On the distribution of the surplus of the D–E model prior to and at ruin

In this paper, the methods concerning (Embrechts, P., Schmidli, H., 1994. Advances in Applied Probability 26, 404–422) are used to investigate the distribution of the surplus of a Dassios–Embrechts model at ruin, by which we can transform the calculation of the distribution into that of a limit, which refers to the probabilities of some first hitting times. We will also consider briefly the distribution and the density of the surplus immediately prior to ruin and the joint density of the surplus immediately prior to and at ruin.