Hierarchical Cont-Bouchaud Model

• Authors: R. Paluch , K. Suchecki , J. Hołyst
• Languages of publication: EN

Abstracts

EN

We extend the well-known Cont-Bouchaud model to include a hierarchical topology of agent's interactions. The influence of hierarchy on system dynamics is investigated by two models. The first one is based on a multi-level, nested Erdős-Rényi random graph and individual decisions by agents according to Potts dynamics. This approach does not lead to a broad return distribution outside a parameter regime close to the original Cont-Bouchaud model. In the second model we introduce a limited hierarchical Erdős-Rényi graph, where merging of clusters at a level h+1 involves only clusters that have merged at the previous level h and we use the original Cont-Bouchaud agent dynamics on resulting clusters. The second model leads to a heavy-tail distribution of cluster sizes and relative price changes in a wide range of connection densities, not only close to the percolation threshold.

Keywords

EN

89.65.-s; 89.65.Gh; 89.75.-k; 05.40.-a

Discipline

• 89.65.-s: Social and economic systems
• 89.75.-k: Complex systems(for complex chemical systems, see 82.40.Qt; for biological complexity, see 87.18.-h)
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)
• 05.40.-a: Fluctuation phenomena, random processes, noise, and Brownian motion(for fluctuations in superconductivity, see 74.40.-n; for statistical theory and fluctuations in nuclear reactions, see 24.60.-k; for fluctuations in plasma, see 52.25.Gj; for nonlinear dynamics and chaos, see 05.45.-a)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2015
• Volume: 127
• Issue: 3A
• Pages: A-108-A-112

Dates

published

2015-03

Contributors

author

R. Paluch

• Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland

author

K. Suchecki

• Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland

author

J. Hołyst

• Center of Excellence for Complex Systems Research, Faculty of Physics, Warsaw University of Technology, Koszykowa 75, PL-00662 Warsaw, Poland
• ITMO University, 19, Kronverkskiy av., 197101 Saint Petersburg, Russia

References

• [1] D. Kahneman, A. Tversky, Econometrica 47, 263 (1979)
• [2] D.S. Scharfstein, J.C. Stein, Am. Econ. Rev. 80, 465 (1990)
• [3] M. Grinblatt, S. Titman, R. Wermers Am. Econ. Rev. 85, 1088 (1995)
• [4] J.A. Lipski, R. Kutner, Acta Phys. Pol. A 123, 584 (2013), doi: 10.12693/APhysPolA.123.584
• [5] P. Sieczka, J.A. Hołyst, Physica A 387, 1218 (2008), doi: 10.1016/j.physa.2007.10.048
• [6] A. Sienkiewicz, T. Gubiec, R. Kutner Z.R. Struzik, Acta Phys. Pol. A 123, 615 (2013), doi: 10.12693/APhysPolA.123.615
• [7] A. Szmagliński, Acta Phys. Pol. A 123, 621 (2013), doi: 10.12693/APhysPolA.123.621
• [8] D. Makowiec, Physica A 344, 36 (2004), doi: 10.1016/j.physa.2004.06.084
• [9] M. Wiliński, A. Sienkiewicz, T. Gubiec, R. Kutner, Z.R. Struzik, Physica A 392, 5963 (2013), doi: 10.1016/j.physa.2013.07.064
• [10] R. Cont, J.-P. Bouchaud, Macroecon. Dyn. 4, 170 (2000)
• [11] D. Stauffer, T.J.P. Penna, Physica A 256, 284 (1998), doi: 10.1016/S0378-4371(98)00223-4
• [12] D. Stauffer, P.M.C de Oliveira, A.T. Bernardes, Int. J. Theor. Appl. Finance 2, 83 (1998), doi: 10.1142/S0219024999000066
• [13] I. Chang, D. Stauffer, Physica A 264, 294 (1999), doi: 10.1016/S0378-4371(98)00441-5
• [14] D. Stauffer, D. Sornette, Physica A 271, 496 (1999), doi: 10.1016/S0378-4371(99)00290-3
• [15] D. Stauffer, N. Jan, Physica A 277, 215 (2000), doi: 10.1016/S0378-4371(99)00587-7
• [16] D. Chowdhury, D. Stauffer, Eur. Phys. J. B 8, 477 (1999), doi: 10.1007/s100510050714
• [17] R.B. Pandey, D. Stauffer, Int. J. Theor. Appl. Finance 3, 479 (2000), doi: 10.1142/S0219024900000437
• [18] F. Castiglione, D. Stauffer, Physica A 300, 531 (2001), doi: 10.1016/S0378-4371(01)00365-X
• [19] I. Chang, D. Stauffer, R.B. Pandey, Int. J. Theor. Appl. Finance 5, 585 (2002), doi: 10.1142/S0219024902001584
• [20] L. Kullmann, J. Kertész, Int. J. Mod. Phys. C 12, 1211 (2001), doi: 10.1142/S0129183101002449
• [21] I. Chang, D. Stauffer, Physica A 299, 547 (2001), doi: 10.1016/S0378-4371(01)00270-9
• [22] L.R. Da Silva, D. Stauffer, Physica A 294, 235 (2001), doi: 10.1016/S0378-4371(01)00118-2
• [23] E. Ravasz, A.-L. Barabási, Phys. Rev. E 67, 026112 (2003), doi: 10.1103/PhysRevE.67.026112
• [24] P. Kondratiuk, J.A. Hołyst, Acta Phys. Pol. A 121, B67 (2012)
• [25] A. Czaplicka, J.A. Hołyst, P.M.A. Sloot, Sci. Rep. 3, 1223 (2013), doi: 10.1038/srep01223

Identifiers

DOI

10.12693/APhysPolA.127.A-108