, Volume 70, Issue 4, pp 595–647 | Cite as

On the Computational Complexity of Measuring Global Stability of Banking Networks

  • Piotr Berman
  • Bhaskar DasGupta
  • Lakshmi Kaligounder
  • Marek Karpinski


Threats on the stability of a financial system may severely affect the functioning of the entire economy, and thus considerable emphasis is placed on the analyzing the cause and effect of such threats. The financial crisis in the current and past decade has shown that one important cause of instability in global markets is the so-called financial contagion, namely the spreadings of instabilities or failures of individual components of the network to other, perhaps healthier, components. This leads to a natural question of whether the regulatory authorities could have predicted and perhaps mitigated the current economic crisis by effective computations of some stability measure of the banking networks. Motivated by such observations, we consider the problem of defining and evaluating stabilities of both homogeneous and heterogeneous banking networks against propagation of synchronous idiosyncratic shocks given to a subset of banks. We formalize the homogeneous banking network model of Nier et al. (J. Econ. Dyn. Control 31:2033–2060, 2007) and its corresponding heterogeneous version, formalize the synchronous shock propagation procedures outlined in (Nier et al. J. Econ. Dyn. Control 31:2033–2060, 2007; M. Eboli Mimeo, 2004), define two appropriate stability measures and investigate the computational complexities of evaluating these measures for various network topologies and parameters of interest. Our results and proofs also shed some light on the properties of topologies and parameters of the network that may lead to higher or lower stabilities.


Banking networks Systemic stability Stability index Algorithms Approximation hardness 



The authors would like to thank the organizers of the Industrial-Academic Workshop on Optimization in Finance and Risk Management at the Fields Institute in Toronto (Canada) for an opportunity to discuss some of the results in this paper and receive valuable feedbacks.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Piotr Berman
    • 1
  • Bhaskar DasGupta
    • 2
  • Lakshmi Kaligounder
    • 2
  • Marek Karpinski
    • 3
  1. 1.Department of Computer Science & EngineeringPennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of Computer ScienceUniversity of Illinois at ChicagoChicagoUSA
  3. 3.Department of Computer ScienceUniversity of BonnBonnGermany

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