Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity

30 Pages Posted: 14 Mar 2022 Last revised: 29 Mar 2023

See all articles by Gareth Peters

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Matteo Malavasi

University of New South Wales (UNSW) - School of Actuarial Studies

Georgy Sofronov

Macquarie University - Department of Mathematics and Statistics

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics

Stefan Trück

Macquarie University Sydney - Department of Applied Finance and Actuarial Studies; Financial Research Network (FIRN); Centre for International Finance and Regulation (CIFR); Macquarie University, Macquarie Business School

Jiwook Jang

Macquarie University, Macquarie Business School

Date Written: January 16, 2022

Abstract

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 parameters uncertainty. We demonstrate how to quantify the effect of model risk in this analysis by incorporating various robust estimators for key model parameter estimates that apply in both marginal and joint cyber risk loss process modelling. We contrast these robust techniques with standard methods previously used in studying insurabilty of cyber risk. This allows us to accurately assess the critical impact that robust estimation can have on tail index estimation for heavy tailed loss models, as well as the effect of robust dependence analysis when quantifying joint loss models and insurance portfolio diversification. We argue that the choice of such methods is akin to a form of model risk and we study the risk sensitivity that arise from choices relating to the class of robust estimation adopted and the impact of the settings associated with such methods on key actuarial tasks such as premium calculation in cyber insurance. 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 insurability of cyber losses. In order to ensure our findings are based on realistic industry informed loss data, we have utilised one of the leading industry cyber loss datasets obtained from Advisen, which represents a comprehensive data set on cyber monetary losses, from which we form our analysis and conclusions.

Keywords: Cyber risk, cyber insurance, model risk, risk sensitivity, robust estimation, robust dependence estimation

Suggested Citation

Peters, Gareth and Malavasi, Matteo and Sofronov, Georgy and Shevchenko, Pavel V. and Trueck, Stefan and Jang, Jiwook, Cyber Loss Model Risk Translates to Premium Mispricing and Risk Sensitivity (January 16, 2022). Available at SSRN: https://ssrn.com/abstract=4009941 or http://dx.doi.org/10.2139/ssrn.4009941

Gareth Peters (Contact Author)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Matteo Malavasi

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney, NSW 2052
Australia

Georgy Sofronov

Macquarie University - Department of Mathematics and Statistics ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://https://researchers.mq.edu.au/en/persons/georgy-sofronov

Pavel V. Shevchenko

Macquarie University - Department of Actuarial Studies and Business Analytics ( email )

Australia

HOME PAGE: http://www.mq.edu.au/research/centre-for-risk-analytics/pavel-shevchenko

Stefan Trueck

Macquarie University Sydney - Department of Applied Finance and Actuarial Studies ( email )

North Ryde
Sydney, New South Wales 2109
Australia
61298508483 (Phone)
61298508483 (Fax)

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

Centre for International Finance and Regulation (CIFR) ( email )

Level 7, UNSW CBD Campus
1 O'Connell Street
Sydney, NSW 2000
Australia

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Jiwook Jang

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

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