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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. (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