SWITCHING RATES AND THE ASYMPTOTIC BEHAVIOR OF HERDING MODELS

Albrecht Irle (), Jonas Kauschke (), Thomas Lux () and Mishael Milaković
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Albrecht Irle: Department of Mathematics, University of Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
Jonas Kauschke: Department of Mathematics, University of Kiel, Ludewig-Meyn-Str. 4, 24098 Kiel, Germany
Thomas Lux: Department of Economics, University of Kiel, Olshausenstr. 40, 24118 Kiel, Germany;

Advances in Complex Systems (ACS), 2011, vol. 14, issue 03, 359-376

Abstract: Markov chains have experienced a surge of economic interest in the form of behavioral agent-based models that aim at explaining the statistical regularities of financial returns. We review some of the relevant mathematical facts and show how they apply to agent-based herding models, with the particular goal of establishing their asymptotic behavior since several studies have pointed out that the ability of such models to reproduce the stylized facts hinges crucially on the size of the agent population (typically denoted byN), a phenomenon that is also known asN-dependence. Our main finding is thatN-(in)dependence traces back to both the topology and the velocity of information transmission among heterogeneous financial agents.

Keywords: Markov chains; agent-based finance; herding; N-dependence; JEL Code: C10; JEL Code: D84; JEL Code: D85; JEL Code: G19; 02.50.Ga; 89.65.Gh (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0219525911002949

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