  Based on a discrete version of the Pollaczeck-Khinchine formula, a general
method to calculate the ultimate ruin probability in the Gerber-Dickson risk
model is provided when claims follow a negative binomial mixture distribution.
The result is then extended for claims with a mixed Poisson distribution. The
formula obtained allows for some approximation procedures. Several examples are
provided along with the numerical evidence of the accuracy of the
approximations.
