Robust Mathematical Formulation and Implementation of Agent-Based Computational Economic Market Models
Emma Pabich and
Papers from arXiv.org
Monte Carlo Simulations of agent-based models in science and especially in the economic literature have become a widely used modeling approach. In many applications the number of agents is huge and the models are formulated as a large system of difference equations. In this study we discuss four numerical aspects which we present exemplified by two agent-based computational economic market models; the Levy-Levy-Solomon model and the Franke-Westerhoff model. First, we discuss finite-size effects present in the Levy-Levy-Solomon model and show that this behavior originates from the scaling within the model. Secondly, we discuss the impact of a low-quality random number generator on the simulation output. Furthermore, we discuss the continuous formulation of difference equations and the impact on the model behavior. Finally, we show that a continuous formulation makes it possible to employ correct numerical solvers in order to obtain correct simulation results. We conclude that it is of immanent importance to simulate the model with a large number of agents in order to exclude finite-size effects and to use a well tested pseudo random number generator. Furthermore, we argue that a continuous formulation of agent-based models is advantageous since it allows the application of proper numerical methods and it admits a unique continuum limit.
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