Summary: The study of precise large deviations of random sums is an important topic in insurance and finance. In this paper, extended precise large deviations of random sums in the presence of an extended negatively de- pendent (END) structure and consistent variation are investigated. The obtained results extend those of Y. Chen
and W. Zhang
[Stat. Probab. Lett. 77, No. 5, 530–538 (2007; Zbl 1117.60025
)] and Y. Chen, A. Chen
and K. W. Ng
[J. Appl. Probab. 47, No. 4, 908–922 (2010; Zbl 1213.60058
)]. As an application, precise large deviations of the prospective-loss process of a quasirenewal model are considered.