival probabilities when the aggregate claims process is a Gamma process. We illustrate how a compound Poisson process can be approximated by a Gamma process and by a process defined as a translated Gamma process. We also show how survival probabilities for a compound Poisson process can be approximated by those for a Gamma process or a translated Gamma process.

Keywords

Gamma processfinite timesurvival probability
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 23 , Issue 2 , November 1993 , pp. 259 - 272
Copyright
Copyright © International Actuarial Association 1993

References

REFERENCES

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Seal, H. L. (1974) The numericl calculation of U(w, t), the probability of non-ruin in an interval(0, t). Scandinavian Acutarial Journal, 121–139.Google Scholar
Seal, H. L. (1978a) From aggregate claims distribution to probability of ruin. ASTIN Bulletin 10, 47–53.CrossRefGoogle Scholar
Seal, H. L. (1978b) Survival probabilities: the goal of risk theory. John Wiley and Sons, New York.Google Scholar