Precise large deviations for compound random sums in the presence of dependence structures

In this paper, we deal with the compound random sums of dependent real-valued random variables with heavy-tailed distributions. We establish a precise large deviation result for a nonstandard renewal risk model in which innovations are extended negatively dependent real-valued random variables with a common dominatedly varying distribution function, their interarrival times are extended negatively dependent nonnegative random variables, and the numbers of innovations caused by individual events are also extended negatively dependent positive random variables. As an illustration of the obtained result, we give two applications related to some insurance risk models.