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Price dynamics on a stock market with asymmetric information

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  • De Meyer, Bernard

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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 69 (2010)
Issue (Month): 1 (May)
Pages: 42-71

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Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:42-71

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Web page: http://www.elsevier.com/locate/inca/622836

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

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References

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  1. Alexandre Marino & Bernard De Meyer, 2005. "Continuous versus Discrete Market Games," Cowles Foundation Discussion Papers 1535, Cowles Foundation for Research in Economics, Yale University.
  2. repec:hal:cesptp:halshs-00390625 is not listed on IDEAS
  3. DE MEYER, Bernard & MOUSSA SALEY, Hadiza, 2000. "On the strategic origin of Brownian motion in finance," CORE Discussion Papers 2000057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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).
  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," Documents de travail du Centre d'Economie de la Sorbonne 09035, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  7. 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).
  8. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
  9. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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Citations

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Cited by:
  1. 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.
  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. 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.

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