Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation

The study of precise large deviations for random sums is an important topic in insurance and finance. In this paper, we extend recent results of Tang (2006) and Liu (2009) to random sums in various situations. In particular, we establish a precise large deviation result for a nonstandard renewal risk model in which innovations, modelled as real-valued random variables, are negatively dependent with common consistentlyvarying-tailed distribution, and their inter-arrival times are also negatively dependent.