Risk Theory with the Gamma Process
- 1 November 1991
- journal article
- Published by Cambridge University Press (CUP) in ASTIN Bulletin
- Vol. 21 (2) , 177-192
- https://doi.org/10.2143/ast.21.2.2005362
Abstract
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
This publication has 6 references indexed in Scilit:
- Actuarial MathematicsJournal of Risk and Insurance, 1990
- On the computation of the aggregate claim distribution when individual claims are Inverse GaussianInsurance: Mathematics and Economics, 1989
- Three Methods to Calculate the Probability of RuinASTIN Bulletin, 1989
- The surpluses immediately before and at ruin, and the amount of the claim causing ruinInsurance: Mathematics and Economics, 1988
- The Poisson-Inverse Gaussian distribution as an alternative to the negative binomialScandinavian Actuarial Journal, 1987
- The Inverse Gaussian Distribution and its Statistical Application—A ReviewJournal of the Royal Statistical Society Series B: Statistical Methodology, 1978