Random Rate Of Return Under The Categories Of Poisson Risk Model, Ruin Probability

Modern risk theory has been developed mainly via stochastic process of mathematical tool, which provides a manager who is serving in financial risk department with theory basis and practical guidance. In risk theory in the present study, most of scholars focus exclusively on generalization to the following three risk models, such as: the compound binomial risk model, poisson risk model and renewal risk model. In this thesis, what to consider is the further expansion of the poisson risk model. It mainly depended on the theory of stochastic point process and the foundation knowledge of probability and studied four kinds of poisson risk model which includes force of random rate of return, and calculated their ruin probabilities.This thesis totals 5 chapters:Chapter 1 is a preface, which mainly introduces the history, the present conditions and the main results of risk theory, and outlines prepare knowledge for this thesis. In this chapter, we especially pay more attention to the classical risk model. Finally we present the main content of this thesis.Chapter 2 introduced the classic poisson risk model and its ruin probability first. Then this chapter built up a new model which includes random rate of return force under of the classic poisson risk model, and calculated its ruin probability.Chapter 3 expanded the classic poisson risk model to the double poisson risk model. In other words, this chapter expanded the insurance policy income process to a poisson process, and supposed it is independent with the compensate process. Then considered the random rate of return force at the double poisson risk, and calculated its ruin probability.Chapter 4 expanded the classic poisson risk model to the generalized compound poisson risk model. In other words, it allowed to pay every trouble, which obey some discrete distribution. Then considered force of the random rate of return on the improved model, and gave the ruin probability to readers. Chapter 5 expanded the classic poisson risk model to the generalized compound double poisson risk model on the foundation of chapter 3 and chapter 4. Then considered force of random rate of return on this model, and got its ruin probability.