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...

In this paper, we present a result on the distribution of the maximum severity of ruin in a perturbed risk process with Markovian arrivals. We show that the distribution of the maximum severity of ruin is closely related to the distributions of one-sided and two-sided passage times.