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Towards a formalization of a two traders market with information exchange

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  • F. Bagarello
  • E. Haven

Abstract

This paper shows that Hamiltonians and operators can also be put to good use even in contexts which are not purely physics based. Consider the world of finance. The work presented here {models a two traders system with information exchange with the help of four fundamental operators: cash and share operators; a portfolio operator and an operator reflecting the loss of information. An information Hamiltonian is considered and an additional Hamiltonian is presented which reflects the dynamics of selling/buying shares between traders. An important result of the paper is that when the information Hamiltonian is zero, portfolio operators commute with the Hamiltonian and this suggests that the dynamics are really due to the information. Under the assumption that the interaction and information terms in the Hamiltonian have similar strength, a perturbation scheme is considered on the interaction parameter. Contrary to intuition, the paper shows that up to a second order in the interaction parameter, a key factor in the computation of the portfolios of traders will be the initial values of the loss of information (rather than the initial conditions on the cash and shares). Finally, the paper shows that a natural outcome from the inequality of the variation of the portfolio of trader one versus the variation of the portfolio of trader two, begs for the introduction of `good' and `bad' information. It is shown that `good' information is related to the reservoirs (where an infinite set of bosonic operators are used) which model rumors/news and external facts, whilst `bad' information is associated with a set of two modes bosonic operators.

Suggested Citation

  • F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    • Handle: RePEc:arx:papers:1412.8725
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    References listed on IDEAS

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    1. Bagarello, F., 2007. "Stock markets and quantum dynamics: A second quantized description," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 283-302.
    2. Schaden, Martin, 2002. "Quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 511-538.
    3. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    4. Piotrowski, Edward W. & Sładkowski, Jan, 2007. "Geometry of financial markets—Towards information theory model of markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 228-234.
    5. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    6. Fabio Bagarello, 2009. "A quantum statistical approach to simplified stock markets," Papers 0907.2531, arXiv.org.
    7. 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.
    8. Martin Schaden, 2002. "Quantum Finance," Papers physics/0203006, arXiv.org, revised Aug 2002.
    9. Bouchaud, Jean-Philippe, 2002. "An introduction to statistical finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 238-251.
    10. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
    11. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    12. Bagarello, F., 2009. "A quantum statistical approach to simplified stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(20), pages 4397-4406.
    13. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
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    Cited by:

    1. Bagarello, F. & Haven, E., 2016. "First results on applying a non-linear effect formalism to alliances between political parties and buy and sell dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 403-414.

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