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...

We consider the Erlang(2) risk model and derive expressions for the density of the time to ruin and the joint density of the time to ruin and the deficit at ruin when the individual claim amount distribution is (i) an exponential distribution and (ii) an Erlang(2) distribution. We also consider...

In this paper, we study a regime-switching risk model with a threshold dividend strategy, in which the rate for the Poisson claim arrivals and the distribution of the claim amounts are driven by an underlying (external) Markov jump process. The purpose of this paper is to study the unified...

Using an approach similar to that of Gerber and Shiu (1998), a recursive formula is given for the expected discounted penalty due at ruin, in the discrete time risk model. With it the joint distribution of three random variables is obtained; time to ruin, the surplus just before ruin and the...

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.