The probability of ruin for the Inverse Gaussian and related processes

Abstract

We consider a family of aggregate claims processes that contains the gamma process, the Inverse Gaussian process, and the compound Poisson process with gamma or degenerate claim amount distribution as special cases. This is a one-parameter family of stochastic processes. It is shown how the probability of ruin can be calculated for this family. Extensive numerical results are given and the role of the parameter is discussed.