The Gerber-Shiu Discounted Penalty Function For Two Types Of Risk Models

Based on the compound Poisson-Geometric risk model and the compound binomial risk model, the perturbed compound Poisson-Geometric risk model under the threshold dividend strategy and compound binomial risk model on paying dividends are established, which has both theoretical significance and application value to consider the risk models. The risk model in the initial dividend strategy was proposed by the De Finetti in 1957, Gerber-Shiu discounted penalty function was proposed by Hans U. Gerber and Elias S. W. Shiu in 1998, then both of them were concerned by excellent scholars. In this paper, we consider the compound Poisson-Geometric risk model and the compound binomial risk model, moreover, we obtain the integro-differential equation of ruin probability, survival probability and the Gerber-Shiu discounted penalty function.The paper is organized as follows:Chapter 1. We introduce the development of the risk theory and the important works, main conclusions of the risk model by scholars.Chapter 2. Firstly, we present the definitions and some main results of L-C classical risk model, the methods of research on risk models and the perturbed classical risk model. Secondly, we also present some conclusions of Poisson-Geometric process which will be used in the next chapter.Chapter 3. We study the perturbed compound Poisson-Geometric risk model under the threshold dividend strategy. Firstly, we infer the Poisson-Geometric process from the homogeneous Poisson process, then translate the Poisson-Geometric risk model into the classical risk model and get some results. Secondly, the integro-differential equations of the ruin probability, the survival probability and Gerber-Shiu discounted penalty function of the perturbed compound Poisson-Geometric risk model under the threshold constant dividend strategy are discussed. Finally, some results of perturbed compound Poisson-Geometric risk model under the linear dividend barrier can be derived. Chapter 4. We consider the compound binomial risk model on paying dividends and obtain the formula of the Gerber-Shiu discounted penalty function of this model.