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Cyber claim analysis using Generalized Pareto regression trees with applications to insurance

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  • Farkas, Sébastien
  • Lopez, Olivier
  • Thomas, Maud

Abstract

With the rise of the cyber insurance market, there is a need for better quantification of the economic impact of this risk and its rapid evolution. Due to the heterogeneity of cyber claims, evaluating the appropriate premium and/or the required amount of reserves is a difficult task. In this paper, we propose a method for cyber claim analysis based on regression trees to identify criteria for claim classification and evaluation. We particularly focus on severe/extreme claims, by combining a Generalized Pareto modeling – legitimate from Extreme Value Theory – and a regression tree approach. Coupled with an evaluation of the frequency, our procedure allows computations of central scenarios and of extreme loss quantiles for a cyber portfolio. Finally, the method is illustrated on a public database.

Suggested Citation

  • Farkas, Sébastien & Lopez, Olivier & Thomas, Maud, 2021. "Cyber claim analysis using Generalized Pareto regression trees with applications to insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 92-105.
    • Handle: RePEc:eee:insuma:v:98:y:2021:i:c:p:92-105
    DOI: 10.1016/j.insmatheco.2021.02.009
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    References listed on IDEAS

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    Cited by:

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    2. 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.
    3. 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.
    4. Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.
    5. Christophe Dutang & Quentin Guibert, 2021. "An explicit split point procedure in model-based trees allowing for a quick fitting of GLM trees and GLM forests," Post-Print hal-03448250, HAL.
    6. 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.
    7. Matteo Malavasi & Gareth W. Peters & Stefan Treuck & Pavel V. Shevchenko & Jiwook Jang & Georgy Sofronov, 2024. "Cyber Risk Taxonomies: Statistical Analysis of Cybersecurity Risk Classifications," Papers 2410.05297, arXiv.org.
    8. Jules Sadefo Kamdem & Danielle Selambi, 2022. "Cyber-Risk Forecasting using Machine Learning Models and Generalized Extreme Value Distributions," Working Papers hal-03814979, HAL.
    9. Dacorogna, Michel & Debbabi, Nehla & Kratz, Marie, 2023. "Building up cyber resilience by better grasping cyber risk via a new algorithm for modelling heavy-tailed data," European Journal of Operational Research, Elsevier, vol. 311(2), pages 708-729.
    10. Yang Qiao & Chou-Wen Wang & Wenjun Zhu, 2024. "Machine learning in long-term mortality forecasting," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 340-362, April.
    11. Hainaut, Donatien, 2022. "Multivariate rough claim processes: properties and estimation," LIDAM Discussion Papers ISBA 2022002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    12. Gu, Zheng & Li, Yunxian & Zhang, Minghui & Liu, Yifei, 2023. "Modelling economic losses from earthquakes using regression forests: Application to parametric insurance," Economic Modelling, Elsevier, vol. 125(C).
    13. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2023. "Bias-reduced and variance-corrected asymptotic Gaussian inference about extreme expectiles," TSE Working Papers 23-1444, Toulouse School of Economics (TSE), revised Nov 2023.

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