Abstract
In this chapter we focus on the Cramér-Lundberg model driven by a claim arrival process with randomly fluctuating rate. We consecutively discuss models in which the arrival rate evolves as an M/G/\(\infty \) queue (to do justice to a fluctuating number of customers), as a shot-noise process (to model the impact of catastrophic events) and as a Hawkes process (to model the effect of claims triggering additional claims). The main objective is to determine, in the light-tailed context, the decay rate of the ruin probability. The proofs rely either on applying a change-of-measure, or on a large deviations based argumentation.
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Mandjes, M., Boxma, O. (2023). Arrival Processes with Clustering. In: The Cramér–Lundberg Model and Its Variants. Springer Actuarial(). Springer, Cham. https://doi.org/10.1007/978-3-031-39105-7_8
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DOI: https://doi.org/10.1007/978-3-031-39105-7_8
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