A stochastic Gordon-Loeb model for optimal security investment under clustered cyber-attacks.

We propose a continuous-time extension of the Gordon-Loeb model for optimal investment in information security under the threat of cyber-attacks. The arrival of attacks is modeled using Hawkes processes, capturing the realistic feature of clustering in cyber-attacks. Each attack may lead to a system breach, with the probability of breach depending on the system's vulnerability. We aim at determining the optimal investment in cyber-security to reduce the system's vulnerability. The problem is formulated as a two-dimensional Markovian stochastic control problem and solved via dynamic programming techniques. We perform a numerical study of the value function and the associated optimal investment strategy in cyber-security, highlighting the impact of randomly arriving clustered cyber-attacks. Based on a joint work with G. Callegaro, C. Hillairet, B. Ongarato.