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

Yiqing Chen (), Kam C. Yuen and Kai W. Ng
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Yiqing Chen: The University of Liverpool
Kam C. Yuen: The University of Hong Kong
Kai W. Ng: The University of Hong Kong

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 4, 821-833

Abstract: 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; 60F10; 60E15; 62H20; 62E20 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s11009-010-9194-7

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