With the growing digitalization of the economy, cyber risk has become one of the most critical  threats to organizations, capable of triggering severe financial losses and challenging traditional insurance mechanisms. To quantify this risk from an insurance perspective, there is a growing need for mathematical models that reflect key features of cyber risk and in particular  its potential systemic nature.  After an introduction to the specificities on cyber-risk, we present a stochastic model  to   capture the cluster features in the arrival of cyber-events,  taking into account attacks contagion, heterogeneity in propagation and exploitation of software vulnerabilities. Although more accurate, this model poses theoretical challenges in the computations of risk valuations. We present a general method to handle this challenge, which combines the Poisson imbedding, the pseudo-chaotic expansion and Malliavin calculus.  The methodology is illustrated on cyber loss process and  the computation of cyber stress scenarios, based on the accumulation of claims or vulnerabilities.

Based on joint works with Yousra Cherkaoui, Thomas Peyrat, Anthony Réveillac