Moderate deviations for sums of dependent claims in a size-dependent renewal risk model

ABSTRACT

In this article, we consider a non standard renewal risk model, in which pairs of claim sizes and its corresponding inter-arrival times are identically distributed, and each pair obeys a dependence structure. By assuming that the claim sizes form a sequence of extended negatively dependent random variables with consistently varying tails, moderate deviations for the aggregate amount of dependent claims are obtained.

KEYWORDS:

• Consistent variation
• Extended negative dependence
• Moderate deviation
• Size-dependent renewal model

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E20
• 60F10

Funding

This project was supported by the National Natural Science Foundation of China (Nos. 11301481, 11101062), Zhejiang Provincial Natural Science Foundation of China (No. LY17A010004), Research Foundation for Doctor of Liaoning Province (No. 20121016), First Class Discipline of Zhejiang-A (Zhejiang Gongshang University-Statistics), and Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics).