Risk Theory with the Gamma Process

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 claims; compound Poisson process; gamma process; infinite divisibility; risk theory; ruin probability; simulation; stable distributions; inverse Gaussian distribution.