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Asymmetric information and quantization in financial economics. (English) Zbl 1258.91129
Summary: We show how a quantum formulation of financial economics can be derived from asymmetries with respect to Fisher information. Our approach leverages statistical derivations of quantum mechanics which provide a natural basis for interpreting quantum formulations of social sciences generally and of economics in particular. We illustrate the utility of this approach by deriving arbitrage-free derivative-security dynamics.

MSC:
91B44 Economics of information
91B69 Heterogeneous agent models
81P68 Quantum computation
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[1] J. E. Stiglitz, “The contributions of the economics of information to twentieth century economics,” Quarterly Journal of Economics, vol. 115, no. 4, pp. 1441-1478, 2000. · Zbl 0970.91515 · doi:10.1162/003355300555015
[2] J. E. Stiglitz, “Information and the change in the paradigm in economics: part 1,” The American Economist, vol. 47, pp. 6-26, 2003.
[3] J. E. Stiglitz, “Information and the change in the paradigm in economics: part 2,” The American Economist, vol. 48, pp. 17-49, 2004.
[4] P. Mirowski, More Heat Than Light: Economics as Social Physics, Physics as Nature’s Economics. Historical Perspectives on Modern Economics, Cambridge University Press, New York, NY, USA, 1991.
[5] A. Yu. Khrennikov, Ubiquitous Quantum Structure, Springer, Berlin, Germany, 2010. · Zbl 1188.91002
[6] M. Reginatto, “Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum Fisher information,” Physical Review A, vol. 58, no. 3, pp. 1775-1778, 1998.
[7] R. A. Fisher and K. Mather, “The inheritance of style length in Lythrum salicaria,” Annals of Eugenics, vol. 12, no. 1, pp. 1-32, 1943.
[8] B. R. Frieden, Physics from Fisher information: A Unification, Cambridge University Press, Cambridge, UK, 1998. · Zbl 0998.81512 · doi:10.1017/CBO9780511622670
[9] B. R. Frieden, Science from Fisher Information: A Unification, Cambridge University Press, Cambridge, UK, 2004. · Zbl 1079.81013 · doi:10.1017/CBO9780511616907
[10] B. R. Frieden, R. J. Hawkins, and J. L. D’Anna, “Financial economics from Fisher information,” in Exploratory Data Analysis Using Fisher Information, B. R. Frieden and R. A. Gatenby, Eds., pp. 42-73, Springer, London, UK, 2007.
[11] B. R. Frieden and R. J. Hawkins, “Asymmetric information and economics,” Physica A, vol. 389, no. 2, pp. 287-295, 2010. · doi:10.1016/j.physa.2009.09.028
[12] R. J. Hawkins and B. R. Frieden, “Fisher information and equilibrium distributions in econophysics,” Physics Letters A, vol. 322, no. 1-2, pp. 126-130, 2004. · Zbl 1118.81362 · doi:10.1016/j.physleta.2003.12.054
[13] R. J. Hawkins, B. R. Frieden, and J. L. D’Anna, “Ab initio yield curve dynamics,” Physics Letters Section A, vol. 344, no. 5, pp. 317-323, 2005. · Zbl 1194.91152 · doi:10.1016/j.physleta.2005.06.079
[14] R. J. Hawkins, M. Aoki, and B. R. Frieden, “Asymmetric information and macroeconomic dynamics,” Physica A, vol. 389, no. 17, pp. 3565-3571, 2010. · doi:10.1016/j.physa.2010.04.032
[15] R. J. Hawkins and B. R. Frieden, “Econophysics,” in Science from Fisher Information: A Unification, B. R. Frieden, Ed., chapter 3, Cambridge University Press, Cambridge, UK, 2004. · Zbl 1118.81362
[16] A. Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, Wiley Finance. John Wiley & Sons, New York, NY , USA, 2nd edition, 2002.
[17] J. L. Synge, “Classical dynamics,” in Handbuch der Physik, pp. 1-225, Springer, Berlin, Germany, 1960. · doi:10.1007/BF01325785
[18] H. Ishio and E. Haven, “Information in asset pricing: a wave function approach,” Annalen der Physik, vol. 18, no. 1, pp. 33-44, 2009. · Zbl 1157.91338 · doi:10.1002/andp.200810333
[19] E. Haven, “Pilot-wave Theory and financial option pricing,” International Journal of Theoretical Physics, vol. 44, no. 11, pp. 1957-1962, 2005. · Zbl 1094.81015 · doi:10.1007/s10773-005-8973-3
[20] E. Haven, “Elementary quantum mechanical principles and social science: is there a connection?” Romanian Journal of Economic Forecasting, vol. 9, no. 1, pp. 41-58, 2008.
[21] E. Haven, “The variation of financial arbitrage via the use of an information wave function,” International Journal of Theoretical Physics, vol. 47, no. 1, pp. 193-199, 2008. · Zbl 1278.81054 · doi:10.1007/s10773-007-9506-z
[22] E. Haven, “Private information and the “information function”: a survey of possible uses,” Theory and Decision, vol. 64, no. 2-3, pp. 193-228, 2008. · Zbl 1136.91438 · doi:10.1007/s11238-007-9054-2
[23] E. Haven, “The Blackwell and Dubins theorem and Rényi’s amount of information measure: some applications,” Acta Applicandae Mathematicae, vol. 109, no. 3, pp. 743-757, 2010. · Zbl 1193.94045 · doi:10.1007/s10440-008-9343-y
[24] O. Al. Choustova, “Quantum Bohmian model for financial market,” Physica A, vol. 374, no. 1, pp. 304-314, 2007. · Zbl 1143.91331 · doi:10.1016/j.physa.2006.07.029
[25] O. A. Shustova, “Quantum modeling of the nonlinear dynamics of stock prices: the Bohmian approach,” Rossiĭskaya Akademiya Nauk, vol. 152, no. 2, pp. 405-415, 2007. · Zbl 1186.91211 · doi:10.1007/s11232-007-0104-2
[26] O. Choustova, “Application of Bohmian mechanics to dynamics of prices of shares: stochastic model of Bohm-Vigier from properties of price trajectories,” International Journal of Theoretical Physics, vol. 47, no. 1, pp. 252-260, 2008. · Zbl 1133.91500 · doi:10.1007/s10773-007-9469-0
[27] O. Choustova, “Quantum probability and financial market,” Information Sciences, vol. 179, no. 5, pp. 478-484, 2009. · Zbl 1182.91133 · doi:10.1016/j.ins.2008.07.001
[28] O. Choustova, “Quantum-like viewpoint on the complexity and randomness of the financial market,” in Coping With the Complexity of Economics, New Economic Windows, F. Petri and F. Hahn, Eds., Springer, Milan, Italy, 2009. · Zbl 1182.91133
[29] A. Khrennivov, “Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social, and anomalous phenomena,” Foundations of Physics, vol. 29, no. 7, pp. 1065-1098, 1999. · doi:10.1023/A:1018885632116
[30] A. Yu. Khrennikov, “Quantum-psychological model of the stock market,” Problems and Perspectives of Management, vol. 1, pp. 136-148, 2003.
[31] F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, pp. 637-654, 1973. · Zbl 1092.91524
[32] R. C. Merton, “On the pricing of corporate debt: the risk structure of interest rates,” Journal of Finance, vol. 29, no. 2, pp. 449-470, 1974.
[33] F. Black and J. C. Cox, “Valuing corporate securities: some effects of bond indenture provisions,” Journal of Finance, vol. 31, no. 2, pp. 351-367, 1976.
[34] E. Madelung, “Quantentheorie in hydrodynamischer form,” Zeitschrift für Physik, vol. 40, no. 3-4, pp. 322-326, 1927. · JFM 52.0969.06 · doi:10.1007/BF01400372
[35] E. Nelson, “Derivation of the Schrödinger equation from Newtonian mechanics,” Physical Review, vol. 150, no. 4, pp. 1079-1085, 1966. · doi:10.1103/PhysRev.150.1079
[36] E. Nelson, Dynamical Theories of Brownian Motion, Princeton University Press, Princeton, NJ, USA, 1967. · Zbl 0165.58502
[37] H. Cramér, Mathematical Methods of Statistics, vol. 9 of Princeton Mathematical Series, Princeton University Press, Princeton, NJ, USA, 1946. · Zbl 0063.01014
[38] C. Radhakrishna Rao, “Information and the accuracy attainable in the estimation of statistical parameters,” Bulletin of the Calcutta Mathematical Society, vol. 37, pp. 81-91, 1945. · Zbl 0063.06420
[39] L. D. Landau and E. M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, vol. 3 of Course of Theoretical Physics, Pergamon Press, New York, NY, USA, 3rd edition, 1977. · Zbl 0178.57901
[40] D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables. I,” Physical Review, vol. 85, pp. 166-179, 1952. · Zbl 0046.21004 · doi:10.1103/PhysRev.85.166
[41] D. Bohm, “A suggested interpretation of the quantum theory in terms of “hidden” variables. II,” Physical Review, vol. 85, pp. 180-193, 1952. · Zbl 0046.21004 · doi:10.1103/PhysRev.85.166
[42] H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientific, River Edge, NJ, USA, 5th edition, 2009. · Zbl 1169.81001
[43] R. Wright, “Statistical structures underlying quantum mechanics and social science,” International Journal of Theoretical Physics, vol. 46, no. 8, pp. 2026-2045, 2007. · Zbl 1128.81003 · doi:10.1007/s10773-006-9297-7
[44] J.-P. Bouchaud and M. Potters, Theory of Financial Risks, Cambridge University Press, Cambridge, UK, 2nd edition, 2003. · Zbl 1194.91008
[45] J. Voit, The Statistical Mechanics of Financial Markets, Texts and Monographs in Physics, Springer, Berlin, Germany, 3rd edition, 2005. · Zbl 1107.91055
[46] B. E. Baaquie, Quantum Finance, Cambridge University Press, Cambridge, UK, 2004. · Zbl 1096.91021 · doi:10.1017/CBO9780511617577
[47] B. E. Baaquie, Interest Rates and Coupon Bonds in Quantum Finance, Cambridge University Press, Cambridge, UK, 2010. · Zbl 1179.91002
[48] K. N. Ilinski, Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing, John Wiley & Sons, Chichester, UK, 2001.
[49] J. M. Keynes, The General Theory of Employment, Interest, and Money, Harvest/Harcourt, San Diego, Calif, USA, 1936.
[50] J. M. Keynes, “The general Theory of employment,” Quarterly Journal of Economics, vol. 51, pp. 209-223, 1937.
[51] F. H. Knight, Risk, Uncertainty and Profit. Reprints of Economic Classics, Augustus M. Kelley, New York, NY, USA, 1921.
[52] M. Aoki and H. Yoshikawa, Reconstructing Macroeconomics: A Perspective from Statistical Physics and Combinatorial Stochastic Processes. Japan-U.S. Center UFJ Bank Monographs on International Financial Markets, Cambridge University Press, New York, NY, USA, 2007.
[53] D. K. Foley, “A statistical equilibrium Theory of markets,” Journal of Economic Theory, vol. 62, pp. 321-345, 1994. · Zbl 0799.90022 · doi:10.1006/jeth.1994.1018
[54] D. K. Foley, “Statistical equilibrium in economics: method, interpretation, and an example,” in General Equilibrium: Problems and Prospects, Routledge Siena Studies in Political Economy, F. Petri and F. Hahn, Eds., chapter 4, Taylor & Francis, London, UK, 2002.
[55] T. Lux, “Applications of statistical physics in finance and economics,” in Handbook of Research on Complexity, J. B. Rosser Jr. and K. L. Cramer, Eds., chapter 9, Edward Elgar, Cheltenham, UK, 2009.
[56] V. M. Yakovenko and J. B. Rosser Jr., “Colloquium: statistical mechanics of money, wealth, and income,” Reviews of Modern Physics, vol. 81, no. 4, pp. 1703-1725, 2009. · doi:10.1103/RevModPhys.81.1703
[57] R. Balian, “Information Theory and statistical entropy,” in From Microphysics to Macrophysics: Methods and Applications of Statistical Physics, vol. 1, chapter 3, Springer, New York, NY, USA, 1982. · Zbl 1131.82302
[58] A. Ben-Naim, A Farewell to Entropy: Statistical Thermodynamics Based on Information, World Scientific, Singapore, 2008. · Zbl 1171.82001
[59] H. Haken, Information and Self-Organization, Springer Series in Synergetics, Springer, Berlin, Germany, 2nd edition, 2000. · Zbl 0945.93004
[60] E. T. Jaynes, Papers on Probability, Statistics and Statistical Physics, vol. 158 of Synthese Library, edited volume of Jaynes’ work edited by R. D. Rosenkrantz, D. Reidel, Dordrecht, The Netherlands, 1983. · Zbl 0501.01026
[61] A. Katz, Principles of Statistical Mechanics: The Information Theory Approach, W. H. Freeman, San Francisco, Calif, USA, 1967.
[62] D. Sornette, Critical Phenomena in Natural Sciences, Springer Series in Synergetics, Springer, Berlin, Germany, 2000. · Zbl 0977.82001
[63] U. Klein, “The statistical origins of quantum mechanics,” Physics Research International, vol. 2010, Article ID 808424, 18 pages, 2010. · doi:10.1155/2010/808424
[64] J. S. Fons, “Using default rates to model the term structure of credit risk,” Financial Analysts Journal, vol. 50, pp. 25-32, 1994.
[65] M. Ausloos and K. Ivanova, “Mechanistic approach to generalized technical analysis of share prices and stock market indices,” European Physical Journal B, vol. 27, no. 2, pp. 177-187, 2002.
[66] J. Karpoff, “The relation between price changes and trading volume: a survey,” Journal of Financial and Quantitative Analysis, vol. 22, no. 1, pp. 109-126, 1987.
[67] L. Blume, D. Easley, and M. O’Hara, “Market statistics and technical analysis: the role of volume,” Journal of Finance, vol. 49, no. 1, pp. 153-181, 1994.
[68] C. M. C. Lee and B. Swaminathan, “Price momentum and trading volume,” Journal of Finance, vol. 55, no. 5, pp. 2017-2069, 2000.
[69] L. S. Schulman, Techniques and Applications of Path Integration, John Wiley & Sons, New York, NY, USA, 1981. · Zbl 1141.28009
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