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A Generalized Linear Mixed Model for Data Breaches and Its Application in Cyber Insurance

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  • Meng Sun

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

  • Yi Lu

    (Department of Statistics and Actuarial Science, Simon Fraser University, 8888 University Drive, Burnaby, BC V5A 1S6, Canada)

Abstract

Data breach incidents result in severe financial loss and reputational damage, which raises the importance of using insurance to manage and mitigate cyber related risks. We analyze data breach chronology collected by Privacy Rights Clearinghouse (PRC) since 2001 and propose a Bayesian generalized linear mixed model for data breach incidents. Our model captures the dependency between frequency and severity of cyber losses and the behavior of cyber attacks on entities across time. Risk characteristics such as types of breach, types of organization, entity locations in chronology, as well as time trend effects are taken into consideration when investigating breach frequencies. Estimations of model parameters are presented under Bayesian framework using a combination of Gibbs sampler and Metropolis–Hastings algorithm. Predictions and implications of the proposed model in enterprise risk management and cyber insurance rate filing are discussed and illustrated. We find that it is feasible and effective to use our proposed NB-GLMM for analyzing the number of data breach incidents with uniquely identified risk factors. Our results show that both geological location and business type play significant roles in measuring cyber risks. The outcomes of our predictive analytics can be utilized by insurers to price their cyber insurance products, and by corporate information technology (IT) and data security officers to develop risk mitigation strategies according to company’s characteristics.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:12:p:224-:d:981498
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    References listed on IDEAS

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    1. Antonio, Katrien & Beirlant, Jan, 2007. "Actuarial statistics with generalized linear mixed models," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 58-76, January.
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    3. Spencer Wheatley & Thomas Maillart & Didier Sornette, 2016. "The extreme risk of personal data breaches and the erosion of privacy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(1), pages 1-12, January.
    4. Kshetri, Nir, 2020. "The evolution of cyber-insurance industry and market: An institutional analysis," Telecommunications Policy, Elsevier, vol. 44(8).
    5. 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.
    6. T. Maillart & D. Sornette, 2010. "Heavy-tailed distribution of cyber-risks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 75(3), pages 357-364, June.
    7. Spencer Wheatley & Thomas Maillart & Didier Sornette, 2016. "The extreme risk of personal data breaches and the erosion of privacy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(1), pages 1-12, January.
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    Cited by:

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    2. Shengkun Xie & Chong Gan, 2023. "Estimating Territory Risk Relativity Using Generalized Linear Mixed Models and Fuzzy C -Means Clustering," Risks, MDPI, vol. 11(6), pages 1-20, May.

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