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.

In this paper, we study the generalized expected discounted penalty (Gerber–Shiu) function in a risk process with credit and debit interests. We define Tu,z to be the first time that the surplus process drops below a certain level z from the initial surplus u(z). The time of ruin and the time...

We study the distributions of [1] the first time that the surplus reaches a given level and [2] the duration of negative surplus in a Sparre Andersen risk process with the inter-claim times being Erlang(2) distributed. These distributions can be obtained through the inversion of Laplace...

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...

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...