The Probability of Bankruptcy under TwoPoisson Risk Model with Spending and with the Rate of Inflation 

Author  LiuZuoYing 
Tutor  KongFanLiang 
School  Harbin University of Science and Technology 
Course  Applied Mathematics 
Keywords  Risk model ruin probability Lundberg inequality Martingale analysis 
CLC  F224 
Type  Master's thesis 
Year  2012 
Downloads  16 
Quotes  0 
Risk theories mainly study the model of stochastic risk in insurance industry, itis not only basic theory of finance and actuarial science,but also the current hotresearch problems in Actuarial science. As the core problem of the theory of risk,ruin theory is mostly discussed by many scholars. Ruin probability is very importantin risk theories, for one thing, ruin probability can provide a risk warning for thebusiness of the insurance company and insurance company leaders, for another, itcan investigated an insurance company in a certain types of financial risk borne bythe important theoretical basis, for the most important one, ruin probability ofinsurance company is the first to ensure the normal operation of insurancesupervision, oversight of the department has to provide strong basis. Because of theimportance of ruin probability, the study of ruin probability has the important theoryand the practical significance. As the primary method, Martingale theory isbecoming a very important mathematical tools applied in various fields, especiallyin the insurance industry in the application.Based on the theoretical study of nonbinominal two risk model withexpenditure factors, combined with previous research results, this paper introducesclassical risk models in details, and then set up a new model with inflation rate andexpenditure factors.The thesis has given the studing content and results for the following severalsapects:First, the method of martingale analysis, stopping theorem and related theory,the introduction of classical risk model and promotion are involved.2. Then, based on the generalized double Poisson risk model, consider inflationrate and expenditure factors, put the premium income process and claims processinto a Poisson process, put expenditure process into Wiener process, and thenestablish a new model, using the martingale method to get the ultimate ruin probability.3. Under the two factors above, considering the reality of the insurance industry,we expend the single insurance to double ones, and the a new model is set up. Atlast, we also use the martingale method to get the ruin probability of the new modeland Lundberg expression.