Promotion Of Dividends On The Classical Risk Model

Dividend strategies for insurance risk model were first proposed by De Finetti in 1957 , and he found that the optimal strategy must be a barrier strategy for the discret risk model. Another extension of classical risk model is that the classical risk model perturbed by diffusion, which was first introduced by Gerber(1970) . Lin et al.([1]) had studied the classical risk model with constant dividend barrier by using the discounted penalty function, which is the famous Gerber-Shiu function.The purpose of this thesis is to present some results on the Gerber-Shiu function under a compound Poisson risk model perturbed by diffusion with a threshold dividend strategy and a risk model involving two independent classes of insurance risks with a constant dividend barrier.In Chapter 1, we consider the classical risk model perturbed by diffusion. We use the approach of [1], i.e., because the Gerber-Shiu function behaves differently, depending on whether its initial surplus u is below or above the barrier level b, so we write it differently into two parts. Integro-differential equations with certain boundary conditions for the Gerber-Shiu functions are derived. We also obtain analytical expressions for the Gerber-Shiu discounted penalty functionsφ_b(u).We state the main results as follows: Theorem 1.4.1. We can obtain analytical expressions for functionsφ_b(u).In Chapter 2, we consider a risk model involving two independent classes of insurance risks. We assumed that the two claim number processes are independent Poisson and generalized Erlang(2) processes, respectively. Two integro-differential equations for the Gerber-Shiu discounted penalty functions are derived.We state the main results as follows: Theorem 2.2.1.where . Then explicit results are derived when the claims from both classes are exponentially distributed.