Exact asymptotics of ruin probabilities with linear Hawkes arrivals

Zbigniew Palmowski, Simon Pojer and Stefan Thonhauser

Stochastic Processes and their Applications, 2025, vol. 182, issue C

Abstract: In this contribution we consider a risk process whose arrivals are driven by a linear marked Hawkes process. Using an appropriate change of measure and a generalized renewal theorem, we are able to derive the exact asymptotics of the process’s ruin probability in the case of light-tailed claims. On the other hand, we can exploit the principle of one large jump to derive the analogous result in the heavy-tailed situation. Furthermore, we derive several intermediate results like the Harris recurrence of the Hawkes intensity process which are of their own interest.

Keywords: Hawkes process; Ruin probability; Cramér asymptotics; Subexponential asymptotics (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spa.2025.104571

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