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A Particle Model for the Herding Phenomena Induced by Dynamic Market Signals

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Abstract

In this paper, we study herding phenomena of agents in financial markets arising from the combined effect of (1) non-coordinated collective interactions between agents and (2) concurrent reactions of agents to dynamic market signals. By interpreting the expected price of an asset and the favorability on the asset as the position and the velocity in phase space, respectively, we construct an agent-based particle model for explaining herding behavior in finance. We then define two types of herding functionals to this model, and show that they satisfy a Gronwall type estimate and a LaSalle type invariance property, respectively. As a result, we show the herding behavior of the agents. Various numerical tests are presented to numerically verify theoretical results.

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Acknowledgements

H.-O. Bae was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2018R1D1A1A09082848). S.-B. Yun was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A1B03935955). J. Yoo was supported by the Social Science Research Program by (NRF-2017S1A5A8022379).

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Authors and Affiliations

  1. Department of Financial Engineering, Ajou University, Suwon, Republic of Korea

    Hyeong-Ohk Bae, Sang-hyeok Lee & Jane Yoo

  2. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Republic of Korea

    Seung-yeon Cho & Seok-Bae Yun

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  1. Hyeong-Ohk Bae
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Correspondence to Seok-Bae Yun.

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Communicated by Eric A. Carlen.

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Bae, HO., Cho, Sy., Lee, Sh. et al. A Particle Model for the Herding Phenomena Induced by Dynamic Market Signals. J Stat Phys 177, 365–398 (2019). https://doi.org/10.1007/s10955-019-02371-8

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