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1、OPTIMALINTERVENTIONINTHEFOREIGNEXCHANGEMARKETWHENINTERVENTIONSAFFECTMARKETDYNAMICSALECN.KERCHEVALANDJUANF.MORENOyAbbreviatedTitle:OptimalinterventioninforeignexchangeAbstract.WeaddresstheproblemofoptimalCentralBankinterventionintheexchangeratemarketwheninterventionscreate
2、feedbackintheratedynamics.Inparticular,weextendtheworkdoneonoptimalimpulsecontrolbyCadenillasandZapatero[2;3]toincorporatetemporarymarketreactions,ofrandomdurationandlevel,toBankinterventions,andtoestablishresultsformoregeneralrateprocesses.Weobtainnewexplicitoptimalimpuls
3、econtrolstrategiesthataccountforthesemarketreactions,andshowthattheycannotbeobtainedsimplybyadjustingtheinterventioncostinamodelwithoutmarketreactions.AMSsubjectclassi cations.93E20,91B70,60G40.Keywords.exchangerate,optimalimpulsecontrol,quasi-variationalinequalities,stopp
4、ingtimes.1.Introduction.Incountriesdependentonforeigntradeandforeigncapital,theCentralBankisnormallyinchargeofexchangeratepolicy.ThisusuallymeansthattheCentralBankhastheabilitytointerveneinthemarketsinordertokeeptheircurrencyrateswithinaband,orclosetoatargetratesetbytheBan
5、k'spolicymakers.Interventioncantaketwodi erent(compatible)forms:adjustmentofdomesticinterestratelevels,whichin
uencestheattractivenessofforeigninvestments;anddirectpurchasesorsalesofforeigncurrencyreservesintheforeignexchangemarket.The rstformofinterventioncanbemodeledasac
6、ontinuous(classical)controlarXiv:0909.1142v1[q-fin.GN]7Sep2009problem,andthesecondasanimpulsecontrolproblem.Inthispaperwefocusonlyonthesecondtypeofintervention,interpretingamarketinterventionasawaytochangetheexchangeratebyadesiredamountviasalesorpurchasesofreservesoveratim
7、eshortenoughtobereasonablymodeledasaninstantaneousimpulse.CORRESPONDINGAUTHOR.ADDRESS:DEPARTMENTOFMATHEMATICS,1017ACADEMICWAY,ROOM208,FLORIDASTATEUNIVERSITY,TALLAHASSEE,FL32306-4510.EMAIL:KERCHEVA@MATH.FSU.EDU,PHONE:850-644-8701,FAX:850-644-4053.yADDRESS:CALLE103A#11B49BQ
8、1APT302,BOGOTA,COLOMBIA.EMAIL:JMORENO@MATH.FSU.EDU,PHONE:5716370221.1Theproblemisto ndano
