IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v71y2009i4p441-460.html
   My bibliography  Save this article

Systemic risk in a unifying framework for cascading processes on networks

Author

Listed:
  • J. Lorenz
  • S. Battiston
  • F. Schweitzer

Abstract

We introduce a general framework for models of cascade and contagion processes on networks, to identify their commonalities and differences. In particular, models of social and financial cascades, as well as the fiber bundle model, the voter model, and models of epidemic spreading are recovered as special cases. To unify their description, we define the net fragility of a node, which is the difference between its fragility and the threshold that determines its failure. Nodes fail if their net fragility grows above zero and their failure increases the fragility of neighbouring nodes, thus possibly triggering a cascade. In this framework, we identify three classes depending on the way the fragility of a node is increased by the failure of a neighbour. At the microscopic level, we illustrate with specific examples how the failure spreading pattern varies with the node triggering the cascade, depending on its position in the network and its degree. At the macroscopic level, systemic risk is measured as the final fraction of failed nodes, $X^\ast$, and for each of the three classes we derive a recursive equation to compute its value. The phase diagram of $X^\ast$ as a function of the initial conditions, thus allows for a prediction of the systemic risk as well as a comparison of the three different model classes. We could identify which model class lead to a first-order phase transition in systemic risk, i.e. situations where small changes in the initial conditions may lead to a global failure. Eventually, we generalize our framework to encompass stochastic contagion models. This indicates the potential for further generalizations.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • 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;EDP Sciences, vol. 71(4), pages 441-460, October.
  • Handle: RePEc:spr:eurphb:v:71:y:2009:i:4:p:441-460
    DOI: 10.1140/epjb/e2009-00347-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2009-00347-4
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1140/epjb/e2009-00347-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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;EDP Sciences, vol. 71(4), pages 441-460, October.
    2. Markus K. Brunnermeier, 2008. "Deciphering the Liquidity and Credit Crunch 2007-08," NBER Working Papers 14612, National Bureau of Economic Research, Inc.
    3. 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.
    4. Mauro Napoletano & Stefano Battiston & Michael König & Frank Schweitzer, 2008. "On algebraic graph theory and the dynamics of innovation networks," SciencePo Working papers Main hal-03609244, HAL.
    5. Didier SORNETTE, 2009. "Dragon-Kings, Black Swans and the Prediction of Crises," Swiss Finance Institute Research Paper Series 09-36, Swiss Finance Institute.
    6. F. Schweitzer & L. Behera, 2009. "Nonlinear voter models: the transition from invasion to coexistence," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 301-318, February.
    7. F. Caruso & V. Latora & A. Pluchino & A. Rapisarda & B. Tadić, 2006. "Olami-Feder-Christensen model on different networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 243-247, March.
    8. D. Sornette, "undated". "Dragon-Kings, Black Swans and the Prediction of Crises," Working Papers CCSS-09-005, ETH Zurich, Chair of Systems Design.
    9. Jackson Matthew O. & Rogers Brian W., 2007. "Relating Network Structure to Diffusion Properties through Stochastic Dominance," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-16, February.
    10. Stephen Morris & Hyun Song Shin, 2008. "Financial Regulation in a System Context," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 39(2 (Fall)), pages 229-274.
    11. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2007. "Credit chains and bankruptcy propagation in production networks," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2061-2084, June.
    12. R. Kinney & P. Crucitti & R. Albert & V. Latora, 2005. "Modeling cascading failures in the North American power grid," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 46(1), pages 101-107, July.
    13. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Mandel, Antoine & Landini, Simone & Gallegati, Mauro & Gintis, Herbert, 2015. "Price dynamics, financial fragility and aggregate volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 51(C), pages 257-277.
    3. Stiglitz Joseph E., 2010. "Contagion, Liberalization, and the Optimal Structure of Globalization," Journal of Globalization and Development, De Gruyter, vol. 1(2), pages 1-47, December.
    4. Michel Alexandre & Thiago Christiano Silva & Colm Connaughton & Francisco A. Rodrigues, 2021. "The Role of (non-)Topological Features as Drivers of Systemic Risk: a machine learning approach," Working Papers Series 556, Central Bank of Brazil, Research Department.
    5. Heinrich, Torsten, 2016. "The Narrow and the Broad Approach to Evolutionary Modeling in Economics," MPRA Paper 75797, University Library of Munich, Germany.
    6. Battiston, Stefano & Gatti, Domenico Delli & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Default cascades: When does risk diversification increase stability?," Journal of Financial Stability, Elsevier, vol. 8(3), pages 138-149.
    7. Claudio J. Tessone & Antonios Garas & Beniamino Guerra & Frank Schweitzer, "undated". "How big is too big? Critical Shocks for Systemic Failure Cascades," Working Papers ETH-RC-12-015, ETH Zurich, Chair of Systems Design.
    8. Haas, Armin & Onischka, Mathias & Fucik, Markus, 2013. "Black swans, dragon kings, and Bayesian risk management," Economics Discussion Papers 2013-11, Kiel Institute for the World Economy (IfW Kiel).
    9. Pasca Lucian, 2015. "A Critical Review of the Main Approaches on Financial Market Dynamics Modelling," Journal of Heterodox Economics, Sciendo, vol. 2(2), pages 151-167, December.
    10. Morteza Alaeddini & Philippe Madiès & Paul J. Reaidy & Julie Dugdale, 2023. "Interbank money market concerns and actors’ strategies—A systematic review of 21st century literature," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 573-654, April.
    11. Christoph Aymanns & J. Doyne Farmer & Alissa M. Keinniejenhuis & Thom Wetzer, 2017. "Models of Financial Stability and their Application in Stress Tests," Working Papers on Finance 1805, University of St. Gallen, School of Finance.
    12. Aymeric Vié & Alfredo J. Morales, 2021. "How Connected is Too Connected? Impact of Network Topology on Systemic Risk and Collapse of Complex Economic Systems," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1327-1351, April.
    13. Rebekka Burkholz & Matt V. Leduc & Antonios Garas & Frank Schweitzer, 2015. "Systemic risk in multiplex networks with asymmetric coupling and threshold feedback," Papers 1506.06664, arXiv.org.
    14. Aymeric Vi'e & Alfredo J. Morales, 2019. "How connected is too connected? Impact of network topology on systemic risk and collapse of complex economic systems," Papers 1912.09814, arXiv.org.
    15. Alexandre, Michel & Silva, Thiago Christiano & Connaughton, Colm & Rodrigues, Francisco A., 2021. "The drivers of systemic risk in financial networks: a data-driven machine learning analysis," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    16. Safarzyńska, Karolina & van den Bergh, Jeroen C.J.M., 2017. "Integrated crisis-energy policy: Macro-evolutionary modelling of technology, finance and energy interactions," Technological Forecasting and Social Change, Elsevier, vol. 114(C), pages 119-137.
    17. Bargigli, Leonardo & Gallegati, Mauro, 2011. "Random digraphs with given expected degree sequences: A model for economic networks," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 396-411, May.
    18. Li, Fei & Kang, Hao & Xu, Jingfeng, 2022. "Financial stability and network complexity: A random matrix approach," International Review of Economics & Finance, Elsevier, vol. 80(C), pages 177-185.
    19. Darrell Jiajie Tay & Chung-I Chou & Sai-Ping Li & Shang You Tee & Siew Ann Cheong, 2016. "Bubbles Are Departures from Equilibrium Housing Markets: Evidence from Singapore and Taiwan," PLOS ONE, Public Library of Science, vol. 11(11), pages 1-13, November.
    20. Arun G. Chandrasekhar & Robert Townsend & Juan Pablo Xandri, 2018. "Financial Centrality and Liquidity Provision," NBER Working Papers 24406, National Bureau of Economic Research, Inc.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:71:y:2009:i:4:p:441-460. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.