Precise large deviations of aggregate claims in a risk model with size dependence and non stationary arrivals. Issue 3 (1st February 2018)

• Record Type: Journal Article
• Authors: Fu, Ke-Ang; Li, Jie
• Is Part Of: Communications in statistics. Volume 47:Issue 3(2018)
• Page Start: 698
• Page End: 707
• Publication Date: 2018-02-01
• Subjects: Consistent variation -- Hawkes process -- Large deviation -- Non stationary arrival process -- Size dependence; Primary 60F10 -- Secondary 91B30, 60K05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1310244
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: Consider a risk model with claims of heavy tails for non stationary arrival processes that satisfy a large-deviation principle. Assume that the claim sizes and interarrival times form a sequence of random pairs, with each pair obeying a dependence structure via the conditional distribution of the interarrival time given the subsequent claim size being large, and then a precise large-deviation formula of the aggregate amount of claims is obtained.