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 (Electron J Probab 11(4):107–120, 2006) and Liu (Stat Probab Lett 79(9):1290–1298, 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 consistently-varying-tailed distribution, and their inter-arrival times are also negatively dependent.
Consistent variation Counting process Lower/upper extended negative dependence Precise large deviation Uniformity
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