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Quantum diffusion of prices and profits

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  • Edward W. Piotrowski
  • Jan Sladkowski

Abstract

We discuss the time evolution of quotation of stocks and commodities and show that quantum-like correction to the orthodox Bachelier model may be important. Our analysis shows that traders act as a sort of (quantum) tomograph and their strategies can be reproduced from the corresponding Wigner functions. The proposed interpretation of the chaotic movement of market prices imply that Orstein-Uhlenbeck corrections to the Bachelier model should qualitatively matter for large $\gamma$ scales. We also propose a solution to the currency preference paradox.

Suggested Citation

  • Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum diffusion of prices and profits," Departmental Working Papers 12, University of Bialtystok, Department of Theoretical Physics.
    • Handle: RePEc:sla:eakjkl:12
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    References listed on IDEAS

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    1. Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2003. "Interference of quantum market strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 516-528.
    2. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    3. Piotrowski, Edward W. & Sładkowski, Jan, 2002. "Quantum bargaining games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 308(1), pages 391-401.
    4. Edward W. Piotrowski & Jan Sladkowski, "undated". "The Thermodynamics of Portfolios," Departmental Working Papers 2, University of Bialtystok, Department of Theoretical Physics.
    5. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum-Like Approach to Financial Risk: Quantum Anthropic Principle," Departmental Working Papers 8, University of Bialtystok, Department of Theoretical Physics.
    6. Piotrowski, E.W. & Sładkowski, J., 2003. "The merchandising mathematician model: profit intensities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 496-504.
    7. Edward W. Piotrowski & Jan Sladkowski, "undated". "The Merchandising Mathematician Model. Stochastic Demand and Supply," Departmental Working Papers 1, University of Bialtystok, Department of Theoretical Physics.
    8. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845.
    9. Stanley, H.Eugene & Nunes Amaral, Luis A. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2001. "Quantifying economic fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 302(1), pages 126-137.
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    Citations

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    Cited by:

    1. Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    2. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    3. Piotrowski, Edward W. & Schroeder, Małgorzata & Zambrzycka, Anna, 2006. "Quantum extension of European option pricing based on the Ornstein–Uhlenbeck process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 176-182.
    4. Bagarello, F. & Haven, E., 2014. "The role of information in a two-traders market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 224-233.
    5. Will Hicks, 2019. "Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion," Papers 1911.11475, arXiv.org, revised Jan 2020.
    6. Pineiro-Chousa, Juan & Vizcaíno-González, Marcos, 2016. "A quantum derivation of a reputational risk premium," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 304-309.

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