Journal of the
Korean Mathematical Society JKMS

In this paper, we consider a multi-risk model based on the policy entrance process with $n$ independent policies. For each policy, the entrance process of the customer is a non-homogeneous Poisson process, and the claim process is a renewal process. The loss process of the single-risk model is a random sum of stochastic processes, and the actual individual claim sizes are described as extended upper negatively dependent (EUND) structure with heavy tails. We derive precise large deviations for the loss process of the multi-risk model after giving the precise large deviations of the single-risk model. Our results extend and improve the existing results in significant ways.

Keywords: precise large deviations, EUND, heavy-tailed distribution, loss process

MSC numbers: 60F10, 60G55, 91B30