Of The Renewal Risk Model

In the thesis we consider the penalty functions for two classes of risk processes and some results on the distribution of dividend payments until ruin and the Gerber-Shiu function under a Sparre Andersen risk model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a constant dividend barrier.The thesis is divided into three chapters according to contents:In Chapter 1, we consider a risk model involving two independent class of insurance risks. We assumed that the two claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Laplace transforms of two types of the Gerber-Shiu functions at ruin are derived from an integro-differential equations system. Finally, we obtain two generalized renewal equations when n = 2.In Chapter 2, we also consider a risk model involving two independent class of insurance risks. We assumed that the two claim number processes are two independent generalized Erlang(2) processes, respectively.Laplace transforms of two types of the Gerber-Shiu functions at ruin are derived from an integro-differential equations system.In Chapter 3, we present some results on the distribution of dividend payments until ruin and the Gerber-Shiu function under a Sparre Andersen risk model perturbed by diffusion with generalized Erlang(n)-distributed inter-claim times and a constant dividend barrier. Integro-differential equations for the moment-generating function and the mth moment of the sum of the discounted dividend payments until ruin are derived. We also derive integro-differential equations for the Gerber-Shiu function.