The Research Of Ruin Probability For The Several Compound Risk Models Disturbed By Diffusion

Risk theory is an important content of the theory of probability and statistics.It is also a hot topic in the financial, insurance and investment field.And the risk theory has certain directive significance related to the study of the insurance industry in the adjustment coefficient and ruin probability. In recent years, the classical risk model is generalized and researched by many scholars.Then a lot of important and meaningful conclusions are obtained. This paper carries out a further study on the basis of existing research results, and the general expression of ruin probability and its inequality are obtained by using some properties of the moment generating function. The main contents are as follows:First of all, it introduces the significance, the research status and some important research directions of the risk theory, and some important properties that this paper will be used are given.Then,the classical risk model is extended to the double compound Poisson risk model with stochastic interest,in which the arrival of the premium incomes and the arrival of the claims are mutual independence.The expression of ruin probability and the Lundberg inequality are derived by using compound Poisson definition and full probability formula.Finally,the risk model whose number of claims obeys the compound Poisson is popularized to the risk model with the constant interest, in which the number of claims is Poisson-Geometric process.The general expression of the ruin probability is obtained by the moment generating function and adjustment coefficient properties, At the same time,the integral equation of the survival probability is got by the Taylor series expansion and total probability formula.