We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon-Loeb model, each attack may result in a breach, with breach probability depending on the system's vulnerability. We aim at determining the optimal cybersecurity investment to reduce vulnerability. The problem is cast as a two-dimensional Markovian stochastic optimal control problem and solved using dynamic programming methods. 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. Fontana and C. Hillairet.