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Relativistic quantum econophysics – new paradigms in complex systems modelling

Saptsin, Vladimir; Соловйов, Володимир Миколайович

URI: http://elibrary.kdpu.edu.ua/handle/0564/1134
https://doi.org/10.31812/0564/1134

Date: 2009-07-07

Abstract:

This work deals with the new, relativistic direction in quantum econophysics, within the bounds of which a change of the classical paradigms in mathematical modelling of socio-economic system is oﬀered. Classical physics proceeds from the hypothesis that immediate values of all the physical quantities, characterizing system’s state, exist and can be accurately measured in principle. Non-relativistic quantum mechanics does not reject the existence of the immediate values of the classical physical quantities, nevertheless not each of them can be simultaneously measured (the uncertainty principle). Relativistic quantum mechanics rejects the existence of the immediate values of any physical quantity in principle, and consequently the notion of the system state, including the notion of the wave function, which becomes rigorously nondeﬁnable. The task of this work consists in econophysical analysis of the conceptual fundamentals and mathematical apparatus of the classical physics, relativity theory, non-relativistic and relativistic quantum mechanics, subject to the historical, psychological and philosophical aspects and modern state of the socio-economic modeling problem. We have shown that actually and, virtually, a long time ago, new paradigms of modeling were accepted in the quantum theory, within the bounds of which the notion of the physical quantity operator becomes the primary fundamental conception(operator is a mathematical image of the procedure, the action), description of the system dynamics becomes discrete and approximate in its essence, prediction of the future, even in the rough, is actually impossible when setting aside the aftereﬀect i.e. the memory. In consideration of the analysis conducted in the work we suggest new paradigms of the economical-mathematical modeling.

Description:

[1] R. N. Mantegna and H. E. Stanley, An Introduction to Econophysics (Cambridge University Press, Cambridge, 2000). [2] M. Yu. Romanovskiy and Yu. M. Romnovskiy, An Introduction to Econophysics. Statistical and dynamic models (IKI, Moscow, ) 2007). [in Russian]. [3] V. M. Solovyov, Mathematical economy. Educational methodical aid for the independent study of discipline (CHNU, Cherkassy, 2008). [in Ukrainian]. [4] D. S. Chernavskiy, N. I. Starkov and A. V. Scherbakov, About the problems of physical economy, Uspehi fizicheskih nauk, 172(9), 1045-1066 (2002). [5] D. Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton University Press, Princeton, NJ, 2003). [6] E. Peters, Fractal market analysis. Applying chaos theory to investment and economics (Jhon Wiley&sons, Inc, New York, 2003). [7] J. Barkley Rosser Jr, Dynamics of Markets. Econophysics and Finance, ( by Joseph L. McCauleyCambridge University Press, Cambridge, 2004). [8] A. Ganchuk, V. Derbentsev and V. Soloviev, Multifractal properties of the Ukraine stock market, arXiv:physics/0608009v1 1 Aug 2006. [9] L. D. Landau and E. M. Lifshits, Statistical Physics. Part 1 (Nauka, Moscow, 1976). ) [in Russian]. [10] V. P. Maslov, Quantum Economics, 2nd ed. (Nauka, Moscow, 2006). ) [in Russian]. [11] A. V. Moseychuk and V. A. Moseychuk, Introduction to the real quantum economy (NTO im. akademika S.I. Vavilova, Moscow, 2006). ) [in Russian]. [12] A. Kondratenko, Physical Modeling of economic systems. Classical and quantum economies (Nauka, Novosibirsk, 2005). ) [in Russian]. [13] M. Schaden, Quantum finance, arXiv:physics/0203006v2 [physics.soc-ph] 6 Aug . [14] B. E. Baaquie, Quantum Finance, (Cambridge University Press, Cambridge, 2004). [15] E. Piotrowski and J. Sladkowski, Quantum market games, Physica A 312, 208–217, (2002), arXiv:quantph/0104006v1 2 Apr 2001. [16] A. Iqbal and A. H. Toor, Quantum repeated games, Physics Letters A 300 (6), 541–546 (2002). [17] A. Iqbal, Studies in the Theory of Quantum Games (PhD thesis, Quaid-i-Azam University, Department of Electronics, 2004). [18] C. P. Goncalves, An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence, April 14, 2007, URL http://ma.utexas.edu/mp arc/c/07/07-89.pdf. [19] V. I. Zverev and A. M. Tishin, Quantum theory of economics ( Physics Department of M. V. Lomonosov Moscow State University, Moscow, 2008 ), URL http://arxiv.org/ftp/arxiv/papers/0901/0901.4767.pdf. [20] V. P. Maslov, Quantum Econophysics, in Econophysics. Modern physics in search of economic theory (MIFI Moscow, 2007). [21] E. Guevara H., Quantum Econophysics, arXiv:physics/0609245v2 [physics.soc-ph] 30 Apr 2007. [22] V. N. Solov’ev and V. M. Saptsin, Quantum econophysics - a physical ground of system conceptions in socio-economic processes, in Analysis, design, management, development of the economic systems: Proceedings of II International School-symposium AMUR-2008 (Sevastopol, on September, 12-18, 2008), edited by O.L. Korolev and A.V. Sigal (Simferopol’, Ukraine, 2008), pp. 94–100. [23] V. I. Yukalov and D. Sornette, Quantum Decision Theory, arXiv:0802.3597v1 [physics.soc-ph] 25 Feb 2008. [24] V. I. Yukalov and D. Sornette, Mathematical basis of quantum decision theory, arXiv:0808.0112v1 [cs.AI] 1 Aug 2008. [25] V. I. Yukalov and D. Sornette, Physics of risk and uncertainty in quantum decision making, arXiv:0812.2388v1 [physics.soc-ph] 12 Dec 2008. [26] V. I. Yukalov and D. Sornette, Quantum decision theory as quantum theory of measurement, arXiv:0903.5188v1 [quant-ph] 30 Mar 2009. [27] F. Bagarello, Stock markets and quantum dynamics: a second quantized description, arXiv:0904.3210v1 [qfin.TR] 21 Apr 2009. [28] D. Sornette and Wei-Xing Zhou, Importance of positive feedbacks and over-confidence in a self-fulfilling Ising model of financial markets, arXiv:cond-mat/0503607v2 30 Mar 2005. [29] Wei-Xing Zhou and D. Sornette, Self-fulfilling Ising model of financial markets, arXiv:physics/0503230v1 [physics.soc-ph] 31 Mar 2005. [30] Wei-Xing Zhou and D. Sornette, Self-organizing Ising model of financial markets, The European Physical Journal B, 55 (2), 175–181 (2007). [31] G. Montagna, O. Nicrosini, G. Passarino and N. Moreni, Pricing exotic options in a path integral approach, Quantitative Finance, 6, bibinfopages55-66 (2004), arXiv:cond-mat/0407321v2 [cond-mat.other] 17 May 2006. [32] B. E. Baaquie, Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates, 1st ed. (Cambridge University Press, Cambridge, 2007 ). [33] J. Dash, Quantitative finance and risk management: a physicist’s approach (World Scientific Pub., 2004). [34] H. Kleinert, Path integrals in quantum mechanics, statistics, polymer physics, and financial markets (World Scientific Pub., 2006). [35] V. P. Maslov, Approximation probabilities, the law of quasistable markets, and phase transitions from the ”condensed” state, arXiv:math/0307265v1 [math.PR] 19 Jul 2003. [36] V. P. Maslov, Economic law of increase of Kolmogorov complexity. Transition from financial crisis 2008 to the zero-order phase transition (social explosion), arXiv:0812.4737v1 [q-fin.GN] 29 Dec 2008. [37] F. Bagarello, An operatorial approach to stock markets, J. Phys. A, 39, 6823–6840 (2006). [38] F. Bagarello, The Heisenberg picture in the analysis of stock markets and in other sociological contexts, Proceedings del Workshop How can Mathematics contribute to social sciences, Bologna 2006, Italia, in Quality and Quantity, 10.1007/s11135-007-9076-4. [39] F. Bagarello, Stock Markets and Quantum Dynamics: A Second Quantized Description, Physica A, 386, 283 (2007). [40] F. Bagarello, Simplified stock markets described by number operators, arXiv:0904.3213v1 [q-fin.TR] 21 Apr 2009. [41] V. P. Maslov and V. E. Nazaikinskii, Mathematics underlying the 2008 financial crisis, and a possible remedy, arXiv:0811.4678v1 [q-fin.GN] 28 Nov 2008. [42] V. P. Maslov, Threshold levels in Economics, arXiv:0903.4783v1 [q-fin.ST] 27 Mar 2009. [43] C. P. Goncalves, Uma Teoria da Empresa Agil Criadora de Conhecimento Contributos. (PhD Thesis, ISCTEBusiness School, 2005). [44] C. P. Goncalves, Criacao de Conhecimento e Agilidade: Novos Desafios Competitivos, Economia Global e Gestao, XI (1), 125–139 (2006). [45] C. P. Goncalves, Herding, 2003, URL. [46] C. P. Goncalves, Artificial financial market, 2003, URL. [47] C. P. Goncalves, Artificial financial market II - Tail risk, 2005, URL. [48] C. P. Goncalves and J. D. Curto, Risco, Agentes e Complexidade, paper presented at the seminar Grupos, Tecnologia e Criatividade, ISCTE, 2005. [49] C. P. Goncalves and M. A. Ferreira, Self-Organized Criticality in Synchronized Loss Dynamics - A Behavioral Account, working paper presented at the seminar Mercado Financeiro Artificial: Simulacao Multiagentes e Dinamicas de Mercado, ISCTE, 2006, URL. [50] E. Guevara H., Quantum replicator dynamics, Physica A 369/2, 393–407 (2006), arXiv:quant-ph/0510238v7. [51] E. Guevara H., Introduction to the study of entropy in quantum games, 2006, arXiv:quant-ph/0604170v2 26 Apr 2006. [52] E. Guevara H., Quantum games entropy, arXiv:quantph/0606045v1 6 Jun 2006. [53] E. Guevara H., Quantum Games and the Relationships between Quantum Mechanics and Game Theory, arXiv:0803.0292v1 [quant-ph] 3 Mar 2008. [54] Yu. Nakayama, Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance, arXiv:0906.4112v1 [hep-th] 23 Jun 2009. [55] T. Vaga, The Coherent Market Hypothesis, Financial Analysts Journal, November/December, 36–49 ( 1990). [56] J. Sapir, Economic theory of heterogeneous systems: an essay on decentralized economies, Translation from French, edited by N.A. Makasheva (GU VSHE, Moscow, 2001 ) [in Russian]. [57] L. D. Landau and E. M. Lifshits, Quantum mechanics. Short course of theoretical physics, Book 2 (Nauka, Moscow, 1972 ) [in Russian]. [58] L. D. Landau and E. M. Lifshits, Quantum mechanics. Non-relativistic theory, (Nauka, Moscow, 1974 ) [in Russian]. [59] P. V. Elyutin and V. D. Krivchenkov, Quantum mechanics with the exercises, edited by academician N.N.Bogolyubov (Nauka, Moscow, 1976 ) [in Russian]. [60] S. L. Rubinshteyn, Bases of general psychologists, (Peter, Saint Petersburg, 2007 ) [in Russian]. [61] D. Sornette, Interdisciplinarity in Socio-economics, mathematical analysis and predictability of complex systems, arXiv:physics/0807.3814 [physics.soc-ph] 24 Jul 2008. [62] V. I. Vernadskiy, Problem of Time, Space and Symmetry 1920–1942. , URL [63] H. Haken, Synergetics, 2nd ed. (Springer-Verlang, Berlin, Heidenberg, New York, 1978). [64] B. Mandelbrot, The fractal geometry of nature (Freeman, San Francisco, 1982). [65] G. G. Malineckiy, A. B. Potapov and A. V. Podlazov, Non-linear dynamics: approaches, results, hopes (URSS, Moscow, 2006) [in Russian]. [66] D. Deutsch, The Fabric of Reality (The Penguing Press, 1997). [67] D. Deutsch, Qubit Field Theory, arXiv:quantph/0401024v1 6 Jan 2004. [68] K. A. Valiev, Quantum informatics: computers, connection and cryptography, Vestnik rosiiskoi akademii nauk, 70 (8), 688–695 ( 2000). [69] C. Camerer, G. Loewenstein and D. Prelec, Neuroeconomics: How Neuroscience Can Inform Economics, J. Econ. Liter., XLIII, 9–64 ( 2005). [70] K. Hensel, Uber eine neue Begrundung der Theorie der algebraischen Zahlen, Jahresbericht der Deutschen Mathematiker-Vereinigung, 6 (3), 83–88 ( 1997). [71] V. S. Vladimirov, I. V. Volovich and E. I. Zelenov, p-Adic analysis and mathematical physics, (Nauka, Moscow, 1994 ) [in Russian]. [72] I. V. Volovich and S. V. Kozyrev p-Adic mathematical physics: basic constructions, application to complex and nanoscope systems. Tutorial ( SGU, Samara, 2009 ) [73] A. A. Bogdanov, Essay on the organizational science, [in Russian], URL http://www.uic.nnov.ru/pustyn/lib/bogdanov.ru.html. [74] A. A. Bogdanov, Tectology: universal organizational science, 2 books (Ekonomika, Moscow, 1989) [in Russian]. [75] A. N. Tolstoy, The Golden key or Adventures of Buratino (Veselka, Kiev, 1986 ) [in Russian]. [76] K. G¨odel, Uber formal unent scheidbare S¨atze der Prin- ¨ cipia Mathematica und verwander System, I, Monatshefte Mathematic Physik, Bd 38, 173–198 ( 1931). [77] E. Nagel and J. R. Newman, G¨odel’s Proof (Univ. Press., New York, 1958). [78] D. Hofstadter, Godel, Escher, Bach: An Eternal Golden Braid (Basic Books, 1999), ISBN 0465026567. [79] T. J. Yeh. About the axiom of choice, in reference book on mathematical logic, Part II, Theory of sets (Moscow, 1982), p. 35–63. [80] P. J. Cohen, Set theory and the continuum hypothesis (Stanford University, W.A.Benjamin Inc., New York, Amsterdam, 1966). [81] L. von Bertalanffy, General System Theory - A Critical Review, General Systems, VII, 1-20 (1962). [82] L. von Bertalanffy, General System theory: Foundations, Development, Applications ( George Braziller, revised edition, New York, 1976) ISBN 0-8076-0453-4. [83] N. N. Moiseev, The mathematical problems of systems analysis (Nauka, Moskow, 1981 ) [in Russian]. [84] N. E. Kobrinskiy, E. Z. Mayminas and A. D. Smirnov, Economic cybernetics (Ekonomika, Moscow, 1982 ) [in Russian]. [85] V. I. Lyamec and A. D. Tevyashev, Systems analysis, 2nd ed. (KHNURE, Kharkov ) [in Russian]. [86] A. A. Fraenkel and Yehoshu Bar-Hiller, Foundations of set theory (North-Holland publishing company, Amsterdam, 1958). [87] A. N. Kolmogorov and A. G. Dragalin, Mathematical logics (URSS, Moscow, 2005 ) [in Russian]. [88] A. N. Kolmogorov, Combinatorial grounds of information theory, Uspehi matematicheskih nauk, 38(4), 27-36 ( 1983). [89] N. N. Moiseev, Human. Environment. Society, (Nauka, Moscow, 1982 ) [in Russian]. [90] Technology of system design, (edited by S. V. Emel’yanov, V. V. Kalashnikov, M. Franc, A. Yavor, Mashinostroenie, Moscow, Tehnik, Berlin, 1988 ) [in Russian]. [91] S. L. Bluymin, Discreteness against continuity at a system design in time and/or in space, Sistemy upravleniya i informacionnye tehnologii, 1(13), 4–9 (2004). [92] S. L. Bluymin, Discreteness against continuity in information technologies: quantum calculation and his alternatives, Sistemy upravleniya i informacionnye tehnologii, 1,2(31), 217–221 (2008). [93] L. D. Landau and E. M. Lifshits, Mechanics, (Nauka, Moscow, 1973) [in Russian]. [94] Robert Anton Wilson, Quantum Psychology (New Falcon Publications, Amazon.com., 1990). [95] T. K. Grechko, Application of quantum sociology to activity of civil servant, Workshop ”Science: Theory and practice”, Vol. 2, (Publishing house ”Education and Science”, Prague, 2005). [96] V. L. Vasyukov, Quantum logics (PER SE, Moscow, 2005) [in Russian]. [97] B. C. Van Fraassen, The Labyrinth of Quantum Logic, Logico-algebraic approach to quantum mechanics, Vol. 1 (Reidel, Dordrecht-Boston, 1975). [98] The ultimate guide to the LHC - LHC’s official FAQ. [99] S. A. Slavatinskiy, Fundamental particles, SOZH, 2, 62– 68 (2001). [100] I. L. Bukhbinder, Fundamental interactions, SOZH, 5, 66–73 (1997). [101] S. S. Gershteyn, What is colour charge, or what forces quarks are linked by, SOZH, 6, 78–84 (2000). [102] A. G. Lisi, An Exceptionally Simple Theory of Everything, arXiv:0711.0770v1 [hep-th] 6 Nov 2007. [103] J. P. Serre, Lie algebras and lie groups (Benjamin, New York - Amsterdam, 1966). [104] V. Uspenskiy, N. Vereschagin and A. Shen’, Kolmogorov‘s complexity, eprint, 2004, URL http://lj.streamclub.ru/books/complex/uspen.ps. [105] Hanz-Valter Lorenz, Nonlinear Dynamical Economics and Chaotic Motion (Springer-Verlag, 1989). [106] P. D. Wasserman, Neural computing: theory and practice (Van Nostrand Reinhold, New York, 1989). [107] I. S. Surovcev, V. I. Klyukin and R. P. Pivovarova, Neural networks (VGU, Voronezh, 1994) [in Russian]. [108] A. A. Ezhov and S. A. Shumskiy, Neurocomputing and it’s applications in economics and business (MIFI, Moscow, 1998) [in Russian]. [109] B. P. Demidovich, I. A. Maron and E. Z. Shuvalova, Numerical methods of analysis. Approaching of functions, differential and integral equations (Nauka, Moskow, 1967) [in Russian]. [110] P.-F. Verhulst, Notice sur la loi que la population suit dans son accroissement, Correspondence Mathematique et Physique, Bruxelles, 10, 113–121 (1838). [111] P.-F. Verhulst, Recherches mathematiques sur la loi d’accroissement de la population, Nouveaux Momoires de 1’Academie Royale des Sciences et Belles Lettres de Braxelles, 18, 1-38 (1845). [112] J. Feder, Fractals (Plenum Press, New York, 1988). [113] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci. 20, 130–141 (1963). [114] A. Khrennikov, On the cognitive experiments to test quantum-like behaviour of mind, arXiv:quantph/0205092v2 16 Jan 2003. [115] A. Khrennikov, A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorovian model, arXiv:math/0609197v1 [math.PR] 7 Sep 2006. [116] A. Khrennikov, Quantum-like Probabilistic Models outside Physics, arXiv:physics/0702250v2 [physics.gen-ph] 5 Jun 2007. [117] O. Choustova, Toward Quantum Behavioral Finances: Bohmian Approach, arXiv:quant-ph/0109122v5 7 Jan 2007. [118] Bryce Seligman DeWitt and R. Neill Graham, eds., The Many-Worlds Interpretation of Quantum Mechanics, Princeton Series in Physics, (Princeton University Press, 1973), pp. 3-140. [119] H. Everett, Relative State Formulation of Quantum Mechanics, Reviews of Modern Physics, 29, 454–462, (1957). [120] A. A. Bogdanov, Empiriomonizm: articles on philosophy (Republic, Moscow, 2003) [in Russian]. [121] J. E. Stiglinz, Information and the Change in the Paradigm in Economics, From Les Prix Nobel. The Nobel Prizes 2001, Editor Tore Frangsmyr, [Nobel Foundation], Stockholm, 2002, pp. 472–540. [122] V. L. Tambovcev, Fifth market: economic problems of information production (MGU, Moscow, 1993) [in Russian]. [123] V. Polterovich, Strategies of institutional reforms. Perspective trajectories, Ekonomika i matematicheskie metody, 42(1), ( 2006). [124] V. Polterovich, The Economic Crisis in 2008: A Breakdown of Institutions and Views, Zhurnal novoy ekonomicheskoy associacii, 1-2, 262-264 ( 2009). [125] V. Dyuk and A. Samoylenko, Data Mining: educational course (Peter, Saint Petersburg, 2001) [in Russian]. [126] I. A. Chubukova, Data Mining: Tutorial (Internetuniversity of information technologies: BINOM: Laboratory of knowledges, Moscow, 2006) [in Russian]. [127] L. D. Landau and E. M. Lifshits, Field theory, (Nauka, Moscow, 1973) [in Russian]. [128] V. Soloviev, V. Saptsin and D. Chabanenko, Adaptive methodology of prediction based on complex Markov chains, in Computer technologies in building: Proceedings of VI International theoretical and practical conference ”KOMTEKHBUD 2008”: Kyiv-Sevastopol, on September, 9-12, 2008 (Ministry of regional development and building of Ukraine, Kyiv, 2008) pp. 59–60. [129] V. Saptsin, Experience of application genetically complex Markov chains for neural networks technology prediction, Visnyk Krivoriz‘kogo ekonomichnogo institutu KNEU, Kriviy Rig, 2(18), 56–66 (2009). [130] V. Soloviev, V. Saptsin and D. Chabanenko, Prediction of financial time series with the technology of high-order Markov chains, Working Group on Physics of Socioeconomic Systems (AGSOE).-Drezden, 2009, URL http://www.dpg-verhandlungen.de/2009/dresden/agsoe.pdf

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