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Kinetic models for socio-economic dynamics of speculative markets

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  • Maldarella, Dario
  • Pareschi, Lorenzo

Abstract

In this paper we introduce a simple model for a financial market characterized by a single stock or good and an interplay between two different trader populations, chartists and fundamentalists, which determine the price dynamics of the stock. The model has been inspired by the microscopic Lux–Marchesi model (Lux and Marchesi (2000, 1999) [3,25]). The introduction of kinetic equations permits to study the asymptotic behavior of the investments and the price distributions and to characterize the regimes of lognormal behavior and the formation of power law tails.

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  • Maldarella, Dario & Pareschi, Lorenzo, 2012. "Kinetic models for socio-economic dynamics of speculative markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 715-730.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:715-730
    DOI: 10.1016/j.physa.2011.08.013
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    2. Torsten Trimborn & Lorenzo Pareschi & Martin Frank, 2017. "Portfolio Optimization and Model Predictive Control: A Kinetic Approach," Papers 1711.03291, arXiv.org, revised Feb 2019.
    3. Simon Cramer & Torsten Trimborn, 2019. "Stylized Facts and Agent-Based Modeling," Papers 1912.02684, arXiv.org.
    4. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Working Papers hal-00967662, HAL.
    5. Pierre Degond & Jian-Guo Liu & Christian Ringhofer, 2014. "Evolution of wealth in a nonconservative economy driven by local Nash equilibria," Papers 1403.7800, arXiv.org.
    6. Brugna, Carlo & Toscani, Giuseppe, 2018. "Kinetic models for goods exchange in a multi-agent market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 362-375.
    7. Lorenzo Pareschi & Giuseppe Toscani, 2014. "Wealth distribution and collective knowledge. A Boltzmann approach," Papers 1401.4550, arXiv.org.
    8. Guharay, Samar K. & Thakur, Gaurav S. & Goodman, Fred J. & Rosen, Scott L. & Houser, Daniel, 2013. "Analysis of non-stationary dynamics in the financial system," Economics Letters, Elsevier, vol. 121(3), pages 454-457.
    9. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2018. "Simulation of Stylized Facts in Agent-Based Computational Economic Market Models," Papers 1812.02726, arXiv.org, revised Nov 2019.
    10. Xia Zhou & Shaoyong Lai, 2023. "The mutual influence of knowledge and individual wealth growth," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-22, June.
    11. Gualandi, Stefano & Toscani, Giuseppe, 2019. "Size distribution of cities: A kinetic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 221-234.
    12. Torsten Trimborn & Martin Frank & Stephan Martin, 2017. "Mean Field Limit of a Behavioral Financial Market Model," Papers 1711.02573, arXiv.org.
    13. Hu, Chunhua & Lai, Shaoyong & Lai, Chong, 2020. "Investigations to the price evolutions of goods exchange with CES utility functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    14. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2020. "Robust Mathematical Formulation And Probabilistic Description Of Agent-Based Computational Economic Market Models," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-41, September.
    15. Maximilian Beikirch & Simon Cramer & Martin Frank & Philipp Otte & Emma Pabich & Torsten Trimborn, 2019. "Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models," Papers 1904.04951, arXiv.org, revised Mar 2021.
    16. Torsten Trimborn, 2018. "A Macroscopic Portfolio Model: From Rational Agents to Bounded Rationality," Papers 1805.11036, arXiv.org, revised Oct 2018.
    17. Trimborn, Torsten & Frank, Martin & Martin, Stephan, 2018. "Mean field limit of a behavioral financial market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 613-631.
    18. Zhong, Yue & Lai, Shaoyong & Hu, Chunhua, 2021. "Investigations to the dynamics of wealth distribution in a kinetic exchange model," Applied Mathematics and Computation, Elsevier, vol. 404(C).
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    20. Gualandi, Stefano & Toscani, Giuseppe, 2018. "Pareto tails in socio-economic phenomena: A kinetic description," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-17.

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