On the strategic origin of Brownian motion in finance

De Meyer, Bernard;Moussa Saley, Hadiza
(2000)

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  • De Meyer, Bernard
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  • Moussa Saley, Hadiza
    Author
Abstract
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 ~ , 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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De Meyer, B., & Moussa Saley, H. (2000). On the strategic origin of Brownian motion in finance (CORE Discussion Papers 2000/57). https://hdl.handle.net/2078.5/34889