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In this paper, we consider a discrete-time risk model with the claim number following a Poisson ARCH process. In this model, the mean of the current claim number depends on the previous observations. We study the large deviations for the aggregate amount for claims. For a heavy-tailed case, we obtain a precise large deviation formula, which agrees with existing ones in the literature. In computing the moderate deviation principle required by the structure of the claim-number process, our treatment substantially relies on an algorithm specifically designed for the autoregressive structure of our models

Precise large deviations of aggregate claims in a discrete-time risk model with Poisson ARCH claim-number process