Abstract
In economics and financial theory, analysts use random walk and more general martingale techniques to model behavior of asset prices, in particular share prices on stock markets, currency exchange rates and commodity prices. This practice has its basis in the presumption that investors act rationally and without bias, and that at any moment they estimate the value of an asset based on future expectations. Under these conditions, all existing information affects the price, which changes only when new information comes out. By definition, new information appears randomly and influences the asset price randomly. Corresponding continuous time models are based on stochastic processes (this approach was initiated in the thesis of [4]), see, e.g., the books of [33] and [37] for historical and mathematical details.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Accardi, L. (1997). Urne e Camaleoni: Dialogo sulla realta, le leggi del caso e la teoria quantistica. Il Saggiatore, Rome.
Aerts, D. and Aerts, S. (1995). Applications of quantum statistics in psychological studies of decision-proceses. Foundations of Science 1, 1–12.
Arthur, W.B., Holland, J.H., LeBaron, B., Palmer, R. and Tayler, P. (1997). Asset pricing under endogenous expectations in an artificial stock market. In: Arthur WA, Lane D, and Durlauf SN (eds) The economy as evolving, complex system-2. Addison-Wesley, Redwood City.
Bachelier, L. (1890). Annales Scientifiques de L’Ecole Normale Suprieure de Paris 111–17, 21–121.
Barnett, W.A. and Serletis, A. (1998). Martingales, nonlinearity, and chaos. Dept. Economics, Washington University — St. Louis Working Papers.
Beja, A. and Goldman, M.B. (1980). On the dynamic behavior of prices in disequilibrium. Journal of Finances 35, 235–248.
Bohm, D. (1951). Quantum theory. Englewood Cliffs, New-Jersey, Prentice-Hall.
Bohm, D. and Hiley, B. (1993). The undivided universe: an ontological interpretation of quantum mechanics. Routledge and Kegan Paul, London.
Brock, W.A. and Sayers, C. (1988). Is business cycle characterized by deterministic chaos? Journal of Monetary Economics 22, 71–90.
Campbell, J.Y., Lo, A.W. and MacKinlay, A.C. (1997). The econometrics of financial markets. Princeton University Press, Princeton.
Choustova, O.A. (2001). Pilot wave quantum model for the stock market. http://www.arxiv.org/abs/quant-ph/0109122.
Choustova, O.A. (2004). Bohmian mechanics for financial processes. Jornal of Modern Optics 51, 1111.
Choustova, O.A. (2007). Quantum Bohmian model for financial market. Physica A: Statistical Physics and its Applications 374(1), 304–314.
Conte, E., Todarello, O., Federici, A., Vitiello, F., Lopane, M., Khrennikov, A.Yu and Zbilut, J.P. (2006). Some remarks on an experiment suggesting quantum-like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics. Chaos, Solitons and Fractals 31, 1076–1088.
DeCoster, G.P. and Mitchell, D.W. (1991). Journal of Business and Economic Statistics 9, 455–462.
Dirac, P.A.M. (1995). The Principles of Quantum Mechanics. Claredon Press, Oxford.
Fama, E.F. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work. Journal of Finance 25, 383–401.
Grib, A., Khrennikov, A., Parfionov, G. and Starkov, K. (2006). Quantum equilibria for macroscopic systems. Physics A: Mathematical and General 39, 8461–8475.
Haven, E. (2002). A Discussion on embedding the Black-Scholes option pricing model in a quantum physics setting. Physica A 304, 507–524.
Haven, E. (2003). A Black-Scholes Schrdinger Option Price: bit versus qubit. Physica A 324, 201–206.
Haven, E. (2004). The wave-equivalent of the Black-Scholes option price: an interpretation. Physica A 344, 142–145.
Haven, E. (2006). Bohmian mechanics in a macroscopic quantum system. In: Khrennikov AYu (ed) Foundations of Probability and Physics-3. American Institute of Physics, Melville, New York, 810, 330–340.
Heisenberg, W. (1930). Physical principles of quantum theory. Chicago Univ. Press, Chicago.
Hiley, B. (2001). From the Heisenberg picture to Bohm: a new perspective on active information and its relation to Shannon information. In: Khrennikov AYu (ed) Quantum Theory: Reconsideration of Foundations, Växjö University Press, Växjö, ser. Mathematical Modelling 10, 234–244.
Hiley, B. and Pylkkänen, P. (1997). Active information and cognitive science — A reply to Kieseppä. In: Pylkkänen P, Pylkkö P and Hautamäki A. (eds) Brain, mind and physics. IOS Press, Amsterdam, 121–134.
Holland, P. (1993). The quantum theory of motion. Cambridge Univ. Press, Cambridge.
Hsieh, D.A. (1991). Chaos and Nonlinear Dynamics: Application to Financial Markets. Journal of Finance 46, 1839–1850.
Khrennikov, A.Yu (2004). Information dynamics in cognitive, psychological and anomalous phenomena. Kluwer Academic, Dordreht.
Khrennikov, A.Yu (1999). (second edition, 2004) Interpretations of Probability. VSP Int. Sc. Publishers, Utrecht/Tokyo.
Khrennikov, A.Yu (2005). The principle of supplementarity: A contextual probabilistic viewpoint to complementarity, the interference of probabilities, and the incompatibility of variables in quantum mechanics. Foundations of Physics 35, 1655–1693.
Khrennikov, A.Yu (2006). Quantum-like brain: Interference of minds. BioSystems 84, 225–241.
Lux, T. (1998). The socio-economic dynamics of speculative markets: interacting agents, chaos, and fat tails of return distributions. Journal of Economic Behavior and Organization 33, 143–165.
Mantegna, R.N. and Stanley, H.E. (2000). Introduction to econophysics. Cambridge Univ. Press, Cambridge.
Piotrowski, E.W. and Sladkowski, J. (2001). Quantum-like approach to financial risk: quantum anthropic principle. http://www.arxiv.org/abs/quant-ph/0110046.
Samuelson, P.A. (1965). Rational theory of warrant pricing. Industrial Management Review 6, 41–61.
Segal, W. and Segal, I.E. (1998). The BlackScholes pricing formula in the quantum context. Proceedings of the National Academy of Sciences USA 95, 4072–4080.
Shiryaev, A.N. (1999). Essentials of Stochastic Finance: Facts, Models, Theory. World Scientific Publishing Company, Singapore.
Soros, J. (1987). The alchemy of finance. Reading of mind of the market. J. Wiley and Sons, Inc., New-York.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Italia
About this chapter
Cite this chapter
Choustova, O. (2009). Quantum-like Viewpoint on the Complexity and Randomness of the Financial Market. In: Faggini, M., Lux, T. (eds) Coping with the Complexity of Economics. New Economic Windows. Springer, Milano. https://doi.org/10.1007/978-88-470-1083-3_4
Download citation
DOI: https://doi.org/10.1007/978-88-470-1083-3_4
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-1082-6
Online ISBN: 978-88-470-1083-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)