How big is too big? Critical Shocks for Systemic Failure Cascades
AbstractExternal or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical constellations determine whether this cascade remains finite or reaches the size of the system, i.e. leads to systemic risk. We investigate the critical parameters for such cascades in a simple model, where agents are characterized by an individual threshold \theta_i determining their capacity to handle a load \alpha\theta_i with 1-\alpha being their safety margin. If agents fail, they redistribute their load equally to K neighboring agents in a regular network. For three different threshold distributions P(\theta), we derive analytical results for the size of the cascade, X(t), which is regarded as a measure of systemic risk, and the time when it stops. We focus on two different regimes, (i) EEE, an external extreme event where the size of the shock is of the order of the total capacity of the network, and (ii) RIE, a random internal event where the size of the shock is of the order of the capacity of an agent. We find that even for large extreme events that exceed the capacity of the network finite cascades are still possible, if a power-law threshold distribution is assumed. On the other hand, even small random fluctuations may lead to full cascades if critical conditions are met. Most importantly, we demonstrate that the size of the "big" shock is not the problem, as the systemic risk only varies slightly for changes of 10 to 50 percent of the external shock. Systemic risk depends much more on ingredients such as the network topology, the safety margin and the threshold distribution, which gives hints on how to reduce systemic risk.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1209.0959.
Date of creation: Sep 2012
Date of revision: Apr 2013
Publication status: Published in Journal of Statistical Physics, Vol. 151, pp. 765-783 (2013)
Contact details of provider:
Web page: http://arxiv.org/
Other versions of this item:
- Claudio J. Tessone & Antonios Garas & Beniamino Guerra & Frank Schweitzer, . "How big is too big? Critical Shocks for Systemic Failure Cascades," Working Papers ETH-RC-12-015, ETH Zurich, Chair of Systems Design.
- NEP-ALL-2012-09-09 (All new papers)
- NEP-BAN-2012-09-09 (Banking)
- NEP-NET-2012-09-09 (Network Economics)
- NEP-RMG-2012-09-09 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012.
"Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 36(8), pages 1121-1141.
- Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce C. Greenwald & Joseph E. Stiglitz, 2009. "Liaisons Dangereuses: Increasing Connectivity, Risk Sharing, and Systemic Risk," NBER Working Papers 15611, National Bureau of Economic Research, Inc.
- Claudio J. Tessone & Markus M. Geipel & F. Schweitzer, . "Sustainable growth in complex networks," Working Papers CCSS-10-008, ETH Zurich, Chair of Systems Design.
- Jan Lorenz & Stefano Battiston & Frank Schweitzer, .
"Systemic Risk in a Unifying Framework for Cascading Processes on Networks,"
CCSS-09-011, ETH Zurich, Chair of Systems Design.
- J. Lorenz & S. Battiston & F. Schweitzer, 2009. "Systemic risk in a unifying framework for cascading processes on networks," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 71(4), pages 441-460, October.
- Jan Lorenz & Stefano Battiston & Frank Schweitzer, 2009. "Systemic Risk in a Unifying Framework for Cascading Processes on Networks," Papers 0907.5325, arXiv.org, revised Jan 2010.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.