On the expected discounted penalty function for the continuous-time compound binomial risk model

In this paper, we consider the expected discounted penalty function (i.e., the Gerber–Shiu function) for the continuous-time compound binomial risk model. A recursive equation and the Laplace transform of this function are obtained. Some properties related to the moment of the surplus immediately before ruin, the moment of the deficit at ruin and the Laplace transform of the ruin time are obtained by appropriate choices of parameters of the penalty function. Finally, an example is given for the case when the claim-size distribution is geometric.