Cyber Risk Assessment for Capital Management

TL;DR

This work tackles the challenge of managing cyber risk under budget constraints by proposing a two-pillar framework that couples a cascade-based, tensorized risk assessment with a holistic capital-allocation optimization. The risk pillar models cyber incidents through a cascade of threats, vulnerabilities, assets, and controls using tensors, enabling explicit representation of dependencies and the impact reduction from controls via a scaling vector $\boldsymbol{\theta}$. The capital pillar then optimizes ex- ante cybersecurity investments $\mathbf{M}$, cyber insurance coverage $\mathbf{I}$, and ex-post loss reserves $\mathbf{K}$ to minimize a weighted sum of residual risk, investment costs, insurance premiums, and reserve-related penalties, under budget constraints. A case study on Company X and a broader industry analysis demonstrate the approach’s practicality, showing how price, effectiveness of controls, and budget constraints shape optimal allocations and resilience; the framework also yields actionable insights such as the importance of cyber scanning to map attack paths and the differential strategies of small versus large firms. Overall, the paper provides a concrete, implementable methodology that links structural cyber-system information to quantitative risk quantification and capital decisions, with potential integration into existing standards like CIS Controls and implications for regulatory risk management.

Abstract

This paper introduces a two-pillar cyber risk management framework to address the pervasive challenges in managing cyber risk. The first pillar, cyber risk assessment, combines insurance frequency-severity models with cybersecurity cascade models to capture the unique nature of cyber risk. The second pillar, cyber capital management, facilitates informed allocation of capital for a balanced cyber risk management strategy, including cybersecurity investments, insurance coverage, and reserves. A case study, based on historical cyber incident data and realistic assumptions, demonstrates the necessity of comprehensive cost-benefit analysis for budget-constrained companies with competing objectives in cyber risk management. In addition, sensitivity analysis highlights the dependence of the optimal strategy on factors such as the price of cybersecurity controls and their effectiveness. The framework's implementation across a diverse range of companies yields general insights on cyber risk management.

Figures (8)

• Figure 1: Cyber cascade model, and example of cyber incident, due to the second threat, where the first (resp. third) vulnerability is partially (resp. fully) patched by the first (resp. third) control
• Figure 2: Example of tensor representation for cyber cascade model
• Figure 3: Example of tensor-based cyber loss model
• Figure 4: Impact aggregation across vulnerabilities and assets in Example \ref{['example1']}
• Figure 5: Trade-off between ex-ante and ex-post-loss capitals for cyber risks

Theorems & Definitions (2)

• Example 2.1
• Example 2.2