Large Deviations For The Partial Sums And Random Sums Of ND Sequences In The Class Of C

Financial risk theory is the most interestest issue in the current actuar-ial profession, many researchers are very interested in it.The large deviation problems during claim,one of the main research directions in the financial risk theory,has been widely used in the field of finance and insurance.In the charac-terizing extreme events,large deviations has played a vital role, therefore,to the study of such problems,we studies the problem mainly on the various types of heavy-tailed large deviations.Many researchers,such as Nagaev.A.V,Cline Hs-ing,had made discussion and research in their writings.In2000,Kotzet[32] introduced the concept of ND sequences.However,there are not many article about ND sequences. In this paper,we mainly study large deviations for the partial sums and random sums of ND sequences. This paper consists of three parts:The first part introduces some common heavy tailed distributions, and the corresponding given its simple nature, then the large deviations of the fine research background and have the results of the review, the last on this paper to study the contents of a simple summary.The second part of the first introduction of a negative dependent (ND) sequence of concept, and gives some of its simple nature, then consider the family of the ERV heavy tailed distributions, and has been on the same fam-ily of ERV distribution distribution negative dependent (ND) sequences and large deviation results, the last on this basis and given a random case of large deviation results.The third part of the basis in the second part of the conditions we will be weakened further promote negative dependencies (ND) and with random sequences and the large deviation results are obtained in different distribution of D distributions and orthogonal dependent negative (ND) and with random sequences and the large deviation results.