Precise large deviations of aggregate claim amount in a dependent renewal risk model. Issue 5 (4th March 2017)

• Record Type: Journal Article
• Authors: Liu, Xijun; Yu, Changjun; Gao, Qingwu
• Is Part Of: Communications in statistics. Volume 46:Issue 5(2017)
• Page Start: 2354
• Page End: 2363
• Publication Date: 2017-03-04
• Subjects: Dependence structure -- precise large deviations -- renewal risk model.; Primary 60F10 -- Secondary 62P05 -- 91B30; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1044666
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: In this paper, we consider a dependent risk model, in which the claim sizes are ofdependence structure, their inter-arrival times are independent, identically distributed (i.i.d.), and the claim size and its corresponding inter-arrival time satisfy a certain dependence structure described via the conditional distribution of the inter-arrival time given the subsequent claim size being large. We obtain the asymptotics of the lower and upper bounds of precise large deviations for the aggregate amount of claims, which holds uniformly for all x in an infinite interval of t .