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Fluctuation analysis of the three agent groups herding model

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  • Vygintas Gontis
  • Aleksejus Kononovicius

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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  • Vygintas Gontis & Aleksejus Kononovicius, 2013. "Fluctuation analysis of the three agent groups herding model," Papers 1305.5958, arXiv.org.
  • Handle: RePEc:arx:papers:1305.5958
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    References listed on IDEAS

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    1. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, Oxford University Press, vol. 108(1), pages 137-156.
    2. M. Cristelli & L. Pietronero & A. Zaccaria, 2011. "Critical Overview of Agent-Based Models for Economics," Papers 1101.1847, arXiv.org.
    3. 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, vol. 316(1), pages 662-670.
    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, vol. 391(4), pages 1309-1314.
    5. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
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