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On absence of steady state in the Bouchaud-M\'ezard network model

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  • Zhiyuan Liu
  • R. A. Serota

Abstract

In the limit of infinite number of nodes (agents), the It\^o-reduced Bouchaud-M\'ezard network model of economic exchange has a time-independent mean and a steady-state inverse gamma distribution. We show that for a finite number of nodes the mean is actually distributed as a time-dependent lognormal and inverse gamma is quasi-stationary, with the time-dependent scale parameter.

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  • Zhiyuan Liu & R. A. Serota, 2017. "On absence of steady state in the Bouchaud-M\'ezard network model," Papers 1704.02377, arXiv.org.
    • Handle: RePEc:arx:papers:1704.02377
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    References listed on IDEAS

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    1. Ma, Tao & Serota, R.A., 2014. "A model for stock returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 89-115.
    2. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    3. Liu, Z. & Serota, R.A., 2017. "Correlation and relaxation times for a stochastic process with a fat-tailed steady-state distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 301-311.
    4. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    5. Jean-Philippe Bouchaud, 2015. "On growth-optimal tax rates and the issue of wealth inequalities," Papers 1508.00275, arXiv.org, revised Aug 2015.
    6. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    7. Ma, Tao & Holden, John G. & Serota, R.A., 2013. "Distribution of wealth in a network model of the economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2434-2441.
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