Research Of Ruin Probability Under The Some Of Heavy-tailed Distribuiont

The risk theory,as an important theory in actuarial science,has become a popular subject of the research field.Simultaneously, as avital method of measuring the risk of insurance,i.e.,ruin theory,the ruin probability becomes a main object in the theory of risk.in the different angles,this paper obtains equality relation of the tail probabilities of weighted sums,and extends the classical risk model.The details are given as follow:Chapter(1):Introduction of the risk of bankruptcy in particular, the theory of background knowledge and comprehensive theory, focusing on heavy-tailed probability of insolvency under the conditions of classical risk model and the main structure and research progress.Chapter(2): This paper obtains equality relation of the tail probabilities of weighted sums of negatively associated(NA) random variables with common distribution.By some asymptotics for the tail probabilities of maximum of sums,random sums of identically distributed,negatively associated random variables,and inequality of probability obtains equality relation of the tail probabilities of weighted sums,obtained results weaken the conditions of indepent of some literature ,in the condition of negatively associated random variables with common distribution.Tt promotes the result of Tang Qihe etc who have done,the derived conclusion are more universal,many nature which derived can be widely used in finance and insurance and the unexpected eventsChapter(3):In this case.under independent random variables with different distribution functions.the uniformly asymptotic relation And some of asymptotic ruin probability can be proposed.Chapter(4):We consider a discrete-time insurance risk model,in which the financial risks constitute a stationary process with finite dimensional distributions of Farlie–Gumbel–Morgenstern type.We obtain an exact asymptotic formula for the ruin probability, reflecting the impact of this kind of association structure among the financial risks. the derived conclusion are promotes the result of Tang Qihe etc who have done.