In this paper, we consider the Gerber-Shiu expected discounted penalty function for the perturbed compound Poisson risk process with constant force of interest. We decompose the Gerber-Shiu function into two parts: the expected discounted penalty at ruin that is caused by a claim and the...

In this paper, we consider a risk model with stochastic return on investments. We mainly discuss the ruin probability, the surplus distribution at the time of ruin and the supremum distribution of the surplus before ruin. We prove some properties for these distributions and derive the...

In this paper, we consider the renewal risk process with stochastic interest. For this risk process, we derive exact expressions and integral equations for the Gerber-Shiu expected discounted penalty function and the ultimate ruin probability. When the interest is received at a constant rate and...

This paper investigates the compound Poisson risk model with debit interest. The model assumes that the company is allowed to borrow at some debit interest rate when the surplus turns negative. We obtain the Laplace-Stieltjes transform (LST) of the hitting time of the risk process with constant...

We consider scheduling for heterogeneous server systems, where tasks arrive according to a Poisson process, with their processing requirements following a discrete distribution with finite support. For a system with a dispatcher and several heterogeneous servers, we propose an optimized...

In this paper we investigate the distribution function and the Laplace-Stieltjes Transform(L-S-T) of the first [beta] point of the surplus process {U(t),t[greater-or-equal, slanted]0} using its strong Markov property and the theory of renewal measure. We find the distribution function of in some...