IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v450y2016icp253-263.html
   My bibliography  Save this article

Application of quantum master equation for long-term prognosis of asset-prices

Author

Listed:
  • Khrennikova, Polina

Abstract

This study combines the disciplines of behavioral finance and an extension of econophysics, namely the concepts and mathematical structure of quantum physics. We apply the formalism of quantum theory to model the dynamics of some correlated financial assets, where the proposed model can be potentially applied for developing a long-term prognosis of asset price formation. At the informational level, the asset price states interact with each other by the means of a “financial bath”. The latter is composed of agents’ expectations about the future developments of asset prices on the finance market, as well as financially important information from mass-media, society, and politicians. One of the essential behavioral factors leading to the quantum-like dynamics of asset prices is the irrationality of agents’ expectations operating on the finance market. These expectations lead to a deeper type of uncertainty concerning the future price dynamics of the assets, than given by a classical probability theory, e.g., in the framework of the classical financial mathematics, which is based on the theory of stochastic processes. The quantum dimension of the uncertainty in price dynamics is expressed in the form of the price-states superposition and entanglement between the prices of the different financial assets. In our model, the resolution of this deep quantum uncertainty is mathematically captured with the aid of the quantum master equation (its quantum Markov approximation). We illustrate our model of preparation of a future asset price prognosis by a numerical simulation, involving two correlated assets. Their returns interact more intensively, than understood by a classical statistical correlation. The model predictions can be extended to more complex models to obtain price configuration for multiple assets and portfolios.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:253-263
    DOI: 10.1016/j.physa.2015.12.135
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116000091
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.12.135?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    2. Hawkins, Raymond J. & Aoki, Masanao & Roy Frieden, B., 2010. "Asymmetric information and macroeconomic dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3565-3571.
    3. Herbert A. Simon, 1955. "A Behavioral Model of Rational Choice," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 69(1), pages 99-118.
    4. Hiroshi Takahashi & Takao Terano, 2003. "Agent-Based Approach to Investors? Behavior and Asset Price Fluctuation in Financial Markets," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 6(3), pages 1-3.
    5. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    6. Shubik, Martin, 1999. "Quantum economics, uncertainty and the optimal grid size," Economics Letters, Elsevier, vol. 64(3), pages 277-278, September.
    7. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," PSE-Ecole d'économie de Paris (Postprint) halshs-00754332, HAL.
    8. Choustova, Olga Al., 2007. "Quantum Bohmian model for financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 304-314.
    9. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    10. Bailey,Roy E., 2005. "The Economics of Financial Markets," Cambridge Books, Cambridge University Press, number 9780521612807.
    11. Emmanuel Haven, 2008. "Private Information and the ‘Information Function’: A Survey of Possible Uses," Theory and Decision, Springer, vol. 64(2), pages 193-228, March.
    12. 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.
    13. Jérôme Busemeyer & Ariane Lambert-Mogiliansky & Zheng Wang, 2009. "Empirical Comparison of Markov and Quantum models of decision-making," Post-Print halshs-00754332, HAL.
    14. Gerd Gigerenzer & Reinhard Selten (ed.), 2002. "Bounded Rationality: The Adaptive Toolbox," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262571641, December.
    15. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    16. Herbert A. Simon, 1991. "Bounded Rationality and Organizational Learning," Organization Science, INFORMS, vol. 2(1), pages 125-134, February.
    17. Schinckus, Christophe, 2009. "Economic uncertainty and econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4415-4423.
    18. Shefrin, Hersh & Statman, Meir, 1994. "Behavioral Capital Asset Pricing Theory," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(3), pages 323-349, September.
    19. Ehtibar N Dzhafarov & Janne V Kujala, 2013. "All-Possible-Couplings Approach to Measuring Probabilistic Context," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-9, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bagarello, F. & Di Salvo, R. & Gargano, F. & Oliveri, F., 2018. "(H,ρ)-induced dynamics and large time behaviors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 355-373.
    2. Gzyl, Henryk & ter Horst, Enrique & Molina, Germán, 2019. "A model-free, non-parametric method for density determination, with application to asset returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 210-221.
    3. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    4. Di Salvo, Rosa & Gorgone, Matteo & Oliveri, Francesco, 2020. "Generalized Hamiltonian for a two-mode fermionic model and asymptotic equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    5. Khrennikova, Polina & Patra, Sudip, 2019. "Asset trading under non-classical ambiguity and heterogeneous beliefs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 562-577.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Khrennikova, Polina & Patra, Sudip, 2019. "Asset trading under non-classical ambiguity and heterogeneous beliefs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 562-577.
    2. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    3. Monica Martinez-Blasco & Vanessa Serrano & Francesc Prior & Jordi Cuadros, 2023. "Analysis of an event study using the Fama–French five-factor model: teaching approaches including spreadsheets and the R programming language," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-34, December.
    4. Giuseppe Pernagallo & Benedetto Torrisi, 2020. "A theory of information overload applied to perfectly efficient financial markets," Review of Behavioral Finance, Emerald Group Publishing Limited, vol. 14(2), pages 223-236, October.
    5. Linnenluecke, Martina K. & Chen, Xiaoyan & Ling, Xin & Smith, Tom & Zhu, Yushu, 2017. "Research in finance: A review of influential publications and a research agenda," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 188-199.
    6. Kentaro Imajo & Kentaro Minami & Katsuya Ito & Kei Nakagawa, 2020. "Deep Portfolio Optimization via Distributional Prediction of Residual Factors," Papers 2012.07245, arXiv.org.
    7. Hervé, Fabrice & Zouaoui, Mohamed & Belvaux, Bertrand, 2019. "Noise traders and smart money: Evidence from online searches," Economic Modelling, Elsevier, vol. 83(C), pages 141-149.
    8. Lu Zhang, 2019. "Q-factors and Investment CAPM," NBER Working Papers 26538, National Bureau of Economic Research, Inc.
    9. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    10. Daniel, Kent & Hirshleifer, David & Teoh, Siew Hong, 2002. "Investor psychology in capital markets: evidence and policy implications," Journal of Monetary Economics, Elsevier, vol. 49(1), pages 139-209, January.
    11. Polk, Christopher & Lou, Dong & Huang, Shiyang, 2016. "The Booms and Busts of Beta Arbitrage," CEPR Discussion Papers 11531, C.E.P.R. Discussion Papers.
    12. Nicolau, Juan Luis & Sharma, Abhinav, 2022. "A review of research into drivers of firm value through event studies in tourism and hospitality: Launching the Annals of Tourism Research curated collection on drivers of firm value through event stu," Annals of Tourism Research, Elsevier, vol. 95(C).
    13. Yundan Guo & Li Shen, 2023. "Commercial Retirement FOFs in China: Investment and Persistence Performance Analysis," Sustainability, MDPI, vol. 15(18), pages 1-22, September.
    14. Jun, So Young & Kim, Dong Sung & Jung, Suk Yoon & Jun, Sang Gyung & Kim, Jong Woo, 2022. "Stock investment strategy combining earnings power index and machine learning," International Journal of Accounting Information Systems, Elsevier, vol. 47(C).
    15. Ailie Charteris & Mukashema Rwishema & Tafadzwa-Hidah Chidede, 2018. "Asset Pricing and Momentum: A South African Perspective," Journal of African Business, Taylor & Francis Journals, vol. 19(1), pages 62-85, January.
    16. Kent Daniel & David Hirshleifer, 2015. "Overconfident Investors, Predictable Returns, and Excessive Trading," Journal of Economic Perspectives, American Economic Association, vol. 29(4), pages 61-88, Fall.
    17. Martin Rohleder & Dominik Schulte & Janik Syryca & Marco Wilkens, 2018. "Mutual Fund Stock†Picking Skill: New Evidence from Valuation†versus Liquidity†Motivated Trading," Financial Management, Financial Management Association International, vol. 47(2), pages 309-347, June.
    18. Jennie Bai & Turan G. Bali & Quan Wen, 2019. "Is There a Risk-Return Tradeoff in the Corporate Bond Market? Time-Series and Cross-Sectional Evidence," NBER Working Papers 25995, National Bureau of Economic Research, Inc.
    19. Thomas Holtfort, 2019. "From standard to evolutionary finance: a literature survey," Management Review Quarterly, Springer, vol. 69(2), pages 207-232, June.
    20. Levon Goukasian & Emily J. Huang & Qingzhong Ma & Wei Zhang, 2019. "Are Acquirers Efficiently Priced? Evidence from Subsequent Earnings Announcements," Review of Economics & Finance, Better Advances Press, Canada, vol. 16, pages 15-30, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:450:y:2016:i:c:p:253-263. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.