Research On Cox Risk Model In Random Environment

As the core content of risk theory -- the ruin theory, mainly researching on long-term changes in earnings of the insurance company. Specifically,the insurance company’s earnings changes along with the development of insurance business, when the surplus value is negative, the insurance company will go bankrupt. So the ruin probability is an important index to measure the insurance company operate normal or not over a long period of time. High probability of ruin, indicating the insurance company to take effective management methods to stabilize company avoid bankruptcy happens.Since the classical risk model proposed,many researchers to improve it based on the actual reality of the business of insurance companies. One of the major improvements model has the following three aspects:Firstly, using different points of the process described in the number of claims in different circumstances, secondly,the constant is change, in reality, the premium rate is not static, thirdly, adds disturbance factors in the classical risk model, which is to consider the actual operation of the interest rate, and other factors affecting the rate of inflation.This article is based on previous research, we constructed three different risk model to promoted the classical risk model by considering the point process description of the number of claims, the premium income of the process, interest rates, the interference of the four factors, which makes the model more in line with the actual insurance business.we using the random process, risk theory and probability theory and other disciplinary theoretical knowledge to study these three models and by using the martingale method to calculate the expression of the ruin probability. Content Framework are as follows:Chapter One: Firstly,we introduces the significance of this study; secondly, according to the main contents of this paper we reviews the related research at home and abroad briefly; and finally we introduces the main research content of this paper.Chapter two:According to the research content of this paper we introduces the classical risk model; secondly we list some theorems, definitions, and related disciplines of knowledge.Chapter Three: The main work is to establish premium reinvestment in the Cox risk model and premium reinvestment in the double Cox risk model, using martingale method to calculate the probability of ruin Lundberg inequality and make inferences on the ruin probability inequality.Chapter four: Based on the study of the third chapter, we establish the Cox risk model with premium reinvestment and interference, using the martingale method to calculate the Lundberg inequality of the ruin probability and also make inferences on the ruin probability inequality.