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Pricing Of Cyber Insurance Contracts In A Network Model

Author

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  • Fahrenwaldt, Matthias A.
  • Weber, Stefan
  • Weske, Kerstin

Abstract

We develop a novel approach for pricing cyber insurance contracts. The considered cyber threats, such as viruses and worms, diffuse in a structured data network. The spread of the cyber infection is modeled by an interacting Markov chain. Conditional on the underlying infection, the occurrence and size of claims are described by a marked point process. We introduce and analyze a new polynomial approximation of claims together with a mean-field approach that allows to compute aggregate expected losses and prices of cyber insurance. Numerical case studies demonstrate the impact of the network topology and indicate that higher order approximations are indispensable for the analysis of non-linear claims.

Suggested Citation

  • Fahrenwaldt, Matthias A. & Weber, Stefan & Weske, Kerstin, 2018. "Pricing Of Cyber Insurance Contracts In A Network Model," ASTIN Bulletin, Cambridge University Press, vol. 48(3), pages 1175-1218, September.
    • Handle: RePEc:cup:astinb:v:48:y:2018:i:03:p:1175-1218_00
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    Citations

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    Cited by:

    1. 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.
    2. Caroline Hillairet & Olivier Lopez & Louise d'Oultremont & Brieuc Spoorenberg, 2022. "Cyber contagion: impact of the network structure on the losses of an insurance portfolio," Post-Print hal-03388840, HAL.
    3. Caroline Hillairet & Olivier Lopez, 2021. "Propagation of cyber incidents in an insurance portfolio: counting processes combined with compartmental epidemiological models," Post-Print hal-02564462, HAL.
    4. Zhang, Xiaoyu & Xu, Maochao & Su, Jianxi & Zhao, Peng, 2023. "Structural models for fog computing based internet of things architectures with insurance and risk management applications," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1273-1291.
    5. Yeftanus Antonio & Sapto Wahyu Indratno & Rinovia Simanjuntak, 2021. "Cyber Insurance Ratemaking: A Graph Mining Approach," Risks, MDPI, vol. 9(12), pages 1-34, December.
    6. 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.
    7. Caroline Hillairet & Olivier Lopez & Louise d'Oultremont & Brieuc Spoorenberg, 2021. "Cyber contagion: impact of the network structure on the losses of an insurance portfolio," Working Papers hal-03388840, HAL.
    8. Daniel Zängerle & Dirk Schiereck, 2023. "Modelling and predicting enterprise-level cyber risks in the context of sparse data availability," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 434-462, April.
    9. Da, Gaofeng & Xu, Maochao & Zhao, Peng, 2021. "Multivariate dependence among cyber risks based on L-hop propagation," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 525-546.
    10. Gabriela Zeller & Matthias Scherer, 2023. "Risk mitigation services in cyber insurance: optimal contract design and price structure," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 502-547, April.
    11. 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.
    12. Jevtić, Petar & Lanchier, Nicolas, 2020. "Dynamic structural percolation model of loss distribution for cyber risk of small and medium-sized enterprises for tree-based LAN topology," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 209-223.
    13. Yeftanus Antonio & Sapto Wahyu Indratno & Suhadi Wido Saputro, 2021. "Pricing of cyber insurance premiums using a Markov-based dynamic model with clustering structure," PLOS ONE, Public Library of Science, vol. 16(10), pages 1-28, October.
    14. Ma, Boyuan & Chu, Tingjin & Jin, Zhuo, 2022. "Frequency and severity estimation of cyber attacks using spatial clustering analysis," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 33-45.
    15. 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.
    16. 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.
    17. Michel Dacorogna & Marie Kratz, 2022. "Special Issue “Cyber Risk and Security”," Risks, MDPI, vol. 10(6), pages 1-4, May.
    18. Kerstin Awiszus & Yannick Bell & Jan Luttringhaus & Gregor Svindland & Alexander Vo{ss} & Stefan Weber, 2022. "Building Resilience in Cybersecurity -- An Artificial Lab Approach," Papers 2211.04762, arXiv.org, revised Sep 2023.

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