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Fluctuation analysis of the three agent groups herding model

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  • Vygintas Gontis
  • Aleksejus Kononovicius
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    Abstract

    We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar composition of the agents. We demonstrate how the sophisticated statistical features of the absolute return in the financial markets can be reproduced by extending the herding interaction of the agents and introducing the third agent state. As well we consider possible extension of proposed herding model introducing additional exogenous noise. Such consistent microscopic and macroscopic model precisely reproduces empirical power law statistics of the return in the financial markets.

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    File URL: http://arxiv.org/pdf/1305.5958
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1305.5958.

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    Date of creation: May 2013
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    Handle: RePEc:arx:papers:1305.5958

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    1. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
    2. Ashkenazy, Yosef & M. Hausdorff, Jeffrey & Ch. Ivanov, Plamen & Eugene Stanley, H, 2002. "A stochastic model of human gait dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 316(1), pages 662-670.
    3. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 108(1), pages 137-56, February.
    4. Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 391(4), pages 1309-1314.
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