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Escaping the Brownian stalkers

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  • Alexander Weiss

Abstract

We propose a simple model for the behaviour of longterm investors on a stock market, consisting of three particles, which represent the current price of the stock and the opinion of the buyers, respectively sellers, about the right trading price. As time evolves, both groups of traders update their opinions with respect to the current price. The update speed is controled by a parameter $\gamma$, the price process is described by a geometric Brownian motion. We consider the stability of the market in terms of the distance between the buyers' and sellers' opinion, and prove that the distance process is recurrent/transient in dependence on $\gamma$.

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  • Alexander Weiss, 2008. "Escaping the Brownian stalkers," Papers 0803.3590, arXiv.org.
    • Handle: RePEc:arx:papers:0803.3590
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    References listed on IDEAS

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    1. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    2. Anton Bovier & Jiří Černý & Ostap Hryniv, 2006. "The Opinion Game: Stock Price Evolution From Microscopic Market Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 91-111.
    3. Gur Huberman & Werner Stanzl, 2005. "Optimal Liquidity Trading," Review of Finance, Springer, vol. 9(2), pages 165-200, June.
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