STABILITY OF THE BANKING SYSTEM WITH APOLLONIAN GRAPH STRUCTURE
( Pp. 36-44)
More about authors
Karaev Alan K.
doktor tehnicheskih nauk, professor, glavnyy nauchnyy sotrudnik Departamenta obschestvennyh finansov
Financial University under the Government of the Russian Federation Melnichuk Marina V. doktor ekonomicheskih nauk, professor, rukovoditel Departamenta angliyskogo yazyka i professionalnoy podgotovki, professor Departamenta angliyskogo yazyka i professionalnoy podgotovki
Financial University under the Government of the Russian Federation
Moscow, Russian Federation
Financial University under the Government of the Russian Federation Melnichuk Marina V. doktor ekonomicheskih nauk, professor, rukovoditel Departamenta angliyskogo yazyka i professionalnoy podgotovki, professor Departamenta angliyskogo yazyka i professionalnoy podgotovki
Financial University under the Government of the Russian Federation
Moscow, Russian Federation
Abstract:
The work carried out the banking system stability analysis of the structure in the form of Apollonian graph based on such characteristics of the banking system as a modular and non-uniform distribution of banks by degree, on the basis of the extended mid-field model Nier (static approach based on a simplified balance sheet of assets and liabilities of the bank) which analyzed the prevalence of the process of bankruptcy of banks after the default of one of the banks in the banking system. The obtained results of research of stability of banking systems based on the Apollonian graphs indicate that the presence in the structure of banking systems modeling features such as modularity (i.e. clustering), and the heterogeneity of banks allows them to be most appropriate «isomorphic structure», characteristic for the majority of real social and biological complex adaptive systems.
How to Cite:
Karaev A.K., Melnichuk M.V., (2016), STABILITY OF THE BANKING SYSTEM WITH APOLLONIAN GRAPH STRUCTURE. Business in Law, 4 => 36-44.
Reference list:
Karaev A.K., Mel nichuk M.V., (2015) Teoreticheskaya model finansovoy nestabil nosti rossiyskogo mezhbankovskogo kreditnogo rynka: setevoy podkhod. Biznes v zakone. Ekonomiko-yuridicheskiy zhurnal, 5: 222-226
Karaev A.K., Mel nichuk M.V., (2015) Teoreticheskaya model prognozirovaniya finansovoy nestabil nosti rossiyskogo mezhbankovskogo kreditnogo rynka na osnove semeystva epidemiologicheskikh modeley. Biznes v zakone. Ekonomiko-yuridicheskiy zhurnal, 5: 219-222
Maevskiy V.I., CHernavskiy D.S., Ierarkhicheski organizovannyy vybor, http://spkurdyumov.ru/economy/ierarxicheski-organizovannyj-vybor/
Albert R., Jeong H., Barabasi A. Error and Attack Tolerance of Complex Networks. Nature. 2000;406:378-382. doi: 10.1038/35019019 PMID: 10935628
Allen F., Gale D. Financial contagion , Journal of Political Economy, Vol.108, No.1, 2000.
Anderson Complexity theory and organization science , Organization Science, Vol. 10, No.3, 1999.
Andrade R.F.S., Andrade J.S., Herrmann H.J. Ising model on the Apollonian network with nondependent interactions // Phys. Rev. E 79 (2009) 036105.
Andrade R.F.S, Herrmann H.J. Magnetic models on Apollonian networks // Phys. Rev. E 71 (2005) 056131.
Andrade Jr. J.S., Herrmann H.J., Andrade R.F.S., da Silva L.R. Apollonian Networks: Simultaneously Scale-Free, Small World, Euclidean, Space Filling, and with Matching Graphs. Phys. Rev. Lett. 94, 01870-1-4, 2005.
Araujo N.A.M., Andrade R.F.S., Herrmann H.J. q-state Potts model on the Apollonian network // Phys. Rev. E 82 (2010) 046109.
Assenza S., Gutierrez R., Gomez-Gardanes J., Latora V., Boccaletti S. Emergence of structural patterns out of synchronization in networks with competitive interactions , Scientific Reports, No.99, Vol.1, 2011.
Barabasi A.-L. Network Science. Cambridge University Press, Cambridge, UK, 2015.
Barabasi A.-L., Albert R. Emergence of Scaling in Random Networks , Science, Vol.286, October, 1999.
Barrat A., Barthelemy M., Vespignani A. Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.
Bassett D.S., Gazzaniga M.S. Understanding complexityin the human brain//Trends Cogn. Sci.15,200(2011).
Bullmore E., Sporns O. Complex brain networks: Graph theoretical analysis of structural and functional systems // Nat Rev Neurosci, vol. 10, no. 3, pp. 186-198, (2009)
Cohen R., Erez K., Ben-Avraham D., Havlin S. Breakdown of the Internet under intentional attack. Physical review letters. 2001; 86(16):3682-3685. doi: 10.1103/PhysRevLett.86.3682 PMID: 11328053
Cohen R., Havlin S. Complex Networks: Structure, Robustness and Function. Cambridge University Press, 2010.
Da Silva L.F., Costa Filho R.N., Soares D.J.B., Macedo-Filho A., Fulco U.L., Albuquerque E.L. Critical properties of contact process on the Apollonian network//Physica A: Statistical Mechanics and its Applications, Vol. 392, Issue 6, 15 March 2013, P. 1532-1537
Eriksen K.A., Simonsen I., Maslov S., Sneppen K. Modularity and Extreme Edges of the Internet//Phys.Rev. Lett.90, 148701(2003).
Gai, P. and S. Kapadia, (2010). Contagion in financial networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 466(2120), 2401-2423.
Gallos L.K., Makse H., Sigman M. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. // Proc Natl Acad Sci USA 109, (2012) 2825-2830.
Girvan M., Newman M. E. J. Community structure in social and biological networks. Proc. Natl Acad. Sci. USA 99, 7821-7826
Guimera R., Sales-Pardo M., Amaral LAN. Modularity from fluctuations in random graphs and complex networks // Phys. Rev. E 70, art. no. 025101 (2004)
Haldane A.G. Rethinking the financial network , Speech delivered at the Financial Student Association (Amsterdam, Netherlands), April, 2009.
Haldane A., May R.M. Systemic risk in banking ecosystems , Nature, Vol.469, January, 2011.
Herrmann H.J., Schneider C.M., Moreira A.A., Andrade J.S., Havlin S. Onion-like network topology enhances robustness against malicious attacks. Journal of Statistical Mechanics: Theory and Experiment. 2011; 2011(01):027-035. doi: 10.1088/1742-5468/2011/01/P01027
Holland J.H. The global economy as an adaptive process , SFI Studies in the Sciences of Complexity, Perseus Books Publishing, 1998.
Kambhu J., Weidman S., Krishnan N. New Directions for Understanding Systemic Risk, Federal Reserve Bank of New York Economic Policy Review, Vol.13, No.2, November,2012
Leon C., Machado C. Designing an expert-knowledge-based systemic importance index for financial institutions , Journal of Financial Market Infrastructures, No.1, Vol.2, 2013.
Leon C., Machado C., Murcia A. Macro-prudential assessment of Colombian financial institutions systemic importance , Borradores de Economia, No.800, Banco de la Republica, 2013.
Leon C., Perez J. Authority Centrality and Hub Centrality as Metrics of Systemic Importance of Financial Market Infrastructures , Borradores de Economia, No. 754, Banco de la Republica, 2014. forthcoming in Journal of Financial Market Infrastructures
Li Rq., Sun Sw., Ma Yl, Wang L., Xia Cy. Effect of clustering on attack vulnerability of interdependent scale-free networks. Chaos, Solitons and Fractals. 2015; 80:109-116. doi: 10.1016/j.chaos.2015.06.022
Markose S.M. Systemic risk from Global Financial Derivatives: A Network Analysis of Contagion and its Mitigation with Super-Spreader Tax , IMF Working Paper, No.WP/12/282, International Monetary Fund (IMF , 2012.
Matisziw T.C., Grubesic T.H., Guo J. Robustness elasticity in complex networks. Plos one. 2012; 7(7):e39788. doi: 10.1371/journal.pone.0039788 PMID: 22808060
May, R., and Arinaminpathy Systemic risk: the dynamics of model banking system,// N J. R. Soc. Interface, (2010) Vol.7, pp.823-838
May R.M., Levin S.A., Sugihara G. Ecology for bankers // Nature, Vol.451, February, 2008.
Mendes G.A., da Silva L.R., Herrmann H.J. Traffic gridlock on complex networks // Physica A 391 (2012) 362.
Miller J.H., Page S.E. Complex Adaptive Systems, Princeton University Press, 2007.
A.A., Paula D.R., Costa Filho R.N., Andrade J.S. Competitive cluster growth in complex networks. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics , v. 73, p. 065101, 2006.
Newman M. E. J. Networks: An Introduction. Oxford University Press, Oxford, 2010.
Nier, E., Yang, J., Yorulmazer, T., Alentorn, A. Network Models and Financial Stability, Journal of Economic Dynamics and Control, 31 (2007), p. 2033-2060.
Pan R.K, Sinha S. Modular networks with hierarchical organization: The dynamical implications of complex structure // RAMANA - journal of physics, August 2008, Vol. 71, No. 2, p. 331-340
Pastor-Satorras R., Castellano C., Mieghem P. Van, Vespignani A. Epidemic processes in complex networks // Rev. Mod. Phys. 87, 925 - Published 31 August 2015.
Pastor-Satorras R., Vespignani A. Evolution and Structure of the Internet: A Statistical Physics Approach, Cambridge University Press, Cambridge,England, 2004.
Pellegrini G.L., de Arcangelis L., Herrmann H.J., Perrone-Capano C. Modelling the brain as an Apollonian network // Physical Review E 76, 016107 (2007).
Roland Molontay Networks and fractals BSc Thesis/ Budapest University of Technology and Economics Institute of Mathematics Department of Stochastics. 2013
Simon H.A. The architecture of complexity , Proceedings of the American Philosophical Society, Vol. 106, No. 6, 1962.
Spirin V., Mirny L.A. Protein complexes and functional modules in molecular networks // Proc. Natl. Acad. Sci. USA100, 12123(2003).
Stanley H.E. Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971.
Sun S., Li R., Wang L., Xia C. Reduced synchronizability of dynamical scale-free networks with onion-like topologies. Applied Mathematics and Computation. 2015; 252:249-256. doi: 10.1016/j.amc.2014.12.044
Sun S., Liu Z., Chen Z., Yuan Z. Error and attack tolerance of evolving networks with local preferential attachment. Physica A: Statistical Mechanics and its Applications. 2007; 373:851-860. doi: 10.1016/j.physa.2006.05.049
Tanizawa T., Havlin S., Stanley H. Robustness of onion-like correlated networks against targeted attacks. Physical review E, Statistical, nonlinear, and soft matter physics. 2012; 85(4):046109-046117. doi: 10.1103/PhysRevE.85.046109 PMID: 22680540
Toivanen M. Contagion in the interbank network: An epidemiological approach // Bank of Finland Research Discussion Paper No. 19/2013
Vespignani A. Complex networks: The fragility of interdependency. Nature 464, 984-985 (2010).
Wu Z.X, Holme P. Onion structure and network robustness. Physical Review E. 2011;84(2):026106-026110.doi: 10.1103/PhysRevE.84.026106
Yuan X., Shao S., Stanley H.E., Havlin S. How breadth of degree distribution influences network robustness: Comparing localized and random attacks. Physical Review E. 2015; 92(3):032122-032130. doi:10.1103/PhysRevE.92.032122
Zeng A., Liu W. Enhancing network robustness against malicious attacks. Physical review E, Statistical, nonlinear, and soft matter physics. 2012; 85(6):066130-066135. doi: 10.1103/PhysRevE.85.066130 PMID: 23005185
Zhongzhi Zhang, Lili Rong, and Francesc Comellas High-dimensional random apollonian networks. Physica A: Statistical Mechanics and its Applications, 364:610-618, 2006.
Zhongzhi Zhang, Lili Rong, and Shuigeng Zhou Evolving apollonian networks with small-world scalefree topologies. Physical Review E,74(4):046105, 2006.
von Bertalanffy L. General System Theory - A critical review, General Systems, 7:1-20, 1962.
Karaev A.K., Mel nichuk M.V., (2015) Teoreticheskaya model prognozirovaniya finansovoy nestabil nosti rossiyskogo mezhbankovskogo kreditnogo rynka na osnove semeystva epidemiologicheskikh modeley. Biznes v zakone. Ekonomiko-yuridicheskiy zhurnal, 5: 219-222
Maevskiy V.I., CHernavskiy D.S., Ierarkhicheski organizovannyy vybor, http://spkurdyumov.ru/economy/ierarxicheski-organizovannyj-vybor/
Albert R., Jeong H., Barabasi A. Error and Attack Tolerance of Complex Networks. Nature. 2000;406:378-382. doi: 10.1038/35019019 PMID: 10935628
Allen F., Gale D. Financial contagion , Journal of Political Economy, Vol.108, No.1, 2000.
Anderson Complexity theory and organization science , Organization Science, Vol. 10, No.3, 1999.
Andrade R.F.S., Andrade J.S., Herrmann H.J. Ising model on the Apollonian network with nondependent interactions // Phys. Rev. E 79 (2009) 036105.
Andrade R.F.S, Herrmann H.J. Magnetic models on Apollonian networks // Phys. Rev. E 71 (2005) 056131.
Andrade Jr. J.S., Herrmann H.J., Andrade R.F.S., da Silva L.R. Apollonian Networks: Simultaneously Scale-Free, Small World, Euclidean, Space Filling, and with Matching Graphs. Phys. Rev. Lett. 94, 01870-1-4, 2005.
Araujo N.A.M., Andrade R.F.S., Herrmann H.J. q-state Potts model on the Apollonian network // Phys. Rev. E 82 (2010) 046109.
Assenza S., Gutierrez R., Gomez-Gardanes J., Latora V., Boccaletti S. Emergence of structural patterns out of synchronization in networks with competitive interactions , Scientific Reports, No.99, Vol.1, 2011.
Barabasi A.-L. Network Science. Cambridge University Press, Cambridge, UK, 2015.
Barabasi A.-L., Albert R. Emergence of Scaling in Random Networks , Science, Vol.286, October, 1999.
Barrat A., Barthelemy M., Vespignani A. Dynamical Processes on Complex Networks, Cambridge University Press, Cambridge, 2008.
Bassett D.S., Gazzaniga M.S. Understanding complexityin the human brain//Trends Cogn. Sci.15,200(2011).
Bullmore E., Sporns O. Complex brain networks: Graph theoretical analysis of structural and functional systems // Nat Rev Neurosci, vol. 10, no. 3, pp. 186-198, (2009)
Cohen R., Erez K., Ben-Avraham D., Havlin S. Breakdown of the Internet under intentional attack. Physical review letters. 2001; 86(16):3682-3685. doi: 10.1103/PhysRevLett.86.3682 PMID: 11328053
Cohen R., Havlin S. Complex Networks: Structure, Robustness and Function. Cambridge University Press, 2010.
Da Silva L.F., Costa Filho R.N., Soares D.J.B., Macedo-Filho A., Fulco U.L., Albuquerque E.L. Critical properties of contact process on the Apollonian network//Physica A: Statistical Mechanics and its Applications, Vol. 392, Issue 6, 15 March 2013, P. 1532-1537
Eriksen K.A., Simonsen I., Maslov S., Sneppen K. Modularity and Extreme Edges of the Internet//Phys.Rev. Lett.90, 148701(2003).
Gai, P. and S. Kapadia, (2010). Contagion in financial networks. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 466(2120), 2401-2423.
Gallos L.K., Makse H., Sigman M. A small world of weak ties provides optimal global integration of self-similar modules in functional brain networks. // Proc Natl Acad Sci USA 109, (2012) 2825-2830.
Girvan M., Newman M. E. J. Community structure in social and biological networks. Proc. Natl Acad. Sci. USA 99, 7821-7826
Guimera R., Sales-Pardo M., Amaral LAN. Modularity from fluctuations in random graphs and complex networks // Phys. Rev. E 70, art. no. 025101 (2004)
Haldane A.G. Rethinking the financial network , Speech delivered at the Financial Student Association (Amsterdam, Netherlands), April, 2009.
Haldane A., May R.M. Systemic risk in banking ecosystems , Nature, Vol.469, January, 2011.
Herrmann H.J., Schneider C.M., Moreira A.A., Andrade J.S., Havlin S. Onion-like network topology enhances robustness against malicious attacks. Journal of Statistical Mechanics: Theory and Experiment. 2011; 2011(01):027-035. doi: 10.1088/1742-5468/2011/01/P01027
Holland J.H. The global economy as an adaptive process , SFI Studies in the Sciences of Complexity, Perseus Books Publishing, 1998.
Kambhu J., Weidman S., Krishnan N. New Directions for Understanding Systemic Risk, Federal Reserve Bank of New York Economic Policy Review, Vol.13, No.2, November,2012
Leon C., Machado C. Designing an expert-knowledge-based systemic importance index for financial institutions , Journal of Financial Market Infrastructures, No.1, Vol.2, 2013.
Leon C., Machado C., Murcia A. Macro-prudential assessment of Colombian financial institutions systemic importance , Borradores de Economia, No.800, Banco de la Republica, 2013.
Leon C., Perez J. Authority Centrality and Hub Centrality as Metrics of Systemic Importance of Financial Market Infrastructures , Borradores de Economia, No. 754, Banco de la Republica, 2014. forthcoming in Journal of Financial Market Infrastructures
Li Rq., Sun Sw., Ma Yl, Wang L., Xia Cy. Effect of clustering on attack vulnerability of interdependent scale-free networks. Chaos, Solitons and Fractals. 2015; 80:109-116. doi: 10.1016/j.chaos.2015.06.022
Markose S.M. Systemic risk from Global Financial Derivatives: A Network Analysis of Contagion and its Mitigation with Super-Spreader Tax , IMF Working Paper, No.WP/12/282, International Monetary Fund (IMF , 2012.
Matisziw T.C., Grubesic T.H., Guo J. Robustness elasticity in complex networks. Plos one. 2012; 7(7):e39788. doi: 10.1371/journal.pone.0039788 PMID: 22808060
May, R., and Arinaminpathy Systemic risk: the dynamics of model banking system,// N J. R. Soc. Interface, (2010) Vol.7, pp.823-838
May R.M., Levin S.A., Sugihara G. Ecology for bankers // Nature, Vol.451, February, 2008.
Mendes G.A., da Silva L.R., Herrmann H.J. Traffic gridlock on complex networks // Physica A 391 (2012) 362.
Miller J.H., Page S.E. Complex Adaptive Systems, Princeton University Press, 2007.
A.A., Paula D.R., Costa Filho R.N., Andrade J.S. Competitive cluster growth in complex networks. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics , v. 73, p. 065101, 2006.
Newman M. E. J. Networks: An Introduction. Oxford University Press, Oxford, 2010.
Nier, E., Yang, J., Yorulmazer, T., Alentorn, A. Network Models and Financial Stability, Journal of Economic Dynamics and Control, 31 (2007), p. 2033-2060.
Pan R.K, Sinha S. Modular networks with hierarchical organization: The dynamical implications of complex structure // RAMANA - journal of physics, August 2008, Vol. 71, No. 2, p. 331-340
Pastor-Satorras R., Castellano C., Mieghem P. Van, Vespignani A. Epidemic processes in complex networks // Rev. Mod. Phys. 87, 925 - Published 31 August 2015.
Pastor-Satorras R., Vespignani A. Evolution and Structure of the Internet: A Statistical Physics Approach, Cambridge University Press, Cambridge,England, 2004.
Pellegrini G.L., de Arcangelis L., Herrmann H.J., Perrone-Capano C. Modelling the brain as an Apollonian network // Physical Review E 76, 016107 (2007).
Roland Molontay Networks and fractals BSc Thesis/ Budapest University of Technology and Economics Institute of Mathematics Department of Stochastics. 2013
Simon H.A. The architecture of complexity , Proceedings of the American Philosophical Society, Vol. 106, No. 6, 1962.
Spirin V., Mirny L.A. Protein complexes and functional modules in molecular networks // Proc. Natl. Acad. Sci. USA100, 12123(2003).
Stanley H.E. Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971.
Sun S., Li R., Wang L., Xia C. Reduced synchronizability of dynamical scale-free networks with onion-like topologies. Applied Mathematics and Computation. 2015; 252:249-256. doi: 10.1016/j.amc.2014.12.044
Sun S., Liu Z., Chen Z., Yuan Z. Error and attack tolerance of evolving networks with local preferential attachment. Physica A: Statistical Mechanics and its Applications. 2007; 373:851-860. doi: 10.1016/j.physa.2006.05.049
Tanizawa T., Havlin S., Stanley H. Robustness of onion-like correlated networks against targeted attacks. Physical review E, Statistical, nonlinear, and soft matter physics. 2012; 85(4):046109-046117. doi: 10.1103/PhysRevE.85.046109 PMID: 22680540
Toivanen M. Contagion in the interbank network: An epidemiological approach // Bank of Finland Research Discussion Paper No. 19/2013
Vespignani A. Complex networks: The fragility of interdependency. Nature 464, 984-985 (2010).
Wu Z.X, Holme P. Onion structure and network robustness. Physical Review E. 2011;84(2):026106-026110.doi: 10.1103/PhysRevE.84.026106
Yuan X., Shao S., Stanley H.E., Havlin S. How breadth of degree distribution influences network robustness: Comparing localized and random attacks. Physical Review E. 2015; 92(3):032122-032130. doi:10.1103/PhysRevE.92.032122
Zeng A., Liu W. Enhancing network robustness against malicious attacks. Physical review E, Statistical, nonlinear, and soft matter physics. 2012; 85(6):066130-066135. doi: 10.1103/PhysRevE.85.066130 PMID: 23005185
Zhongzhi Zhang, Lili Rong, and Francesc Comellas High-dimensional random apollonian networks. Physica A: Statistical Mechanics and its Applications, 364:610-618, 2006.
Zhongzhi Zhang, Lili Rong, and Shuigeng Zhou Evolving apollonian networks with small-world scalefree topologies. Physical Review E,74(4):046105, 2006.
von Bertalanffy L. General System Theory - A critical review, General Systems, 7:1-20, 1962.
Keywords:
financial stability, financial contagion, the network approach, polonovski count.
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