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On the strategic origin of Brownian motion in finance

Author

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  • Hadiza Moussa Saley

    (Institut Elie Cartan, Université Nancy 1 , B.P. 239, 54506 Vandoeuvre les Nancy Cedex.)

  • Bernard De Meyer

    (CERMSEM, Université Paris 1 , Maison des sciences économiques, 106-112, Bd de l'Hopital, 75647 Paris cedex 13.)

Abstract

This paper is concerned with the strategic use of a private information on the stock market. A repeated auction model is used to analyze the evolution of the price system on a market with asymmetric information. The model turns out to be a zero-sum repeated game with one-sided information, as introduced by Aumann and Maschler. The stochastic evolution of the price system can be explicitly computed in the n times repeated case. As n grows to \infty, this process tends to a continuous time martingale related to a Brownian Motion. This paper provides in this way an endogenous justification for the appearance of Brownian Motion in Finance theory.

Suggested Citation

  • Hadiza Moussa Saley & Bernard De Meyer, 2003. "On the strategic origin of Brownian motion in finance," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(2), pages 285-319.
    • Handle: RePEc:spr:jogath:v:31:y:2003:i:2:p:285-319
    Note: Received: February 2002
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. De Meyer, Bernard, 2010. "Price dynamics on a stock market with asymmetric information," Games and Economic Behavior, Elsevier, vol. 69(1), pages 42-71, May.
    3. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    4. Jovanovic, Franck & Andreadakis, Stelios & Schinckus, Christophe, 2016. "Efficient market hypothesis and fraud on the market theory a new perspective for class actions," Research in International Business and Finance, Elsevier, vol. 38(C), pages 177-190.
    5. Bernard de Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Post-Print halshs-00390625, HAL.
    6. Chu, Yinxiao, 2024. "Ambiguity and informativeness of (non-)trading," Games and Economic Behavior, Elsevier, vol. 148(C), pages 367-384.
    7. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    8. Bernard De Meyer, 2007. "Price Dynamics on a Stock Market with Asymmetric Information," Levine's Bibliography 321307000000000841, UCLA Department of Economics.
    9. Johannes Horner & Julian Jamison, 2006. "Private Information in Sequential Common-Value Auctions," Discussion Papers 1422, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    10. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.
    11. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02383135, HAL.
    12. Miles Gietzmann & Adam Ostaszewski, 2014. "Why managers with low forecast precision select high disclosure intensity: an equilibrium analysis," Review of Quantitative Finance and Accounting, Springer, vol. 43(1), pages 121-153, July.
    13. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2018. "Belief-free price formation," Journal of Financial Economics, Elsevier, vol. 127(2), pages 342-365.
    14. Marina Sandomirskaia, 2017. "Repeated Bidding Games with Incomplete Information and Bounded Values: On the Exponential Speed of Convergence," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-7, March.
    15. Bernard De Meyer & Gaëtan Fournier, 2015. "Price dynamics on a risk averse market with asymmetric information," Documents de travail du Centre d'Economie de la Sorbonne 15054, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    16. Domansky, V. & Kreps, V., 2011. "Game Theoretic Bidding Model: Strategic Aspects of Price Formation at Stock Markets," Journal of the New Economic Association, New Economic Association, issue 11, pages 39-62.
    17. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    18. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    19. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Post-Print halshs-02383135, HAL.
    20. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2010. "Evaluating Information in Zero-Sum Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 35(4), pages 851-863, November.

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