ROBUST MATHEMATICAL FORMULATION AND PROBABILISTIC DESCRIPTION OF AGENT-BASED COMPUTATIONAL ECONOMIC MARKET MODELS

Maximilian Beikirch, Simon Cramer, Martin Frank, Philipp Otte, Emma Pabich and Torsten Trimborn
Additional contact information
Maximilian Beikirch: RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany
Simon Cramer: #x2020;WZL, RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, Germany
Martin Frank: #x2021;Steinbuch Center for Computing, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
Philipp Otte: #xA7;Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre, Institute for Advanced Simulation, 52425 Jülich, Germany
Emma Pabich: #xB6;Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Dennewartstraße 27, 52068 Aachen, Germany
Torsten Trimborn: #x2225;NRW.BANK, Kavalleriestraße 22, 40213 Düsseldorf, Germany

Advances in Complex Systems (ACS), 2020, vol. 23, issue 06, 1-41

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 descriptions of agent-based models. Exemplified, we show two probabilistic descriptions of the Levy–Levy–Solomon and Franke–Westerhoff model.

Keywords: Agent-based models; Monte Carlo simulations; time scaling; continuous formulation; mesoscopic description; kinetic theory (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:23:y:2020:i:06:n:s0219525920500174

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DOI: 10.1142/S0219525920500174

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