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Exact asymptotics of ruin probabilities with linear Hawkes arrivals

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  • Palmowski, Zbigniew
  • Pojer, Simon
  • Thonhauser, Stefan

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.

Suggested Citation

  • Palmowski, Zbigniew & Pojer, Simon & Thonhauser, Stefan, 2025. "Exact asymptotics of ruin probabilities with linear Hawkes arrivals," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:spapps:v:182:y:2025:i:c:s0304414925000109
    DOI: 10.1016/j.spa.2025.104571
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    References listed on IDEAS

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    1. Bessy-Roland, Yannick & Boumezoued, Alexandre & Hillairet, Caroline, 2021. "Multivariate Hawkes process for cyber insurance," Annals of Actuarial Science, Cambridge University Press, vol. 15(1), pages 14-39, March.
    2. Hansjörg Albrecher & Søren Asmussen c, 2006. "Ruin probabilities and aggregrate claims distributions for shot noise Cox processes," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2006(2), pages 86-110.
    3. Gabriele Stabile & Giovanni Luca Torrisi, 2010. "Risk Processes with Non-stationary Hawkes Claims Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 12(3), pages 415-429, September.
    4. Zhu, Lingjiong, 2013. "Ruin probabilities for risk processes with non-stationary arrivals and subexponential claims," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 544-550.
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