Risk Model, Dependent The Barriers Premium In The Case Of Randomization

In this paper, we consider a risk process with dependence between inter-premium arrivals and premium, random income, a constant barrier. We derive two integral equa-tions for the Gerber-Shiu discounted penalty function and expected discounted dividend payments. Some explicit results are obtained for exponential premium and exponential claims.In chapter one, we introduce the background of risk model and the risk model which we will study in this paper.In chapter two, we derive an integral equation for the Gerber-Shiu discounted penalty function Furtherly, we derive the Laplace transform of the ruinThen we consider the special case where the premium sizes are exponential distri-bution, we show that the Gerber-Shiu discounted penalty function satisfies an Volterra equation of the second kindBased on the Volterra equation we derive the general solution for the Gerber-Shiu discounted penalty functionIn chapter three, at first, we derive an integral equation for the expected discounted dividend payments Then we derive an Volterra equation of the second kind for the expected discounted dividend paymentsBased on it we derive the general solution,for the expected discounted dividend payments...