Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 936301, 10 pages
http://dx.doi.org/10.1155/2013/936301
Research Article

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

Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Received 26 February 2013; Accepted 8 May 2013

Academic Editors: E. Di Nardo and D. Luchinsky

Copyright © 2013 Yu Chen and Zhihui Qu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.