An analysis of the effect of noise in a heterogeneous agent financial market model

Publisher:
Elsevier Inc
Publication Type:
Journal Article
Citation:
Journal of Economic Dynamics and Control, 2011, 35 (1), pp. 148 - 162
Issue Date:
2011-01
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Heterogeneousagentmodels(HAMs)infinanceandeconomicsareoftencharacterised by highdimensionalnonlinearstochasticdifferentialordifferencesystems.Becauseof thecomplexityoftheinteractionbetweenthenonlinearitiesandnoise,acommonly used,oftencalledindirect,approachtothestudyofHAMscombinestheoreticalanalysis of theunderlyingdeterministicskeletonwithnumericalanalysisofthestochastic model.However,itiswellknownthatthisindirectapproachmaynotproperly characterisethenatureofthestochasticmodel.Thispaperaimstotacklethisissueby developingadirectandanalyticalapproachtotheanalysisofastochasticmodelof speculativepricedynamicsinvolvingtwotypesofagents,fundamentalistsand chartists,andthemarketpriceequilibriaofwhichcanbecharacterisedbythe stationarymeasuresofastochasticdynamicalsystem.Usingthestochasticmethodof averagingandstochasticbifurcationtheory,weshowthatthestochasticmodeldisplays behaviourconsistentwiththatoftheunderlyingdeterministicmodelwhenthetimelag in theformationofpricetrendsusedbythechartistsisfarawayfromzero.However, whenthislagapproacheszero,suchconsistencybreaksdown.
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