Journal of Applied Mathematics
Volume 2012 (2012), Article ID 436531, 12 pages
http://dx.doi.org/10.1155/2012/436531
Research Article

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

Shijie Wang1 and Wensheng Wang2

1School of Mathematic Sciences, Anhui University, Hefei, Anhui 230601, China
2Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

Received 6 November 2011; Accepted 30 December 2011

Academic Editor: Ying U. Hu

Copyright © 2012 Shijie Wang and Wensheng Wang. 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

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.