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On the strategic origin of Brownian motion in finance

Author

Listed:
  • 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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    References listed on IDEAS

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    1. MERTENS, Jean-François & ZAMIR, Shmuel, 1995. "Incomplete Information Games and the Normal Distribution," CORE Discussion Papers 1995020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. CALCAGNO, Riccardo & LOVO, Stefano M., 1998. "Bid-ask price competition with asymmetric information between market makers," CORE Discussion Papers 1998016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, May.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, May.
    4. Calcagno, Riccardo & Lovo, Stefano M., 1998. "Bid-Ask Price Competition with Asymmetric Information between Market Makers," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1998012, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
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    Citations

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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. repec:eee:jfinec:v:127:y:2018:i:2:p:342-365 is not listed on IDEAS
    3. repec:wsi:igtrxx:v:19:y:2017:i:01:n:s0219198916500171 is not listed on IDEAS
    4. repec:hal:journl:halshs-01169563 is not listed on IDEAS
    5. Hörner, Johannes & Lovo, Stefano, 2017. "Belief-free Price Formation," TSE Working Papers 17-790, Toulouse School of Economics (TSE).
    6. Fedor Sandomirskiy, 2016. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," HSE Working papers WP BRP 148/EC/2016, National Research University Higher School of Economics.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. repec:hal:journl:halshs-00390625 is not listed on IDEAS
    13. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    14. Victor Domansky & Victoria Kreps, 2012. "Game-theoretic model of financial markets with two risky assets," HSE Working papers WP BRP 16/EC/2012, National Research University Higher School of Economics.
    15. 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.
    16. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    17. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    18. 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.

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