Precise large deviations for actual aggregate loss process in a dependent compound customer-arrival-based insurance risk model

Abstract

In this paper, we investigate a dependent compound customer-arrival-based insurance risk model, in which the kth customer purchases a random number of insurance contracts, his/her actual individual claim sizes are described as negatively dependent consistently varying-tailed random variables multiplied by a general shot noise function, and the individual customer-arrival process is a Poisson process. We obtain some precise large deviation results for the actual aggregate loss process, which extend and close the gaps of the related results of Shen et al. [X. Shen, Z. Lin, and Y. Zhang, Precise large deviations for the actual aggregate loss process, Stoch. Anal. Appl., 27:1000–1013, 2009].