Methodology and Computing in Applied Probability

, Volume 13, Issue 4, pp 821–833

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

Article

Abstract

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.

Keywords

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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Copyright information

© 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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