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Properties of the wealth process in a market microstructure model

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  • Ted Theodosopoulos
  • Ming Yuen

Abstract

In this short paper we define the wealth process in a spin model for market microstructure, for individual agents and in aggregate. The agents in our model try to balance their desire to belong to the local majority (herding behavior), defined over random network neighborhoods, and the occasional advantage of belonging to the global minority (contrarian trading). We arrive at a classification of the martingale properties of this wealth process and use it to determine the strategic stability of the agents' interactions. Our goal is to add a behavioral interpretation to this stochastic agent-based model for market fluctuations.

Suggested Citation

  • Ted Theodosopoulos & Ming Yuen, 2005. "Properties of the wealth process in a market microstructure model," Papers math/0502105, arXiv.org, revised Feb 2005.
    • Handle: RePEc:arx:papers:math/0502105
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    2. Burgos, E. & Ceva, Horacio & Perazzo, R.P.J., 2004. "The evolutionary minority game with local coordination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 635-644.
    3. Kaizoji, Taisei & Bornholdt, Stefan & Fujiwara, Yoshi, 2002. "Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 441-452.
    4. Challet, Damien & Marsili, Matteo & De Martino, Andrea, 2004. "Stylized facts in minority games with memory: a new challenge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 143-150.
    5. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
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    Cited by:

    1. Ted Theodosopoulos & Ming Yuen, 2006. "Imbalance attractors for a strategic model of market microstructure," Papers math/0605421, arXiv.org.

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