Precise Moderate Deviation For Multidimensional Dependent Risk Models

This dissertation focuses on the precise moderate deviation for the multidimensional dependent risk model,and the main contents is as follows:In the first chapter,several families of heavy-tailed distributions are introduced.Coupla functions and their properties are presented.In the second chapter,assumptions of the multidimensional dependent risk model are stated.Let(?)be a sequence of m-dimensional independentidentically distributed nonnegative random vectors,whose univariate marginal distributions have finite means and consistently varying tails.The components of X_i can be dependent,and the correlation between the components can be described by the Coupla function.Let (?)be a nonnegative integer value process independent of the sequence{X _i,i≥1}.In the third chapter,the main results of this paper are stated.Under the assumptions of the second chapter,firstly the precise moderate deviation for partial sum(?) is studied.Then,based on some certain conditions imposed on N(t)t,the moderate deviation for random sum(?) is investigated.