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Subjective modelling of supply and demand—the minimum of Fisher information solution

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  • Piotrowski, Edward W.
  • Sładkowski, Jan
  • Syska, Jacek

Abstract

Two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand/supply profiles if one considers closing of a position as a random process. We would like to present the analysis of a subjectivity in such trading models. In our model, the trader gets the maximal profit intensity when the probability of transaction is ∼0.5853. We also present a comparison with the model based on the Maximum of Entropy Principle. To the best of our knowledge, this is one of the first analyses that show a concrete situation in which trader profit optimal value is in the class of price-negotiating algorithms (strategies) resulting in non-monotonic demand (supply) curves of the Rest of the World (a collective opponent). Our model suggests that there might be a new class of rational trader strategies that (almost) neglects the supply–demand profile of the market. This class emerges when one tries to minimize the information that strategies reveal.

Suggested Citation

  • Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2010. "Subjective modelling of supply and demand—the minimum of Fisher information solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4904-4912.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:21:p:4904-4912
    DOI: 10.1016/j.physa.2010.06.062
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    Citations

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    Cited by:

    1. Bednarek, Ilona & Makowski, Marcin & Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2015. "Generalization of the Aoki–Yoshikawa sectoral productivity model based on extreme physical information principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 161-172.
    2. Marcin Makowski & Edward W. Piotrowski & Piotr Frk{a}ckiewicz & Marek Szopa, 2022. "Transactional Interpretation for the Principle of Minimum Fisher Information," Papers 2203.12607, arXiv.org.
    3. Jankowski, Robert & Makowski, Marcin & Piotrowski, Edward W., 2014. "Parameter estimation by fixed point of function of information processing intensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 558-563.
    4. Makowski, Marcin & Piotrowski, Edward W. & Sładkowski, Jan & Syska, Jacek, 2017. "Profit intensity and cases of non-compliance with the law of demand/supply," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 53-59.
    5. Domino, Krzysztof, 2012. "The use of the Hurst exponent to investigate the global maximum of the Warsaw Stock Exchange WIG20 index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 156-169.
    6. Marcin Makowski & Edward W. Piotrowski & Jan S{l}adkowski & Jacek Syska, 2015. "The intensity of the random variable intercept in the sector of negative probabilities," Papers 1503.07495, arXiv.org.

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