IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v10y2022i11p220-d976085.html
   My bibliography  Save this article

An Overview of Security Breach Probability Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/10/11/220/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/10/11/220/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Wang, Shaun S., 2019. "Integrated framework for information security investment and cyber insurance," Pacific-Basin Finance Journal, Elsevier, vol. 57(C).
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. 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.
    24. Albina Orlando, 2021. "Cyber Risk Quantification: Investigating the Role of Cyber Value at Risk," Risks, MDPI, vol. 9(10), pages 1-12, October.
    25. 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.
    26. Maochao Xu & Lei Hua, 2019. "Cybersecurity Insurance: Modeling and Pricing," North American Actuarial Journal, Taylor & Francis Journals, vol. 23(2), pages 220-249, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alessandro Mazzoccoli, 2023. "Optimal Cyber Security Investment in a Mixed Risk Management Framework: Examining the Role of Cyber Insurance and Expenditure Analysis," Risks, MDPI, vol. 11(9), pages 1-14, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alessandro Mazzoccoli, 2023. "Optimal Cyber Security Investment in a Mixed Risk Management Framework: Examining the Role of Cyber Insurance and Expenditure Analysis," Risks, MDPI, vol. 11(9), pages 1-14, August.
    2. 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.
    3. Mazaher Kianpour & Stewart J. Kowalski & Harald Øverby, 2021. "Systematically Understanding Cybersecurity Economics: A Survey," Sustainability, MDPI, vol. 13(24), pages 1-28, December.
    4. Gareth W. Peters & Matteo Malavasi & Georgy Sofronov & Pavel V. Shevchenko & Stefan Trück & Jiwook Jang, 2023. "Cyber loss model risk translates to premium mispricing and risk sensitivity," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 372-433, April.
    5. 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.
    6. Loretta Mastroeni & Alessandro Mazzoccoli & Maurizio Naldi, 2022. "Pricing Cat Bonds for Cloud Service Failures," JRFM, MDPI, vol. 15(10), pages 1-18, October.
    7. Kjartan Palsson & Steinn Gudmundsson & Sachin Shetty, 2020. "Analysis of the impact of cyber events for cyber insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 45(4), pages 564-579, October.
    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. 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.
    10. Domenico Giovanni & Arturo Leccadito & Marco Pirra, 2021. "On the determinants of data breaches: A cointegration analysis," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 141-160, June.
    11. Spencer Wheatley & Annette Hofmann & Didier Sornette, 2021. "Addressing insurance of data breach cyber risks in the catastrophe framework," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 46(1), pages 53-78, January.
    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. 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.
    14. Kjartan Palsson & Steinn Gudmundsson & Sachin Shetty, 0. "Analysis of the impact of cyber events for cyber insurance," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 0, pages 1-16.
    15. Pavel V. Shevchenko & Jiwook Jang & Matteo Malavasi & Gareth W. Peters & Georgy Sofronov & Stefan Truck, 2022. "The Nature of Losses from Cyber-Related Events: Risk Categories and Business Sectors," Papers 2202.10189, arXiv.org, revised Mar 2022.
    16. 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.
    17. 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.
    18. Zängerle, Daniel & Schiereck, Dirk, 2022. "Modelling and predicting enterprise‑level cyber risks in the context of sparse data availability," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 136276, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    19. Bennet Skarczinski & Mathias Raschke & Frank Teuteberg, 2023. "Modelling maximum cyber incident losses of German organisations: an empirical study and modified extreme value distribution approach," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 48(2), pages 463-501, April.
    20. Xing Gao & Weijun Zhong, 2015. "Information security investment for competitive firms with hacker behavior and security requirements," Annals of Operations Research, Springer, vol. 235(1), pages 277-300, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:10:y:2022:i:11:p:220-:d:976085. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.