Precise large deviations of aggregate claims in a risk model with size dependence and non stationary arrivals

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.

KEYWORDS:

• Consistent variation
• Hawkes process
• Large deviation
• Non stationary arrival process
• Size dependence

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 60F10
• Secondary 91B30, 60K05

Acknowledgments

The authors thank the referees for pointing out some errors in a previous version, as well as for several comments that have led to improvements in this work.

Funding

Project supported by Zhejiang Provincial Natural Science Foundation of China (No. LY17A010004), the Humanities and Social Sciences Foundation of the Ministry of Education of China (No. 17YJC910002), First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics), and Foundation for Young Talents of ZJGSU.