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Extended precise large deviations of random sums in the presence of END structure and consistent variation. (English) Zbl 1236.60031

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.

MSC:

60F10 Large deviations
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