Trading a mean-reverting asset Buy low and sell high

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1、Automatica44(2008)1511–1518www.elsevier.com/locate/automaticaTradingamean-revertingasset:BuylowandsellhighIHanqinZhanga,QingZhangb,∗aAcademyofMathematicsandSystemsScience,AcademiaSinica,Beijing,100080,ChinabDepartmentofMathematics,UniversityofGeorgia,Athens,GA30602,UnitedStatesReceiv

2、ed11October2006;receivedinrevisedform6October2007;accepted9November2007Availableonline20February2008AbstractThispaperisconcernedwithanoptimaltrading(buyandsell)rule.Theunderlyingassetpriceisgovernedbyamean-revertingmodel.Theobjectiveistobuyandselltheassetsoastomaximizetheoverallretur

3、n.Slippagecostisimposedoneachtransaction.TheassociatedHJBequations(quasi-variationalinequalities)areusedtocharacterizethevaluefunctions.Itisshownthatthesolutiontotheoriginaloptimalstoppingproblemcanbeobtainedbysolvingtwoquasi-algebraicequations.Sufficientconditionsaregivenintheformofa

4、verificationtheorem.Anumericalexampleisreportedtodemonstratetheresults.c2008ElsevierLtd.Allrightsreserved.Keywords:Optimalstopping;Quasi-variationalinequalities;Mean-revertingprocess1.Introductionenergymarkets(seeBlancoandSoronow(2001)anddeJongandHuisman(2002)).Seealsorelatedresultsin

5、optionpricingThispaperisconcernedwithtradinganassetthatissubjectwithamean-reversionassetbyBos,Ware,andPavlov(2002).torandomfluctuationinitsprice.ThetradingruleconsistsofTradingrulesinfinancialmarketshavebeenstudiedfortwocomponents:buyandsell.Atraditionaltradingstrategymanyyears.Forexam

6、ple,Zhang(2001)consideredasellinginfinancialmarketsistobuylowandsellhigh.However,inruledeterminedbytwothresholdlevels,atargetpriceandapractice,identifyingtheselowandhighlevelsisextremelystop-losslimit.Onemakesasellingdecisionwheneverthepricechallenginganddifficult.Itisthepurposeofthisp

7、apertoreacheseitherthetargetpriceorthestop-losslimit.ThestockexaminehowtoquantifylowsandhighswhentheunderlyingpriceobservesaswitchinggeometricBrownianmotion(GBM).assetpriceisdictatedbyamean-reversionmodel.TheobjectiveistodeterminethesethresholdlevelstomaximizeAmean-reversionmodelisof

8、tenusedinfina