SOME RESULTS ON A RISK MODEL WITH DEPENDENCE BETWEEN CLAIM SIZES AND CLAIM INTERVALS

In this article, the risk model with a dependent setting is considered. By using diferential argument, an integro-diferential equation for some Gerber-Shiu discounted penalty functions for the exponentially distributed claim sizes is derived. Applications of the integrodiferential equation are given to the Laplace transform of the time of ruin, the deficit at ruin, and the surplus immediately before ruin occurs. Finally, we analyze the expected present value of dividend payments in the same risk model with a constant dividend barrier.