Two Types Of Discrete Risk Model Bankruptcy

The risk theory is the basic discipline of learning financial mathematics and the actuarial mathematics of insurance and its core is the study of the ruin theory. Modern risk theory has been developed mainly via stochastic process of mathematical tools, which provides a manager who is serving in finance risk department with theory basis and practical guidance. In this text, the theory of classical martingale and stochastic point process are applied in studying generalized poisson process whose premium is a stochastic process with constant interest force in discrete situation and the binomial risk model with double type insurance. Finally we obtain some expressions or characters of the variables about ruin.Four chapters constitute this text.In the first chapter, we simply introduce the history, the present conditions and the main results of the risk theory, and we especially pay more attention on the classical risk model. Finally we present the main content of this text and the main result of my research.In the second chapter, we outline the knowledge about generalized Poisson process, Markov process, martingale and so on. This knowledge is also the foundation of the text.In the third chapter, we introduce the generalized Poisson risk model: In the classical risk model, the collection of premiums is continuous and the claim process is a compound Poisson process. This paper discuss the random premiums in the discrete situation, at the same time generalize the claim process to a generalized compound Poisson process with constant force of interest in consideration. From the three aspects to generalize the classic risk model, and obtain the upper bound of the ruin probability by martingale approaches.In the fourth chapter, we generalize the classical compound binomial risk model to a binomial process which the premium inner process independent with the claim process.Then,the surplus process includes two binomial processes. Using martingale approaches to obtain the upper bound of the ruin probability and it's expression.