The Large Deviation Of The Compound Poisson Risk Model With Constant Interest Rate Perturbation And Its Application

It is very important to build the model of financial risk management.In order to control the risk,we need to optimize the development of the classical model.The main work of this paper is based on the classical risk model,considering two aspects of interest rate and disturbance.We focus on the estimation of the risk process with the large deviation principle because the large deviation tool can be used to quantify the extreme claims.This paper is divided into the following sections:The first chapter introduces the classical risk model and relevant important conclusions,the basic model in two aspects of the promotion,the attention of constant interest perturbed compound Poisson risk model;then gives several risk models limit properties results;The last section is the main work of this paper.The second chapter introduces the related basic knowledge.We give the basic concepts and important theorems,including Poisson shot noise,measure logarithmic transformation,large deviation of the general definition,Cramer theorem and Gartner-Ellis theorem and Varadhan theorem etc.The third chapter contains the main results of this paper.In this paper,we prove that the Cramer-Lundberg risk process satisfies the large deviation principle,we get the asymptotic properties of the surplus process;then we discuss the difference between the present value and the discounted value claim,and prove that the difference process can satisfy the large deviation principle;finally,we by use of Varadhan theorem gives application in the research on entropy risk measure,and obtains the ultimate entropy measure of risk estimation.The fourth chapter is the summary and prospect of this paper.