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Cyber Insurance Premium Setting for Multi-Site Companies under Risk Correlation

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  • Loretta Mastroeni

    (Department of Economics, Roma Tre University, Via Silvio D’Amico 77, 00145 Rome, Italy)

  • Alessandro Mazzoccoli

    (Department of Economics, Roma Tre University, Via Silvio D’Amico 77, 00145 Rome, Italy)

  • Maurizio Naldi

    (Department of Law, Economics, Politics and Modern Languages, LUMSA University, Via Marcantonio Colonna 19, 00192 Rome, Italy)

Abstract

Correlation in cyber risk represents an additional source of concern for utility and industrial infrastructures, where risks may be introduced by connected systems. A major means of reducing risk is to transfer it through insurance. In this paper, we consider a company which has peripheral branches in addition to its headquarters, where risk correlation is present between all of its sites and insurance is adopted to hedge against economic losses. We employ the expected utility principle (which leads to the well-known mean variance premium formula) to derive the insurance premium under risk correlation under several risk scenarios. Under a first-order approximation, a quasi-linear relationship between the premium and the two major risk factors (the number of branches and the risk correlation coefficient) is determined.

Suggested Citation

  • Loretta Mastroeni & Alessandro Mazzoccoli & Maurizio Naldi, 2023. "Cyber Insurance Premium Setting for Multi-Site Companies under Risk Correlation," Risks, MDPI, vol. 11(10), pages 1-18, September.
  • Handle: RePEc:gam:jrisks:v:11:y:2023:i:10:p:167-:d:1245787
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    References listed on IDEAS

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    1. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, April.
    2. Aven, Terje, 2010. "On how to define, understand and describe risk," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 623-631.
    3. Kunreuther, Howard & Heal, Geoffrey, 2003. "Interdependent Security," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 231-249, March-May.
    4. 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.
    5. Nagurney, Anna & Shukla, Shivani, 2017. "Multifirm models of cybersecurity investment competition vs. cooperation and network vulnerability," European Journal of Operational Research, Elsevier, vol. 260(2), pages 588-600.
    6. 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.
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