Methodology and Computing in Applied Probability

, Volume 13, Issue 4, pp 821–833 | Cite as

Precise Large Deviations of Random Sums in Presence of Negative Dependence and Consistent Variation

  • Yiqing Chen
  • Kam C. Yuen
  • Kai W. Ng


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 

AMS 2000 Subject Classifications

60F10 60E15 62H20 62E20 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesThe University of LiverpoolLiverpoolUK
  2. 2.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongHong Kong

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