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An Overview of Security Breach Probability Models

Author

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  • Alessandro Mazzoccoli

    (Department of Law, Economics, Politics and Modern Languages, LUMSA University, Via Marcantonio Colonna 19, 00192 Rome, Italy
    These authors contributed equally to this work.)

  • Maurizio Naldi

    (Department of Law, Economics, Politics and Modern Languages, LUMSA University, Via Marcantonio Colonna 19, 00192 Rome, Italy
    These authors contributed equally to this work.)

Abstract

Cybersecurity breach probability functions describe how cybersecurity investments impact the actual vulnerability to cyberattacks through the probability of success of the attack. They essentially use mathematical models to make cyber-risk management choices. This paper provides an overview of the breach probability models that appear in the literature. For each of them, the form of the mathematical functions and their properties are described. The models exhibit a wide variety of functional relationships between breach probability and investments, including linear, concave, convex, and a mixture of the latter two. Each model describes a parametric family, with some models have a single parameter, and others have two. A sensitivity analysis completes the overview to identify the impact of the model parameters: the estimation of the parameters which have a larger influence on the breach probability is more critical and deserves greater attention.

Suggested Citation

  • Alessandro Mazzoccoli & Maurizio Naldi, 2022. "An Overview of Security Breach Probability Models," Risks, MDPI, vol. 10(11), pages 1-29, November.
    • Handle: RePEc:gam:jrisks:v:10:y:2022:i:11:p:220-:d:976085
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    References listed on IDEAS

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    1. Arunabha Mukhopadhyay & Samir Chatterjee & Kallol K. Bagchi & Peteer J. Kirs & Girja K. Shukla, 2019. "Cyber Risk Assessment and Mitigation (CRAM) Framework Using Logit and Probit Models for Cyber Insurance," Information Systems Frontiers, Springer, vol. 21(5), pages 997-1018, October.
    2. M.‐Elisabeth Paté‐Cornell & Marshall Kuypers & Matthew Smith & Philip Keller, 2018. "Cyber Risk Management for Critical Infrastructure: A Risk Analysis Model and Three Case Studies," Risk Analysis, John Wiley & Sons, vol. 38(2), pages 226-241, February.
    3. Martin Eling & Michael McShane & Trung Nguyen, 2021. "Cyber risk management: History and future research directions," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 24(1), pages 93-125, March.
    4. Alessandro Mazzoccoli & Maurizio Naldi, 2020. "Robustness of Optimal Investment Decisions in Mixed Insurance/Investment Cyber Risk Management," Risk Analysis, John Wiley & Sons, vol. 40(3), pages 550-564, March.
    5. Natalie M. Scala & Allison C. Reilly & Paul L. Goethals & Michel Cukier, 2019. "Risk and the Five Hard Problems of Cybersecurity," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2119-2126, October.
    6. Naldi, Maurizio & Nicosia, Gaia & Pacifici, Andrea & Pferschy, Ulrich, 2019. "Profit-fairness trade-off in project selection," Socio-Economic Planning Sciences, Elsevier, vol. 67(C), pages 133-146.
    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.
    8. Alessandro Mazzoccoli & Maurizio Naldi, 2021. "Optimal Investment in Cyber-Security under Cyber Insurance for a Multi-Branch Firm," Risks, MDPI, vol. 9(1), pages 1-28, January.
    9. Kjell Hausken, 2006. "Returns to information security investment: The effect of alternative information security breach functions on optimal investment and sensitivity to vulnerability," Information Systems Frontiers, Springer, vol. 8(5), pages 338-349, December.
    10. Young, Derek & Lopez, Juan & Rice, Mason & Ramsey, Benjamin & McTasney, Robert, 2016. "A framework for incorporating insurance in critical infrastructure cyber risk strategies," International Journal of Critical Infrastructure Protection, Elsevier, vol. 14(C), pages 43-57.
    11. Lu Xu & Yanhui Li & Jing Fu, 2019. "Cybersecurity Investment Allocation for a Multi-Branch Firm: Modeling and Optimization," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    12. Anat Hovav & John D'Arcy, 2003. "The Impact of Denial‐of‐Service Attack Announcements on the Market Value of Firms," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 6(2), pages 97-121, September.
    13. Huang, C. Derrick & Behara, Ravi S., 2013. "Economics of information security investment in the case of concurrent heterogeneous attacks with budget constraints," International Journal of Production Economics, Elsevier, vol. 141(1), pages 255-268.
    14. Terje Aven & Roger Flage, 2020. "Foundational Challenges for Advancing the Field and Discipline of Risk Analysis," Risk Analysis, John Wiley & Sons, vol. 40(S1), pages 2128-2136, November.
    15. Maurizio Naldi & Marta Flamini & Giuseppe D’Acquisto, 2018. "Negligence and sanctions in information security investments in a cloud environment," Electronic Markets, Springer;IIM University of St. Gallen, vol. 28(1), pages 39-52, February.
    16. Eling, Martin & Wirfs, Jan, 2019. "What are the actual costs of cyber risk events?," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1109-1119.
    17. Tsan‐Ming Choi & James H. Lambert, 2017. "Advances in Risk Analysis with Big Data," Risk Analysis, John Wiley & Sons, vol. 37(8), pages 1435-1442, August.
    18. Xing Gao & Weijun Zhong & Shue Mei, 2015. "Security investment and information sharing under an alternative security breach probability function," Information Systems Frontiers, Springer, vol. 17(2), pages 423-438, April.
    19. Loretta Mastroeni & Alessandro Mazzoccoli & Maurizio Naldi, 2019. "Service Level Agreement Violations in Cloud Storage: Insurance and Compensation Sustainability," Future Internet, MDPI, vol. 11(7), pages 1-26, June.
    20. 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.
    21. Wang, Shaun S., 2019. "Integrated framework for information security investment and cyber insurance," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    22. Tiberiu Marian GEORGESCU, 2021. "A Study on How the Pandemic Changed the Cybersecurity Landscape," Informatica Economica, Academy of Economic Studies - Bucharest, Romania, vol. 25(1), pages 42-60.
    23. Albina Orlando, 2021. "Cyber Risk Quantification: Investigating the Role of Cyber Value at Risk," Risks, MDPI, vol. 9(10), pages 1-12, October.
    24. Maochao Xu & Lei Hua, 2019. "Cybersecurity Insurance: Modeling and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(2), pages 220-249, April.
    25. Mayadunne, Sanjaya & Park, Sungjune, 2016. "An economic model to evaluate information security investment of risk-taking small and medium enterprises," International Journal of Production Economics, Elsevier, vol. 182(C), pages 519-530.
    26. 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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