An Analytical Review of Cyber Risk Management by Insurance Companies: A Mathematical Perspective

This article provides an overview of the current state-of-the-art in cyber risk and cyber risk management, focusing on the mathematical models that have been created to help with risk quantification and insurance pricing. We discuss the main ways that cyber risk is measured, starting with vulnerability functions that show how systems react to threats and going all the way up to more complex stochastic and dynamic models that show how cyber attacks change over time. Next, we examine cyber insurance, including the structure and main features of the cyber insurance market, as well as the growing role of cyber reinsurance in strategies for transferring risk. Finally, we review the mathematical models that have been proposed in the literature for setting the prices of cyber insurance premiums and structuring reinsurance contracts, analysing their advantages, limitations, and potential applications for more effective risk management. The aim of this article is to provide researchers and professionals with a clear picture of the main quantitative tools available and to point out areas that need further research by summarising these contributions.