Fine Study Of Large Deviations

In insurance,many great,risks are alwys cused by some large-amount claims.The claims size process which is the main object,is not necessarily mutually independent. It can be a kind of negatively dependent or other dependent process.Correspondingly, the inter-arrival time process is also not necessarily independent.The distribution of the net loss caused by a claim is heavy-tailed and all kinds of researches on the asymptotics for ruin probabilities are much related to large deviation theory.So large deviation theory has caused wide concern by many insurance companies and scholars.In this paper,we summarized the theory of large deviations in oder to make clear the difference between through large deviations and the precise large deviations.In particular,we dissertate the result of the precise large deviations by the heavy-tailed distribution and NA random variables sequence and conditions,summarized their results and applications among the different heavy-tailed distributions.In the end,in virtue of the introduction of heavily heavy-tailed distribution and the lightly heavytailed distribution,we will give an answer to the reason and difficulty in extending the large deviation theory to the class S.