Summary: 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 Q. Tang
[Electron. J. Probab. 11, Paper No. 4, 107–120 (2006; Zbl 1109.60021
)] and L. Liu
[Stat. Probab. Lett. 79, No. 9, 1290–1298 (2009; Zbl 1163.60012
)] 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.