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An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics

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  • Taisei Kaizoji

Abstract

In this paper we present an interacting-agent model of stock markets. We describe a stock market through an Ising-like model in order to formulate the tendency of traders getting to be influenced by the other traders' investment attitudes [1], and formulate the traders' decision-making regarding investment as the maximum entropy principle for nonextensive entropy. We demonstrate that the equilibrium probability distribution function of the traders' investment attitude is the {\it q-exponential distribution}. We also show that the power-law distribution of the volatility of price fluctuations, which is often demonstrated in empirical studies, can be explained naturally by our model which is based on the collective crowd behavior of many interacting agents.

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  • Taisei Kaizoji, 2006. "An interacting-agent model of financial markets from the viewpoint of nonextensive statistical mechanics," Papers physics/0601106, arXiv.org, revised Apr 2006.
    • Handle: RePEc:arx:papers:physics/0601106
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    1. Silvio M. Duarte Queiros & Celia Anteneodo & Constantino Tsallis, 2005. "Power-law distributions in economics: a nonextensive statistical approach," Papers physics/0503024, arXiv.org.
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    Cited by:

    1. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Quanbo Zha & Gang Kou & Hengjie Zhang & Haiming Liang & Xia Chen & Cong-Cong Li & Yucheng Dong, 2020. "Opinion dynamics in finance and business: a literature review and research opportunities," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-22, December.
    3. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    4. Murakami, Ryo & Nakamura, Tomomichi & Kimura, Shin & Manabe, Masashi & Tanizawa, Toshihiro, 2015. "On possible origins of trends in financial market price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 179-189.
    5. Răzvan-Cornel Sfetcu & Vasile Preda, 2023. "Fractal Divergences of Generalized Jacobi Polynomials," Mathematics, MDPI, vol. 11(16), pages 1-12, August.
    6. Martins, Francisco Leonardo Bezerra & do Nascimento, José Cláudio, 2022. "Power law dynamics in genealogical graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    7. Ryo Murakami & Tomomichi Nakamura & Shin Kimura & Masashi Manabe & Toshihiro Tanizawa, 2014. "On possible origins of trends in financial market price changes," Papers 1406.5276, arXiv.org, revised Nov 2014.

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