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Quantum Bohmian model for financial market

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  • Choustova, Olga Al.

Abstract

We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. The Hamiltonian formalism on the price/price-change phase space describes the classical-like evolution of prices. This classical dynamics of prices is determined by “hard” conditions (natural resources, industrial production, services and so on). These conditions are mathematically described by the classical financial potential V(q), where q=(q1,…,qn) is the vector of prices of various shares. But the information exchange and market psychology play important (and sometimes determining) role in price dynamics. We propose to describe such behavioral financial factors by using the pilot wave (Bohmian) model of quantum mechanics. The theory of financial behavioral waves takes into account the market psychology. The real trajectories of prices are determined (through the financial analogue of the second Newton law) by two financial potentials: classical-like V(q) (“hard” market conditions) and quantum-like U(q) (behavioral market conditions).

Suggested Citation

  • Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:1:p:304-314
    DOI: 10.1016/j.physa.2006.07.029
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    References listed on IDEAS

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    1. Haven, Emmanuel, 2003. "A Black-Scholes Schrödinger option price: ‘bit’ versus ‘qubit’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 201-206.
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    Cited by:

    1. Ashtiani, Mehrdad & Azgomi, Mohammad Abdollahi, 2015. "A survey of quantum-like approaches to decision making and cognition," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 49-80.
    2. 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.
    3. J. S. Ardenghi, 2023. "Modeling amortization systems with vector spaces," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(1), pages 1-12, January.
    4. Raymond J. Hawkins & B. Roy Frieden, 2012. "Asymmetric Information and Quantization in Financial Economics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, December.
    5. Ardenghi, J.S., 2021. "Quantum credit loans," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    6. Khrennikova, Polina, 2016. "Application of quantum master equation for long-term prognosis of asset-prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 253-263.
    7. Kumar, Sushil & Kumar, Sunil & Kumar, Pawan, 2020. "Diffusion entropy analysis and random matrix analysis of the Indian stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    8. Anantya Bhatnagar & Dimitri D. Vvedensky, 2022. "Quantum effects in an expanded Black–Scholes model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(8), pages 1-12, August.
    9. Cotfas, Liviu-Adrian, 2013. "A finite-dimensional quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(2), pages 371-380.

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