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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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1604.

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Length: 27 pages
Date of creation: Feb 2007
Date of revision:
Publication status: Published in Games and Economic Behavior (May 2010), 69(1): 42-71
Handle: RePEc:cwl:cwldpp:1604

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Related research

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

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References

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  1. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Hadiza Moussa Saley & Bernard De Meyer, 2003. "On the strategic origin of Brownian motion in finance," International Journal of Game Theory, Springer, vol. 31(2), pages 285-319.
  3. 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).
  4. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
  5. Victor Domansky, 2007. "Repeated games with asymmetric information and random price fluctuations at finance markets," International Journal of Game Theory, Springer, vol. 36(2), pages 241-257, October.
  6. 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.
  7. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  8. 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).
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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. 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.
  3. 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.

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