Abstract:
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.
