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

TL;DR

This paper models cyber risk networks with firewalled edges and SIR spreading, formulates an insurance problem to maximize reputation index under control strategies, and characterizes the value function using linear programming and Hamilton-Jacobi inequalities.

Contribution

It introduces a novel cyber risk network model with SIR dynamics and develops a new approach to characterize the associated $L^ Infty$ control problem.

Findings

Network model with firewalled edges and SIR spreading.

Characterization of the value function via linear programming.

Use of Hamilton-Jacobi inequalities for analysis.

Abstract

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.