Local Precise Large Deviations For Independent Sums In Multi-risk Model

Nowadays, large deviation theory is one of the hot spots in the field of finance and insur-ance. More and more researchers make contributions to it. Recently, there are scholars studying the local large deviations based on the large deviations.In this paper, we study the case of independent sums in multi-risk model. Assume that there exist k types of variables. The ith are denoted by{Xij, j≧1}, which are i.i.d. and finite mean, i=1,...,k. Denote the density function as fi(x),(i=1,...,k). We investigate local large deviations for partial sums (?)Sni=(?)Xij as the density function is in different classes. We give the theorems and proofs for the local large deviations. In addition, we get the asymptotic of the local large deviations. Compared with Yang et al.(2010), we extend the model to the multi-risk model.