Precise large deviations of aggregate claims in a discrete-time risk model with Poisson ARCH claim-number process

Journal of inequalities and applications

Shihang Yu¹ 

关键词: Poisson ARCH process;    precise large deviations;    moderate deviation principle;    60F10;    62J05;    90B30;   

DOI  :  10.1186/s13660-016-1080-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider a discrete-time risk model with the claim number following a Poisson ARCH process. In this model, the mean of the current claim number depends on the previous observations. We study the large deviations for the aggregate amount for claims. For a heavy-tailed case, we obtain a precise large deviation formula, which agrees with existing ones in the literature. In computing the moderate deviation principle required by the structure of the claim-number process, our treatment substantially relies on an algorithm specifically designed for the autoregressive structure of our models.

【 授权许可】

CC BY