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Imbalance attractors for a strategic model of market microstructure

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  • Ted Theodosopoulos
  • Ming Yuen
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    Abstract

    In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition probabilities and analyzed the martingale properties of the ensuing wealth process. Here we relax the assumption on the choices of individual agents by allowing mixed strategies, offering opportunities for the agents to gain intermediate submartingale exposure for their individual wealth processes. We develop a novel two-dimensional spin system to model the critical regions of the wealth process as a reflection of the agents' behaviors. We exhibit strategic conflicts between individual market participants and the market as a whole, and identify a new source of uncertainty arising from `reinforced expectations'.

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    File URL: http://arxiv.org/pdf/math/0605421
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number math/0605421.

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    Date of creation: May 2006
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    Handle: RePEc:arx:papers:math/0605421

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    1. Jerome Renault & Sergio Scarlatti & Marco Scarsini, 2003. "A folk theorem for minority games," ICER Working Papers - Applied Mathematics Series 10-2003, ICER - International Centre for Economic Research.
    2. Taisei Kaizoji & Stefan Bornholdt & Yoshi Fujiwara, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Papers cond-mat/0207253, arXiv.org.
    3. Ted Theodosopoulos & Ming Yuen, 2005. "Properties of the wealth process in a market microstructure model," Papers math/0502105, arXiv.org, revised Feb 2005.
    4. Majka, Arkadiusz & Wiślicki, Wojciech, 2004. "Statistical thermodynamics for choice models on graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 645-663.
    5. Masanao Aoki, 2000. "Cluster Size Distribution of Economics Agents of Many Types in Market," UCLA Economics Online Papers 102, UCLA Department of Economics.
    6. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
    7. Challet, Damien, 2008. "Inter-pattern speculation: Beyond minority, majority and $-games," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 85-100, January.
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