Risk Theory For Some Generalization Risk Models

The classical risk model only contains one type of insurance. And in the early insurance business, insurance company is also a single plant. The classical risk model played an important role in risk prediction and risk management. With rapid development of insurance business and extensive use of risk theory, the classical risk model can't satisfy financial company needs more and more. Many academics have promoted the classical risk model,making it close to the actual situation more. But some models and actual situation is still a gap.In this paper, according to multiple line, by-claim, distracter, interest, we research some risk model in financial insurance on the basis by using renewal theory, random process theory, martingale theory. And we made some analysis on differential and integral calculus expression of ruin probability, upper bound for the ultimate ruin probability, the surplus immediately before ruin and deficit at ruin. In the following aspects:1. In chapter 2, according to two-type insurance and by-claim together, we establish a new risk model. The differential and integral equation for ruin probability, distribution of deficit at ruin and distribution of the time in the red are given by using renewal theory.2. In chapter 3, according to distracter and by-claim together, we establish a new risk model. The differential and integral equation for ruin probability and upper bound for the ultimate ruin probability are given.3. In chapter 4, we consider the risk model which contains two types of insurance, each insurance with a noise term, and two items related to interference. The differential and integral equation for survival probability is given by using renewal theory.4. In chapter 5, considering interest rate factors, we got the differential and integral equation for survival probability on the basis of chapter 4.