Quantifying Stressed Scenarios of Cyber Loss Processes with Dynamic Dependencies

This talk generalizes the classical Cramer Lundberg model for the cumulative loss process, by allowing contagion as well as dynamic dependencies between the frequency and the severity components of the risk. This framework is particularly useful for cyber insurance portfolio or credit portfolio, which exhibit complex clustering features. Although more accurate, this model induces theoretical challenges in the computations of risk valuations. Hence we propose  a general methodology  for calculating different quantities (expectation, covariance..) related to these cumulative loss processes with dependencies.  As an illustration, we quantify systemic exposures and design stress tests that assess cyber portfolio resilience under extreme scenarios. In particular, we derive closed-form formulas for the expected surplus under two stress scenarios: (i) an excess of claims in the portfolio and (ii) a massive disclosure of critical vulnerabilities. By quantifying the impact of these scenarios, our framework offers insurers practical tools for cyber risk stress testing, portfolio management, and regulatory compliance.