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《Derivation of the Boltzmann Equation for Financial Brownian MotionDirect Observation of the Collective Motion of High-Frequency Traders金融布朗运动Boltzmann方程的推导 高频交易者集体运动的直接观察》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、DerivationoftheBoltzmannEquationforFinancialBrownianMotion:DirectObservationoftheCollectiveMotionofHigh-FrequencyTradersKiyoshiKanazawa1;2,TakumiSueshige2,HidekiTakayasu1;3,andMisakoTakayasu1;21InstituteofInnovativeResearch,TokyoInstituteofTechnology,4259Nagatsuta-cho,Midori-ku,Yokoha
2、ma,226-8502,Japan2DepartmentofMathematicalandComputingScience,SchoolofComputing,TokyoInstituteofTechnology,4259Nagatsuta-cho,Midori-ku,Yokohama,226-8502,Japan3SonyComputerScienceLaboratories,3-14-13Higashi-Gotanda,Shinagawa-ku,Tokyo,141-0022,JapanAmicroscopicmodelisestablishedfor nanci
3、alBrownianmotionfromthedirectobservationofthedynamicsofhigh-frequencytraders(HFTs)inaforeignexchangemarket.Furthermore,atheoreticalframeworkparalleltomolecularkinetictheoryisdevelopedforthesystematicdescriptionofthe nancialmarketfrommicroscopicdynamicsofHFTs.Wereport rstonamicroscopice
4、mpiricallawoftraders'trend-followingbehaviorbytrackingthetrajectoriesofallindividuals,whichquanti esthecollectivemotionofHFTsbuthasnotbeencapturedinconventionalorder-bookmodels.WenextintroducethecorrespondingmicroscopicmodelofHFTsandpresentitstheoreticalsolutionparallelingmolecularkine
5、tictheory:Boltzmann-likeandLangevin-likeequationsarederivedfromthemicroscopicdynamicsviatheBogoliubov-Born-Green-Kirkwood-Yvonhierarchy.Ourmodelisthe rstmicroscopicmodelthathasbeendirectlyvalidatedthroughdataanalysisofthemicroscopicdynamics,exhibitingquantitativeagreementswithmesoscopi
6、candmacroscopicempiricalresults.PACSnumbers:89.65.Gh,05.20.Dd,05.10.Gg,05.40.JcIntroduction.{Inphysics,thestudyofcolloidalBrow-idencemicroscopically.Toovercomethiscrucialprob-nianmotionhasalonghistorybeginningwithEin-lemasanempiricalscience,twomissinglinkshavetobestein'sfamouswork[1];t
7、heunderstandingofitsmech-connected:(i)establishmentofthemicroscopicmodelanismhasbeensystematicallydevelopedinkineticthe-bydirectobservationoftraders'dynamics(Fig.1a)andory[2,3].Speci cally,frommicroscopicNewtoniandy-(ii)constructionofakinetictheorytoshowitsconsis-namics,theBoltzmanna
