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We consider a classical risk process with arrival of claims following anon-stationary Hawkes process. We study the asymptotic regime when the premiumrate and the baseline intensity of the claims arrival process are large, andclaim size is small. The main goal of the article is to establish a diffusionapproximation by verifying a functional central limit theorem and to computethe ruin probability in finite-time horizon. Numerical results will also begiven.

Gaussian Approximation of a Risk Model with Non-Stationary Hawkes Arrivals of Claims