The distribution of total dividend payments in a Sparre Andersen model

We study the distribution of the total dividend payments in a Sparre Andersen model with phase-type inter-claim times in the presence of a constant dividend barrier. This paper shows that the distribution of the total dividend payments prior to the time of ruin is a mixture of a degenerate distribution at zero and a phase-type distribution. Further, the total dividends prior to ruin can be expressed as a compound geometric sum.