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Multivariate Hawkes process for cyber insurance

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  • Bessy-Roland, Yannick
  • Boumezoued, Alexandre
  • Hillairet, Caroline

Abstract

In this paper, we propose a multivariate Hawkes framework for modelling and predicting cyber attacks frequency. The inference is based on a public data set containing features of data breaches targeting the US industry. As a main output of this paper, we demonstrate the ability of Hawkes models to capture self-excitation and interactions of data breaches depending on their type and targets. In this setting, we detail prediction results providing the full joint distribution of future cyber attacks times of occurrence. In addition, we show that a non-instantaneous excitation in the multivariate Hawkes model, which is not the classical framework of the exponential kernel, better fits with our data. In an insurance framework, this study allows to determine quantiles for number of attacks, useful for an internal model, as well as the frequency component for a data breach guarantee.

Suggested Citation

  • 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.
    • Handle: RePEc:cup:anacsi:v:15:y:2021:i:1:p:14-39_2
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    Cited by:

    1. Malavasi, Matteo & Peters, Gareth W. & Shevchenko, Pavel V. & Trück, Stefan & Jang, Jiwook & Sofronov, Georgy, 2022. "Cyber risk frequency, severity and insurance viability," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 90-114.
    2. Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    3. Na Ren & Xin Zhang, 2024. "A novel k-generation propagation model for cyber risk and its application to cyber insurance," Papers 2408.14151, arXiv.org.
    4. Meng Sun & Yi Lu, 2022. "A Generalized Linear Mixed Model for Data Breaches and Its Application in Cyber Insurance," Risks, MDPI, vol. 10(12), pages 1-23, November.
    5. Benjamin Avanzi & Xingyun Tan & Greg Taylor & Bernard Wong, 2023. "On the evolution of data breach reporting patterns and frequency in the United States: a cross-state analysis," Papers 2310.04786, arXiv.org, revised Jun 2024.
    6. Frank Cremer & Barry Sheehan & Michael Fortmann & Arash N. Kia & Martin Mullins & Finbarr Murphy & Stefan Materne, 2022. "Cyber risk and cybersecurity: a systematic review of data availability," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 47(3), pages 698-736, July.
    7. Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    8. Hillairet, Caroline & Lopez, Olivier & d'Oultremont, Louise & Spoorenberg, Brieuc, 2022. "Cyber-contagion model with network structure applied to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 88-101.

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