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

Advances in Complex Systems, vol. 23, pp. 2050017

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.

Authors 6

1. Maximilian Beikirch Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany

   RWTH Aachen University, Templergraben 55, 52056, Aachen, Germany

2. Simon Cramer Aachen

   RWTH Aachen University

   Affiliation as printed

   WZL, RWTH Aachen University, Campus-Boulevard 30, 52074 Aachen, Germany

3. Martin Frank

   Karlsruhe Institute of Technology

   Affiliation as printed

   Steinbuch Center for Computing, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany

   Steinbuch Center for Computing, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany.#TAB#

4. Philipp Otte

   Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre, Institute for Advanced Simulation, 52425 Jülich, Germany

5. Emma Pabich Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering, RWTH Aachen University, Dennewartstraße 27, 52068 Aachen, Germany

6. Torsten Trimborn
   Affiliation as printed

   NRW.BANK, Kavalleriestraße 22, 40213 Düsseldorf, Germany