Study On Ruin Probability Of Risk Model And Its Extended Model Under Compound Poisson Distribution

Ruin theory is the core of risk theory.It is significant to study the probability of ruin and its practical application.With the development of the risk theory,it is more and more mature and widely used,the traditional classical risk model is far from meeting the demand,so it is necessary to promote the model in order to get closer to the actual situation.This paper from the classical risk model and other generalized risk models based the traditional view,combined with the actual,two new risk models are established,and to study and summarize the ruin probability and the application of the new risk model to promote the use of martingale method.This paper is divided into 4 chapters: the first chapter gives the background,significance and Prospect of application;the second chapter briefly introduces some basic concepts and methods involved in the text;the third chapter studies the distribution of a single compound Poisson risk model is generalized risk model of insurance for insurance claims occur at the same time.In the model,the premium income is a constant,the m heavy insurance claims at the same time,the claim process is a compound Poisson process.In the fourth chapter,we extend the Poisson risk model to the double compound Poisson process with interference and study it.In each model are first constructed for the adjustment coefficient of the equation,using monotonicity,convexity,extreme value that the adjustment coefficient and only exist,the exact expression of ruin probability is obtained,and the push Lundberg inequality,and then given a limit on ruin probability value.Finally,a comprehensive analysis of the full text is given,and the main conclusions and results are obtained.