  We consider a classical risk process with arrival of claims following a
non-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 the article is to establish a diffusion
approximation by verifying a functional central limit theorem and to compute
the ruin probability in finite-time horizon. Numerical results will also be
given.
