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.

中文翻译：

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非平稳霍克斯到达索赔的风险模型的扩散近似

我们考虑一个经典的风险过程，即非平稳霍克斯过程之后的索赔到达。当保费率和索赔到达过程的基线强度较大且索赔量较小时，我们研究渐近状态。本文的主要目的是通过验证泛函中心极限定理建立扩散近似，并计算有限时间范围内的破产概率。数值结果也将给出。