On the strategic origin of Brownian motion in finance
This paper is concerned with the stategic 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 [infinite] , 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.
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- 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).
- Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
- 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).
- 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).
- 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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