Classical and Quantum-Like Randomness and the Financial Market
The financial market is a complex dynamical system and, since the publication of the thesis of , there were performed numerous studies devoted to various aspects of random description of financial processes . At the first stage of investigations Brownian motion was used to describe randomness of the financial market. This model provided a rather good approximation of some financial processes. However, later it became evident that the diversity of financial stochastic processes could not be reduced to Brownian motion. The next step was consideration of functionals of Brownian motion, especially, geometric Brownian motion . Later there were considered other types of stochastic processes , in particular, general Levy processes.
KeywordsOption Price Quantum Randomness Quantum Formalism Bohmian Mechanic Classical Probabilistic Model
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- 1.Bachelier L. (1890) Ann. Sc. lcole Normale Superiere 111–17: 21–121.Google Scholar
- 2.Bell J.S. (1987) Speakable and unspeakable in quantum mechanics. Cambridge Univ. Press, Cambridge.Google Scholar
- 3.Choustova O. (2001) Pilot wave quantum model for the stock market. http://www.arxiv.org/abs/quant-ph/0109122.Google Scholar
- 6.d’Espagnat B. (1995) Veiled Reality. An analysis of present-day quantum mechanical concepts. Addison-Wesley.Google Scholar
- 10.Haven E. (2003) An ‘h-Brownian motion’ of stochastic option prices, Physica A 344: 151–155.Google Scholar
- 11.Haven E. (2006) Bohmian mechanics in a macroscopic quantum system. In: Adenier G, Khrennikov AYu, and Nieuwenhuizen T. (eds) Foundations of Probability and Physics-3 810: 330–340. American Institute of Physics, Melville, New York.Google Scholar
- 12.Khrennikov A. Yu (1999) Interpretations of Probability. VSP Int. Sc. Publishers, Utrecht/Tokyo (second edition-2004).Google Scholar
- 14.Kolmogoroff A.N. (1933) Grundbegriffe der Wahrscheinlichkeitsrechnung. Springer Verlag, Berlin; reprinted: Kolmogorov A.N. (1956) Foundations of the Probability Theory. Chelsea Publ. Comp., New York.Google Scholar
- 15.Mandelbrot B., Hudson R. (2004) The (mis)behavior of markets. Basic Books Publication.Google Scholar
- 17.Piotrowski E.W., Sladkowski J. (2001) Quantum-like approach to financial risk: quantum anthropic principle. http://www.arxiv.org/abs/quantph/0110046.Google Scholar
- 18.Samuelson P.A. (1965) Industrial Management Review 6, 41.Google Scholar