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Mean field limit of a behavioral financial market model

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  • Trimborn, Torsten
  • Frank, Martin
  • Martin, Stephan

Abstract

In the past decade there has been a growing interest in agent-based econophysical financial market models. The goal of these models is to gain further insights into stylized facts of financial data. We derive the mean field limit of the econophysical Cross model (Cross, 2005) and show that the kinetic limit is a good approximation of the original model. Our kinetic model is able to replicate some of the most prominent stylized facts, namely fat-tails of asset returns, uncorrelated stock price returns and volatility clustering. Interestingly, psychological misperceptions of investors can be accounted to be the origin of the appearance of stylized facts. The mesoscopic model allows us to study the model analytically. We derive steady state solutions and entropy bounds of the deterministic skeleton. These first analytical results already guide us to explanations for the complex dynamics of the model.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:613-631
    DOI: 10.1016/j.physa.2018.03.079
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    Cited by:

    1. 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.
    2. 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.

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