Precise Large Deviations for Compound Renewal Risk Model with Negative Dependence Claims

In this paper, we investigate the precise large deviations for a sum of claims in compound renewal risk model with negative dependence structure, in which we assume that is a sequence of negative dependence rv's with distribution functions and the average of right tails of distribution functions is equivalent to some distribution function with consistently varying tails. We try to build a platform for the classical large deviation theory and for the compound renewal risk model.