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Price Dynamics on a Stock Market with Asymmetric Information

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  • Bernard De Meyer

Abstract

When two asymmetrically informed risk-neutral agents repeatedly exchange a risky asset for numéraire, they are essentially playing an n-times repeated zero-sum game of incomplete information. In this setting, the price Lq at period q can be defined as the expected liquidation value of the risky asset given players' past moves. This paper indicates that the asymptotics of this price process at equilibrium, as n goes to [infinity], is completely independent of the "natural" trading mechanism used at each round: it converges, as n increases, to a Continuous Martingale of Maximal Variation. This martingale class thus provides natural dynamics that could be used in financial econometrics. It contains in particular Black and Scholes' dynamics. We also prove here a mathematical theorem on the asymptotics of martingales of maximal M-variation, extending Mertens and Zamir's paper on the maximal L1-variation of a bounded martingale.
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Suggested Citation

  • Bernard De Meyer, 2007. "Price Dynamics on a Stock Market with Asymmetric Information," Levine's Bibliography 321307000000000841, UCLA Department of Economics.
  • Handle: RePEc:cla:levrem:321307000000000841
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    File URL: http://cowles.econ.yale.edu/P/cd/d16a/d1604.pdf
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    References listed on IDEAS

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    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, March.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, April.
    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.
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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. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications, Elsevier.
    3. repec:eee:jfinec:v:127:y:2018:i:2:p:342-365 is not listed on IDEAS
    4. Gensbittel, Fabien & Grün, Christine, 2017. "Zero-sum stopping games with asymmetric information," TSE Working Papers 17-859, Toulouse School of Economics (TSE).
    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:hal:journl:halshs-01169563 is not listed on IDEAS
    7. Hörner, Johannes & Lovo, Stefano, 2017. "Belief-free Price Formation," TSE Working Papers 17-790, Toulouse School of Economics (TSE).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. repec:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-017-0217-7 is not listed on IDEAS

    More about this item

    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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