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Robust Mathematical Formulation and Probabilistic Description of Agent-Based Computational Economic Market Models

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Listed:
  • Maximilian Beikirch
  • Simon Cramer
  • Martin Frank
  • Philipp Otte
  • Emma Pabich
  • Torsten Trimborn

Abstract

In science and especially in economics, agent-based modeling has become a widely used modeling approach. These models are often formulated as a large system of difference equations. In this study, we discuss two aspects, numerical modeling and the probabilistic description for two agent-based computational economic market models: the Levy-Levy-Solomon model and the Franke-Westerhoff model. We derive time-continuous formulations of both models, and in particular we discuss the impact of the time-scaling on the model behavior for the Levy-Levy-Solomon model. For the Franke-Westerhoff model, we proof that a constraint required in the original model is not necessary for stability of the time-continuous model. It is shown that a semi-implicit discretization of the time-continuous system preserves this unconditional stability. In addition, this semi-implicit discretization can be computed at cost comparable to the original model. Furthermore, we discuss possible probabilistic descriptions of time continuous agent-based computational economic market models. Especially, we present the potential advantages of kinetic theory in order to derive mesoscopic desciptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy-Levy-Solomon and Franke-Westerhoff model.

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  • 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.
    • Handle: RePEc:arx:papers:1904.04951
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    References listed on IDEAS

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