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Phase transitions in operational risk.

Kartik Anand1, Reimer Kühn

  • 1Department of Mathematics, King's College London, Strand, London WC2R 2LS, United Kingdom. kartik.anand@kcl.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
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This study introduces a functional correlation approach for operational risk in complex networks. It reveals that these systems can undergo catastrophic breakdowns, similar to phase transitions in physical systems.

Area of Science:

  • Statistical Physics
  • Network Science
  • Risk Management

Background:

  • Operational risk is a critical concern in complex systems.
  • Understanding network dynamics under heterogeneous failure probabilities is essential.
  • Existing models may not fully capture catastrophic failure modes.

Purpose of the Study:

  • To develop and analyze a functional correlation approach for operational risk.
  • To investigate the behavior of networks with heterogeneous failure probabilities.
  • To identify potential catastrophic breakdown mechanisms in operational systems.

Main Methods:

  • Utilizing a functional correlation approach.
  • Analyzing networks in the limit of sparse connectivity.
  • Deriving self-consistent expressions for dynamical evolution and stationary states.

Related Experiment Videos

  • Employing phase diagrams to analyze theoretical consequences.

    • Main Results:

    • Obtained self-consistent expressions for dynamical evolution and stationary states in sparse networks.
    • Identified coexistence of operational and nonoperational phases, analogous to liquid-gas systems.
    • Demonstrated susceptibility to discontinuous phase transitions leading to catastrophic breakdown.
    • Confirmed the robustness of these findings against variations in microscopic modeling.

    Conclusions:

    • The functional correlation approach provides a robust framework for understanding operational risk.
    • Complex networks exhibit phase transition-like behaviors, including catastrophic failures.
    • These findings have implications for risk assessment and mitigation in various complex systems.