The Research Of Ruin Probability For Poisson Risk Model And Its Generalized Risk Model

Ruin theory is the core of risk theory. The ruin probability of ruin theory and its study to the applications on insurance company is instructive for the management of insurance company. According to conditions is more, theory models is more close to practice, Based on the classical risk model and its generalized risk model, considering the practice, four risk models which is new has been constructed.With martingale ways,a conclusion and study has been done to four risk models which is new has been constructed.The paper has six sections. Chapter 1 gives the background, significance and application prospect. Chapter 2 introduces the basic concept and the method used in the paper. Chapter 3,4,5,6 makes a study of the four new risk model. At first,equations about adjustment coefficient are constructived for each risk model, adjustment coefficient is proved as a single value with the ways of monotonicity and concavity about functions, extreme value is also used. Second, using the martingale ways, the conclusion about the adjustment coefficient conforms to the classical risk model., so the conclusion of the paper has been verified, and the practical significance is clear. Third, combining the convolution, the deficit and surplus immediately before ruin, there is a new way to get the formula of the ruin probabilities in case of exponential claim amouts or premium income, and in case of mixed exponential claim amouts or premium income. Ruin probability and application in risk model with compound Poisson-Geometric process under stochastic interest rate. In this risk model, ruin probability formular is got in case of the stochastic interest rate is constant and the inflation is also considered.At last there is a analysis to the conclusion, the paper also elaborates the developing trend of the risk model.