scholarly journals Precise large deviations for random sums of END real-valued random variables with consistent variation

2013 ◽  
Vol 402 (2) ◽  
pp. 660-667 ◽  
Author(s):  
Shijie Wang ◽  
Xuejun Wang
Keyword(s):  
Large Deviations ◽  
Random Variables ◽  
Random Sums ◽  
Precise Large Deviations ◽  
Consistent Variation

scholarly journals Precise Large Deviations for Random Sums of END Random Variables with Dominated Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Chen ◽  
Zhihui Qu
Keyword(s):  
Asymptotic Behavior ◽  
Large Deviations ◽  
Risk Model ◽  
Random Variables ◽  
Random Sums ◽  
Tail Probabilities ◽  
Precise Large Deviations ◽  
Surplus Process ◽  
End Random Variables ◽  
Renewal Risk

We investigate the precise large deviations for random sums of extended negatively dependent random variables with long and dominatedly varying tails. We find out that the asymptotic behavior of precise large deviations of random sums is insensitive to the extended negative dependence. We apply the results to a generalized dependent compound renewal risk model including premium process and claim process and obtain the asymptotic behavior of the tail probabilities of the claim surplus process.

scholarly journals Extended Precise Large Deviations of Random Sums in the Presence of END Structure and Consistent Variation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Shijie Wang ◽  
Wensheng Wang
Keyword(s):  
Large Deviations ◽  
Random Sums ◽  
Precise Large Deviations ◽  
Consistent Variation ◽  
Loss Process

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 END structure and consistent variation are investigated. The obtained results extend those of Chen and Zhang (2007) and Chen et al. (2011). As an application, precise large deviations of the prospective- loss process of a quasirenewal model are considered.

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