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Document Details :

Title: Risk Theory with the Gamma Process
Author(s): DUFRESNE, François , GERBER, Hans U. , SHIU, Elias S.W.
Journal: ASTIN Bulletin
Volume: 21    Issue: 2   Date: November 1991   
Pages: 177-192
DOI: 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.