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On the strategic origin of Brownian motion in finance

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  • DE MEYER, Bernard
  • MOUSSA SALEY, Hadiza

Abstract

This paper is concerned with the stategic 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 [infinite] , 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

  • DE MEYER, Bernard & MOUSSA SALEY, Hadiza, 2000. "On the strategic origin of Brownian motion in finance," LIDAM Discussion Papers CORE 2000057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2000057
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    1. Mertens, Jean-François & ZAMIR, Shmuel, 1976. "The normal distribution and repeated games," LIDAM Reprints CORE 312, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    3. Riccardo Calcagno & Stefano Lovo, 2006. "Bid-Ask Price Competition with Asymmetric Information between Market-Makers," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(2), pages 329-355.
    4. MERTENS, Jean-François & ZAMIR, Shmuel, 1995. "Incomplete Information Games and the Normal Distribution," LIDAM Discussion Papers CORE 1995020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. CALCAGNO, Riccardo & LOVO, Stefano M., 1998. "Bid-ask price competition with asymmetric information between market makers," LIDAM Discussion Papers CORE 1998016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
    7. Calcagno, Riccardo & Lovo, Stefano M., 1998. "Bid-Ask Price Competition with Asymmetric Information between Market Makers," LIDAM Discussion Papers IRES 1998012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
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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. 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.
    3. Hörner, Johannes & Lovo, Stefano & Tomala, Tristan, 2018. "Belief-free price formation," Journal of Financial Economics, Elsevier, vol. 127(2), pages 342-365.
    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. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    7. Bernard De Meyer, 2007. "Price Dynamics on a Stock Market with Asymmetric Information," Levine's Bibliography 321307000000000841, UCLA Department of Economics.
    8. 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.
    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. 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.
    11. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.
    12. 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.
    13. 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.
    14. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    15. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02383135, HAL.
    16. 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.
    17. 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.
    18. Bernard de Meyer & Moussa Dabo, 2019. "The CMMV Pricing Model in Practice," Post-Print halshs-02383135, HAL.
    19. 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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