1、PhysicaA389(2010)57695775 ContentslistsavailableatScienceDirect PhysicaA journalhomepage: Aquantummodelforthestockmarket ChaoZhang a, ,LuHuang b a SchoolofPhysicsandEngineering,SunYat-senUniversity,Guangzhou510275,China b SchoolofEconomicsandBusinessAdministration,ChongqingUniversity,Chongqing400044
2、,China a r t i c l e i n f o Articlehistory: Received12April2010 Receivedinrevisedform27August2010 Availableonline18September2010 Keywords: Econophysics Quantumfinance Stockmarket Quantummodel Stockprice Rateofreturn a b s t r a c t Beginningwithseveralbasichypothesesofquantummechanics,wegiveanewqua
3、ntum modelineconophysics.Inthismodel,wedefinewavefunctionsandoperatorsofthestock markettoestablishtheSchrdingerequationforstockprice.Basedonthistheoretical framework,anexampleofadriveninfinitequantumwellisconsidered,inwhichwe useacosinedistributiontosimulatethestateofstockpriceinequilibrium.Afteradd
4、ing anexternalfieldintotheHamiltoniantoanalyticallycalculatethewavefunction,the distributionandtheaveragevalueoftherateofreturnareshown. 2010ElsevierB.V.Allrightsreserved. 1. Introduction Thestudyofeconophysicsoriginatedinthe1990s1.Somephysicistsfoundthatafewmodelsofstatisticalphysicscould beusedtod
5、escribethecomplexityoffinancialmarkets2,3.Nowadaysmostoftheeconophysicstheoriesareestablished onthebasisofstatisticalphysics. Statisticalphysicsisonlyonebranchofphysics.Afterseveralyearsdevelopmentofeconophysics,somephysicists begantouseotherphysicaltheoriestostudyeconomics.Thequantumtheoryisoneofth
6、emostimportanttheoriesin contemporaryphysics.Itwasthefirsttimethatthequantumtheorywasappliedtothefinancialmarketswhensomeone usedthequantumfieldtheorytomakeportfoliosafinancialfield4,5,inwhichpathintegralsanddifferentialmanifolds wereintroducedasthetoolstodescribethechangeoffinancialmarketsaftergaug
7、etransformation.Thisideaisthesameas theessenceofthestochasticanalysisinfinance.Therearesomeotherinterestingquantummodels.Forinstance,Schaden originallydescribedassetsandcashheldbytheinvestorasawavefunctiontomodelthefinancialmarkets,whichwas differentfromtheusualfinancialmethodsusingthechangeoftheass
8、etpricetobethedescription6.Inaddition,people paidmoreattentiontothequantumgametheoryandthatwasusefulintradingstrategies7,8. Inrecentyears,anincreasingnumberofquantummodelshavebeenappliedtofinance915,whichattractedgreat attention.Inthispaper,westartfromanewapproachtoexplorethequantumapplicationtothes
9、tockmarket.InSection2 webeginfromseveralbasichypothesesofquantummechanicstoestablishanewquantumfinancemodel,whichcanbe usedtostudythedynamicsofstockprice.InSection3asimpleHamiltonianofastockisgiven.Bysolvingthecorresponding partialdifferentialequation,wequantitativelydescribethevolatilityofthestockintheChinesestockmarketunderthenew frameworkofquantumfinancetheory.AconclusionisillustratedinSection4. Correspondingauthor. E-mailaddress:zhang_(C.Zhang). 0378-4371/$seefrontmatter 2010ElsevierB.V.Allrightsreserved. doi:10.1016/j.physa.2010.09.008
