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Risk Theory with the Gamma Process

Published online by Cambridge University Press:  29 August 2014

François Dufresne ,
Hans U. Gerber  and
Elias S. W. Shiu
François Dufresne*
Affiliation:
Laval University, University of Lausanne and University of Manitoba
Hans U. Gerber*
Affiliation:
Laval University, University of Lausanne and University of Manitoba
Elias S. W. Shiu*
Affiliation:
Laval University, University of Lausanne and University of Manitoba
*
École d'Actuariat, Université Laval, Québec G1K 7P4, Canada.
École des H.E.C., Université de Lausanne, CH-1015 Lausanne, Switzerland.
Department of Actuarial and Management Sciences, Faculty of Management, University of Manitoba, Winnipeg, Manitoba R3T2N2, Canada.
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Abstract

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The aggregate claims process is modelled by a process with independent, stationary and nonnegative increments. Such a process is either compound Poisson or else a process with an infinite number of claims in each time interval, for example a gamma process. It is shown how classical risk theory, and in particular ruin theory, can be adapted to this model. A detailed analysis is given for the gamma process, for which tabulated values of the probability of ruin are provided.

Keywords

Aggregate claimscompound Poisson processgamma processinfinite divisibilityrisk theoryruin probabilitysimulationstable distributionsinverse Gaussian distribution

Information

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 21 , Issue 2 , November 1991 , pp. 177 - 192
Copyright
Copyright © International Actuarial Association 1991

References

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