Continuous versus Discrete Market Games

Alexandre Marino and Bernard De Meyer
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Alexandre Marino: CERMSEM

No 1535, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: De Meyer and Moussa Saley [4] provide an endogenous justification for the appearance of Brownian Motion in Finance by modeling the strategic interaction between two asymmetrically informed market makers with a zero-sum repeated game with one-sided information. The crucial point of this justification is the appearance of the normal distribution in the asymptotic behavior of Vn(P)//n. In De Meyer and Moussa Saley’s model [4], agents can fix a price in a continuous space. In the real world however, the market compels the agents to post prices in a discrete set. The previous remark raises the following question: Does the normal density still appear in the asymptotic of Vn//n for the discrete market game? The main topic of this paper is to prove that for all discretization of the price set, Vn(P)//n converges uniformly to 0. Despite of this fact, we do not reject De Meyer, Moussa analysis: when the size of the discretization step is small as compared to n-1/2, the continuous market game is a good approximation of the discrete one.

Keywords: Insider trading; game of incomplete information; Brownian Motion (search for similar items in EconPapers)
Pages: 20 pages
Date: 2005-09
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Citations: View citations in EconPapers (6)

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