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<p>We explore an optimal impulse control problem wherein an electronic device owner strategically calibrates protection levels against cyber attacks. Utilizing epidemiological compartment models, we qualitatively characterize the dynamics of cyber attacks within the network. We determine the optimal protective measures against effective hacking by formulating and solving a stochastic control problem with optimal switching. We demonstrate that the value function for the cluster owner constitutes a viscosity solution to a system of coupled variational inequalities associated with a fully coupled reflected backward stochastic differential equation (BSDE). Furthermore, we devise a comprehensive algorithm alongside a verification procedure to ascertain the optimal timing for network protection across various cyber attack scenarios. Our findings are illustrated through numerical approximations employing deep Galerkin methods for partial differential equations (PDEs). We visualize the optimal protection strategies and efficiency in the context of two distinct attack scenarios: (1) a constant cyber attack, (2) an exogenous cyber attack strategy modeled with a Poisson process.</p>

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Optimal Impulse Control for Cyber Risk Management

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月24日

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  • Caroline Hillairet,
  • Thibaut Mastrolia,
  • Wissal Sabbagh

摘要

We explore an optimal impulse control problem wherein an electronic device owner strategically calibrates protection levels against cyber attacks. Utilizing epidemiological compartment models, we qualitatively characterize the dynamics of cyber attacks within the network. We determine the optimal protective measures against effective hacking by formulating and solving a stochastic control problem with optimal switching. We demonstrate that the value function for the cluster owner constitutes a viscosity solution to a system of coupled variational inequalities associated with a fully coupled reflected backward stochastic differential equation (BSDE). Furthermore, we devise a comprehensive algorithm alongside a verification procedure to ascertain the optimal timing for network protection across various cyber attack scenarios. Our findings are illustrated through numerical approximations employing deep Galerkin methods for partial differential equations (PDEs). We visualize the optimal protection strategies and efficiency in the context of two distinct attack scenarios: (1) a constant cyber attack, (2) an exogenous cyber attack strategy modeled with a Poisson process.