Exact asymptotics of ruin probabilities with linear Hawkes arrivals

Zbigniew Palmowski; Simon Pojer; Stefan Thonhauser

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arXiv · 2304.03075

Exact asymptotics of ruin probabilities with linear Hawkes arrivals

Zbigniew Palmowski·Simon Pojer·Stefan Thonhauser

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Abstract

In this paper we determine bounds and exact asymptotics of the ruin probability for risk process with arrivals given by a linear marked Hawkes process. We consider the light-tailed and heavy-tailed case of the claim sizes. Main technique is based on the principle of one big jump, exponential change of measure, and renewal arguments.

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Zbigniew Palmowski, Simon Pojer, Stefan Thonhauser. 2023-04-06. Exact asymptotics of ruin probabilities with linear Hawkes arrivals. https://arxiv.org/abs/2304.03075

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