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Precise large deviations of random sums in presence of negative dependence and consistent variation. (English) Zbl 1242.60027
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.

60F10Large deviations
60E15Inequalities in probability theory; stochastic orderings
60H20Stochastic integral equations
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