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Price Dynamics on a Stock Market with Asymmetric Information

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  • Bernard De Meyer

    (Centre d'Economie de la Sorbonne, University of Paris)

Abstract

The appearance of a Brownian term in the price dynamics on a stock market was interpreted in [De Meyer, Moussa-Saley (2003)] as a consequence of the informational asymmetries between agents. To take benefit of their private information without revealing it to fast, the informed agents have to introduce a noise on their actions, and all these noises introduced in the day after day transactions for strategic reasons will aggregate in a Brownian Motion. We prove in the present paper that this kind of argument leads not only to the appearance of the Brownian motion, but it also narrows the class of the price dynamics: the price process will be, as defined in this paper, a continuous martingale of maximal variation. This class of dynamics contains in particular Black and Scholes' as well as Bachelier's dynamics. The main result in this paper is that this class is quite universal and independent of a particular model: the informed agent can choose the speed of revelation of his private information. He determines in this way the posterior martingale L, where L_{q} is the expected value of an asset at stage q given the information of the uninformed agents. The payoff of the informed agent at stage q can typically be expressed as a 1-homogeneous function M of L_{q+1}-L_{q}. In a game with n stages, the informed agent will therefore chose the martingale L? that maximizes the M-variation. Under a mere continuity hypothesis on M, we prove in this paper that L? will converge to a continuous martingale of maximal variation. This limit is independent of M.

Suggested Citation

  • Bernard De Meyer, 2007. "Price Dynamics on a Stock Market with Asymmetric Information," Cowles Foundation Discussion Papers 1604, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1604
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d16/d1604.pdf
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    References listed on IDEAS

    as
    1. DE MEYER, Bernard, 1996. "The Maximal Variation of a Bounded Martingale and the Central Limit Theorem," CORE Discussion Papers 1996035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, March.
    3. 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.
    4. Bernard De Meyer & Ehud Lehrer & Dinah Rosenberg, 2009. "Evaluating information in zero-sum games with incomplete information on both sides," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390625, HAL.
    5. Bernard De Meyer & Alexandre Marino, 2005. "Duality and optimal strategies in the finitely repeated zero-sum games with incomplete information on both sides," Cahiers de la Maison des Sciences Economiques b05027, Université Panthéon-Sorbonne (Paris 1).
    6. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    7. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
    8. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 241-257, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Shino Takayama, 2013. "Price Manipulation, Dynamic Informed Trading and Tame Equilibria: Theory and Computation," Discussion Papers Series 492, School of Economics, University of Queensland, Australia.
    2. 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.
    3. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications, Elsevier.
    4. Fedor Sandomirskiy, 2014. "Repeated games of incomplete information with large sets of states," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 767-789, November.
    5. Pierre Cardaliaguet & Catherine Rainer, 2012. "Games with Incomplete Information in Continuous Time and for Continuous Types," Dynamic Games and Applications, Springer, vol. 2(2), pages 206-227, June.
    6. repec:eee:jfinec:v:127:y:2018:i:2:p:342-365 is not listed on IDEAS
    7. repec:hal:journl:halshs-01169563 is not listed on IDEAS
    8. Bernard De Meyer & Gaëtan Fournier, 2015. "Price dynamics on a risk averse market with asymmetric information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01169563, HAL.
    9. Hörner, Johannes & Lovo, Stefano, 2017. "Belief-free Price Formation," TSE Working Papers 17-790, Toulouse School of Economics (TSE).
    10. repec:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-017-0217-7 is not listed on IDEAS
    11. 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.
    12. Fabien Gensbittel, 2016. "Continuous-time limit of dynamic games with incomplete information and a more informed player," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 321-352, March.
    13. Gensbittel, Fabien & Grün, Christine, 2017. "Zero-sum stopping games with asymmetric information," TSE Working Papers 17-859, Toulouse School of Economics (TSE).

    More about this item

    Keywords

    Asymmetric information; Price dynamics; Martingales of maximal variation; Repeated games;

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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