Dynamical Explanation for the Emergence of Power Law in a Stock Market Model

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1、DynamicalExplanationfortheEmergenceofPowerLawinaStockMarketModelbyMosheLevyandSorinSolomonDepartmentofTheoreticalPhysicsRacahInstituteofPhysicsGivatRamTheHebrewUniversityofJerusalemJerusalem91000,IsraelAbstractPowerlawsarefoundinawiderangeofdierentsystems:fromsandpilestowordoccurrencef

2、requenciesandtothesizedistributionofcities.Thenaturalemergenceofthesepowerlawsinsomanydierentsystems,whichhasbeencalledselforganizedcriticality,seemsrathermysteriousandawaitsarigorousexplanation.Inthisletterwestudythestationaryregimeofapreviouslyintroduceddynamicalmicroscopicmodelofthe

3、stockmarket.Wendscalingintheeconomicparametersofthesystem.Weareabletoexplainthisphenomenonbysimplegeneralconsiderations.Wesuggestthatsimilarconsiderationsmayexplainselforganizedcriticalityinmanyothersystems.Key-words:self-organizedcriticality,powerlaws,complexsystems,computersimulation

4、s,stockmarket.IntroductionTheappearanceofpowerlawsinamultitudeofdiversesystemsseemsapuzzle.Baketal[1-4]whocoinedtheterm"selforganizedcriticality"anddiscoveredthisphenomenainmanysystemssuggestthatmanycomplexsystemshaveanaturaltendencytoconvergetoastatisticallystablestatewhichcannotbechar

5、acterizedbyaspecicscale.Scalinghasbeenrecently1foundinthebehaviorofeconomicsystems[5].Themechanismsdrivingsystemsintothestateofcriticalityremainratherunclear.Therehavebeenrecentattemptstoexplainselforganizedcriticalityviatherenormalizationgroupapproach[6-8].Itisnotyetcertainhowfarthisa

6、pproachcanbestretchedinordertoapplyforalargeclassofgenericcomplexsystems.Inthepresentworkwestudyasimplemicroscopicmodelofthestockmarket[9,10].Inthepresentletterwereporttheemergence(inthetime-stationaryregime)ofpowerlawsinthedistributionofwealthamongtheinvestorsrepresentedinthemodel.Thet

7、imeevolutionofthesystemconsisttheninasuperpositionofrandomwalkswithstepsproportionaltothevariousinvestorwealthesandleadstomarket uctuationsconsistentwiththeexperimentallyfoundLevydistribution[5].Weoerageneralexplanationfortheemergenceofapowerlawinthiscontext.Ourexplanationisre