A Relaxed Control Problem With $L^\infty$ Cost and Jump Dynamics Motivated by Cyber Risks Insurance

This paper has a double aim. One the one hand, we introduce a uni-nodal network model for cyber risks with firewalled edges and SIR intra-edge spreading. In connection to this, we formulate an insurance problem in which one seeks the running maximal reputation index against all control strategies of the companies represented by edges. On the other hand, we seek to characterize the value function with $L^\infty$ cost through linear programming techniques and more standard Hamilton-Jacobi integro-differential inequalities.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-10

• Fields of study

  Mathematics, Computer Science

• Identifiers
  arXiv 2511.07030
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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