The time of ruin, the surplus prior to ruin and the deficit at ruin for the classical risk process perturbed by diffusion

The paper studies the joint distribution of the time of ruin, the surplus prior to ruin and. the deficit at ruin for the classical risk process that is perturbed by diffusion. We prove that the expected discounted penalty satisfies an integro-differential equation of renewal type, the solution of which can be expressed as a convolution formula. The asymptotic behaviour of the expected discounted penalty as the initial capital tends to infinity is discussed. (C) 2003 Elsevier Science B.V. All rights reserved.