Title: Gaussian Approximation of a Risk Model with Stationary Hawkes Arrivals of Claims,
Abstract: We consider a classical risk process with arrival of claims following a
stationary Hawkes process. We study the asymptotic regime when the premium rate
and the baseline intensity of the claims arrival process are large, and claim
size is small. The main goal of this article is to establish a diffusion
approximation by verifying a functional central limit theorem of this model and
to compute both the finite-time and infinite-time horizon ruin probabilities.
Numerical results will also be given.