Expected discounted Penalty Function\\for a Thinning Risk Model

In this paper, we consider a risk model in which the premium arriving number process is a Poisson process with parameter \lambda>0 while the claim number process is the thinning of the pre- mium arriving number process. Under such a model, we obtain the integral equation, the integro- differential equation and the recursive formula for the expected discounted penalty function. Using the integro-differential equation we get the closed form expressions for the Laplace transform of the time of ruin and the deficit at ruin when the premium and the claim sizes are exponentially distributed.