In this paper, precise large deviations of nonnegative,
non-identical distributions and negatively associated random variables are investigated.
Under certain conditions, the lower bound of the precise large deviations for the
non-random sum is solved and the uniformly asymptotic results for the corresponding
random sum are obtained. At the same time, we deeply discussed the compound renewal
risk model, in which we found that the compound renewal risk model can be equivalent
to renewal risk model under certain conditions. The relative research results of
precise large deviations are applied to the more practical compound renewal risk model,
and the theoretical and practical values are verified. In addition, this paper also
shows that the impact of this dependency relationship between random variables to
precise large deviations of the final result is not significant.