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Switching Rates And The Asymptotic Behavior Of Herding Models

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Author Info

  • 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; Kiel Institute for the World Economy, Hindenburgufer 66, 24105 Kiel, Germany)

  • MISHAEL MILAKOVIĆ

    ()
    (Department of Economics, University of Bamberg, Feldkirchenstr. 21, 96052 Bamberg, Germany)

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 by N), a phenomenon that is also known as N-dependence. Our main finding is that N-(in)dependence traces back to both the topology and the velocity of information transmission among heterogeneous financial agents.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal Advances in Complex Systems.

Volume (Year): 14 (2011)
Issue (Month): 03 ()
Pages: 359-376

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Handle: RePEc:wsi:acsxxx:v:14:y:2011:i:03:p:359-376

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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;

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References

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  1. Alfarano, Simone & Lux, Thomas, 2005. "A noise trader model as a generator of apparent financial power laws and long memory," Economics Working Papers 2005,13, Christian-Albrechts-University of Kiel, Department of Economics.
  2. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
  3. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
  4. Alfarano, Simone & Milakovic, Mishael, 2009. "Network structure and N-dependence in agent-based herding models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 78-92, January.
  5. Reiner Franke & Simone Alfarano, 2007. "A Simple Asymmetric Herding Model to Distinguish Between Stock and Foreign Exchange Markets," Working Papers wp07-01, Warwick Business School, Finance Group.
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Cited by:
  1. Alfarano, Simone & Milakovic, Mishael & Raddant, Matthias, 2011. "A Note on institutional hierarchy and volatility in financial markets," MPRA Paper 30902, University Library of Munich, Germany.

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