On the strategic origin of Brownian motion in finance

This paper is concerned with the strategic use of 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.