Controlling Chaos in a Model with Heterogeneous Beliefs

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Controlling Chaos in a Model with Heterogeneous Beliefs

Heilig, Stephan; Schöbel, Rainer
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URI: http://nbn-resolving.de/urn:nbn:de:bsz:21-opus-63999
http://hdl.handle.net/10900/47959
Dokumentart: WorkingPaper
Date: 2001
Source: Tübinger Diskussionsbeiträge der Wirtschaftswissenschaftlichen Fakultät ; 205
Language: English
Faculty: 6 Wirtschafts- und Sozialwissenschaftliche Fakultät
Department: Wirtschaftswissenschaften
DDC Classifikation: 330 - Economics
Keywords: Chaotisches System , Kontrolle
License: http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=de http://tobias-lib.uni-tuebingen.de/doku/lic_ohne_pod.php?la=en
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Abstract:

In this paper we generalize a chaos control method developed by Ott, Grebogi and Yorke (1990) to control saddle points in R2 which are embadded in a strange attractor of a chaotic system. Our generalized method admits to control any unstable equilibrium in R2. We apply our findings to control the dynamics of the chaotic asset pricing model of Brock and Hommes (1998). In this model chaotic price movements are caused by heterogenous market participants. We introduce a control authority which trades the risky asset like the other market participants. Using our control approach, it is possible for the authority to stabilize the market price with minimum effort.

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