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Cyber loss model risk translates to premium mispricing and risk sensitivity

Author

Listed:
  • Gareth W. Peters

    (University of California Santa Barbara)

  • Matteo Malavasi

    (Macquarie University)

  • Georgy Sofronov

    (Macquarie University)

  • Pavel V. Shevchenko

    (Macquarie University
    Saint-Petersburg State University)

  • Stefan Trück

    (Macquarie University)

  • Jiwook Jang

    (Macquarie University)

Abstract

In this paper we focus on model risk and risk sensitivity when addressing the insurability of cyber risk. The standard statistical approaches to assessment of insurability and potential mispricing are enhanced in several aspects involving consideration of model risk. Model risk can arise from model uncertainty and parameter uncertainty. We demonstrate how to quantify the effect of model risk in this analysis by incorporating various robust estimators for key model parameters that apply in both marginal and joint cyber risk loss process modelling. Through this analysis we are able to address the question that, to the best of our knowledge, no other study has investigated in the context of cyber risk: is model risk present in cyber risk data, and how does is it translate into premium mispricing? We believe our findings should complement existing studies seeking to explore the insurability of cyber losses.

Suggested Citation

  • 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.
  • Handle: RePEc:pal:gpprii:v:48:y:2023:i:2:d:10.1057_s41288-023-00285-x
    DOI: 10.1057/s41288-023-00285-x
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    References listed on IDEAS

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    1. Eling, Martin & Jung, Kwangmin, 2018. "Copula approaches for modeling cross-sectional dependence of data breach losses," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 167-180.
    2. 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.
    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. Sajjad Haider Bhatti & Shahzad Hussain & Tanvir Ahmad & Muhammad Aslam & Muhammad Aftab & Muhammad Ali Raza, 2018. "Efficient estimation of Pareto model: Some modified percentile estimators," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-15, May.
    5. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    6. Wang, Shaun & Dhaene, Jan, 1998. "Comonotonicity, correlation order and premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 235-242, July.
    7. Dahen, Hela & Dionne, Georges, 2010. "Scaling models for the severity and frequency of external operational loss data," Journal of Banking & Finance, Elsevier, vol. 34(7), pages 1484-1496, July.
    8. 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.
    9. Peters, Gareth W. & Byrnes, Aaron D. & Shevchenko, Pavel V., 2011. "Impact of insurance for operational risk: Is it worthwhile to insure or be insured for severe losses?," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 287-303, March.
    10. Martin Eling & Werner Schnell, 2016. "What do we know about cyber risk and cyber risk insurance?," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 17(5), pages 474-491, November.
    11. Kwangmin Jung, 2021. "Extreme Data Breach Losses: An Alternative Approach to Estimating Probable Maximum Loss for Data Breach Risk," North American Actuarial Journal, Taylor & Francis Journals, vol. 25(4), pages 580-603, November.
    12. Fröhlich, Andreas & Weng, Annegret, 2018. "Parameter uncertainty and reserve risk under Solvency II," Insurance: Mathematics and Economics, Elsevier, vol. 81(C), pages 130-141.
    13. 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.
    14. Ibragimov, Rustam & Jaffee, Dwight & Walden, Johan, 2011. "Diversification disasters," Journal of Financial Economics, Elsevier, vol. 99(2), pages 333-348, February.
    15. 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.
    16. Matteo Malavasi & Gareth W. Peters & Pavel V. Shevchenko & Stefan Truck & Jiwook Jang & Georgy Sofronov, 2021. "Cyber Risk Frequency, Severity and Insurance Viability," Papers 2111.03366, arXiv.org, revised Mar 2022.
    17. Goegebeur, Yuri & Guillou, Armelle & Verster, Andréhette, 2014. "Robust and asymptotically unbiased estimation of extreme quantiles for heavy tailed distributions," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 108-114.
    18. Rizzo, Maria L., 2009. "New Goodness-of-Fit Tests for Pareto Distributions," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 691-715, November.
    19. Christian Biener & Martin Eling & Jan Hendrik Wirfs, 2015. "Insurability of Cyber Risk: An Empirical Analysis†," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 40(1), pages 131-158, January.
    20. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    21. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
    22. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
    23. Eling, Martin & Loperfido, Nicola, 2017. "Data breaches: Goodness of fit, pricing, and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 126-136.
    24. 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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