Statistical majority model of financial market with price auction
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 179-187
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Mathematical modeling of financial markets has been carried out, their main processes being described on the basis of game theory. The condition of markets on the verge of collapse has been investigated, when strong correlations occur in the market participants' behaviour and, consequently, prices greatly deviate from the usual state. The dependence of statistical characteristics of model market on the parameters of the adopted model has been researched. With a view to getting an objective estimate of adequacy and applicability limits of the constructed model,the calculated characteristics have been compared with statistical characteristics of the real markets. On the basis of the results obtained, ways of improving the models of financial markets are suggested.
Keywords: mathematical market models, statistical market characteristics, game theory.
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T. R. Shahmuratov. Statistical majority model of financial market with price auction. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 179-187. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a15/

[1] Arthur W. B., “Complexity and the economy”, Science, 284 (1999), 107–109 | DOI

[2] Cont R., Bouchaud J. P., Herd behavior and aggregate fluctuations in financial markets, arXiv: cond-mat/9712318

[3] Farmer J. D., “Market force, ecology, and evolution”, Santa Fe Inst. Working Paper, 1998, no. 12, 117–183

[4] Lux T., “Scaling and criticality in a stochastic multi-agent model of a financial market”, Nature, 397 (1999), 498–500 | DOI

[5] Marsili M., Challet D., Trading behavior and excess volatility in toy markets, SISSA Working Paper, 2000, No CM/188/00, 188–202

[6] Nassim N. T., The black swan: the impact of the highly improbable, Random House, N.Y., 2007, 366 pp.

[7] Mandelbrot B., “The variation of certain speculative prices”, J. Business, 36 (1963), 392–419 | DOI

[8] Shiller R. J., Irrational exuberance, Princeton Univ. Press, Princeton, 2000, 344 pp.

[9] Jefferies P., Jhonson N. F., Hart M., Hui P. M., “From market games to real world markets”, Eur. Phys. J. B, 20 (2001), 493–501 | DOI | MR

[10] Jefferies P., Jhonsonm N. F., Designing agent based models, No 010702, Oxford Center for Computational Finance Working Paper, 2002, 32 pp.

[11] Challet D., Zhang Y. C., “Emergence of cooperation and organization in an evolutionary game”, Physica A, 246 (1997), 407–418 | DOI

[12] MMVB/MICEX http://micex.ru/markets/stock/organization/modes/511

[13] Shakhmuratov T. R., “Minoritarnaya model, osnovannaya na agentakh, pri uslovii vzaimodeistviya agentov”, Infokommunikatsionnye tekhnologii globalnogo informatsionnogo soobschestva, Sb. tr. 6-i ezhegodnoi mezhd. nauch.-prakt. konf. (Kazan, 4–5 sent. 2008 g.), Izd-vo OOO “Tsentr Operativnoi Pechati”, Kazan, 2008, 383–393

[14] Campbell J., Lo A. H., McKinlay C., The econometrics of financial markets, Princeton Univ. Press, Princeton, 1997, 632 pp. | Zbl

[15] Pagan A., “The econometrics of financial markets”, J. Empirical Finance, 1996, no. 3, 15–102 | DOI

[16] Massey F. J., “The Kolmogorov–Smirnov test for goodness of fit”, J. Amer. Statist. Assoc., 46:253 (1951), 68–78 | DOI | Zbl

[17] Clauset A., Shalizi C. R., Newman M. E. J., Power-law distributions in empirical data, arXiv: 10706.1062 | MR | Zbl

[18] Bouchaud J.-P., Potters M., Theory of financial risks. From statistical physics to risk management, Cambridge Univ. Press, Cambridge, 2000, 218 pp. | MR | Zbl