Several Types Of The Three Nonhomogeneous Poisson Risk Model Research Of Bankruptcy

Classical risk model is one of the most basic risk models, the conditions of which are ideal and perfect to meet. In real life, the insurance company will be affected by a variety of natural and social factors, and the ideal assumptions of the classical risk model don't comply with and the actual operation of insurance company. This paper is based on the classical risk model, discuss several types of risk models, the security process, the claims process and the surrender process of which are non-homogeneous Poisson process.In the first chapter, we make a brief introduction to some theoretical knowledge related to risk theory, the developments of risk models, some basic concepts and conclusions of LC classical risk model, non-homogeneous Poisson process, martingale, linear dividend, tax risk model and and other preliminaries.In the second chapter, on the basis of the model of Liu(2011), the paper promote the insurance process, the claims process and the surrender process to non-homogeneous Poisson process, then establish a Three non-homogeneous Poisson risk model affected by constant interest and confounding factors. At last, this paper find the expressions of Lundberg inequality meet by the bankrupt probability of insurance company, and upper bound simple expressions under two kinds of special conditions by martingale method.In the third chapter, we introduce investment factor and construct Three non-homogeneous Poisson risk model with constant interest, interference and investment.In the fourth chapter, on the basis of Zhao Jine(2010), we establish a Three non-homogeneous Poisson risk model with linear dividend, find the upper bound estimation of the bankrupt probability of the model, and then obtain the integral-differential equationsrespectively satisfied by survival probability, expected discounted dividend function and expected discounted penalty function..The fifth chapter, on the basis of the model in the Huang Ya(2011), we discuss a Three non-homogeneous Poisson risk model with tax, get ultimate ruin probability formula of the model.