The Research Of Several Types Of Ruin Probability In Risk Modal And Related Issues

In the field of Insurance Actuarial Mathematics, risk theory is concerned by many departments on actuarial theory and its applications recently. The influence of fluctuation of interest rate on insurance agent is tremendous. As the trade of the risk, insurance agent's own risk can't be ignored. According to these, the paper studys deeply the ruin problem of risk models under interest rate. The aim is to make the insurance company better evade risk and work steadily in theory.Firstly, the background of this thesis is introduced. Then the basic theories about ruin probability,random process and martingale are also introduced.Secondly, discuss the continuous risk model. established the premium income and claims are the compound Poisson distribution of pairs of compound Poisson model, based on the classical ruin model. Then discuss the properties of surplus process, ruin probability and the Lundberg upper bound of the general expression . On this basis, the use of the martingale theory, discusses the multi-line compound Poisson model of the ruin probability and the Lundberg upper bound. Finally taking into account interest rates and inflation, as to uncertainty on the income and expenditure, the multiple insurance compound Poisson risk model of ruin probability and the Lundberg upper bound ,given a more practical results.Finally, improve the discrete risk model. Based on the classical binomial model, double binomial model which incomes and claims follow two independent binomial processes. discussed the properties of surplus process, get the general expression of the ruin probability and the Lundberg upper bound. At the same time be considered according to the actual insurance risk model with multi-ruin probability, taking into account the impact of inflation and interest rates, as well as the uncertainty of income and expenditure of insurance companies, using martingale theory, and Chebychev inequality are two ways to arrive at the general expression of the ruin probability and the Lundberg upper bound.