Finite Sum Evaluation of the Negative Binomial Exponential Model

The compound negative binomial distribution with exponential claim amounts (severity) distribution is shown to be equivalent to a compound binomial distribution with exponential claim amounts (severity) with a different parameter. As a result of this, the distribution function and net stop-loss premiums for the Negative Binomial-Exponential model can be calculated exactly as finite sums if the negative binomial parameter a is a positive integer. The result is a generalization of LUNDBERG (1940).