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1、外文翻譯原文OptimaldividendpolicygrowthoptionMaterialSource:SpringerVerlag2006Auth:JeanPaulDecampsStephaneVilleneuveResearchonoptimaldividendpayoutsfacashconstrainedfirmisbasedonthepremisethatthefirmwantstopaysomeofitssurplust

2、otheshareholdersasdividendstherefefollowsadividendpolicythatmaximizestheexpectedpresentvalueofallpayoutsuntilbankruptcy.ThisapproachhasbeenusedinparticulartodeterminethemarketvalueofafirmwhichinlinewithModiglianiMiller[2

3、3]isdefinedasthepresentvalueofthesumoffuturedividends.Indiffusionmodelstheoptimaldividendpolicycanbedeterminedasthesolutionofasingularstochasticcontrolproblem.IntwoinfluentialpapersJeanblancShiryaev[18]RadnerShepp[26]ass

4、umethatthefirmexploitsatechnologydefinedbyacashgeneratingprocessthatfollowsadriftedBrownianmotion.Theyshowthattheoptimaldividendpolicyisacterizedbyathresholdsothatwheneverthecashreservegoesabovethisthresholdtheexcessispa

5、idoutasdividend.Modelsthatinvolvesingularstochasticcontrolsmixedsingularregularstochasticcontrolsarenowwidelyusedinmathematicalfinance.Recentcontributionshavefinstanceemphasizedrestrictionsimposedbyaregulatyagency[25]the

6、interplaybetweendividendriskpolicies[1314]theanalysisofhedginginsurancedecisions[27].Anewclassofmodelsthatcombinefeaturesofbothregularstochasticcontroloptimalstoppinghasrecentlyemerged.TworecentpapersinthislineareMiaoWan

7、g[22]whostudytheinteractionsbetweeninvestmentconsumptionunderincompletemarketsHugonnieretal.[16]whofocusonirreversibleinvestmentfarepresentativeagentinageneralequilibriumframewk.Fromamathematicalviewpointtheproblemwearei

8、nterestedinisdifferentcombinesfeaturesofbothsingularstochasticcontroloptimalstopping.SuchmodelsarelessusualincpatefinancetothebestofourknowledgeonlyGuoPham[13]dealtwithsuchliteratureanalysesoptimalinvestmentpoliciesthatc

9、anbemathematicallydeterminedassolutionsofoptimalstoppingproblems.TheiginalmodelisduetoMcDonaldSiegel[21]hasbeenextendedinvariouswaysbymanyauths.1Animptantassumptionofstardmodelsisthattheinvestmentdecisioncanbemadeindepen

10、dentlyofthefinancingdecision.Incontrastinourpapertwointerrelatedfeaturesdriveourinvestmentproblem.Firstthefirmiscashconstrainedmustfinancetheinvestmentusingitscashreserve.Secondthefirmmustdecideitsdividenddistributionpol

11、icyinviewofitsgrowthopptunity.SuchaperspectivecanberelatedtoBoyleGuthrie[2]whoanalyseinanumericalmodelthedynamicinvestmentdecisionofafirmsubmittedtocashconstraints.Twostatevariablesdrivetheirmodel:thecashprocessaprojectv

12、alueprocessfwhichthedecisionmakerhastopayafixedamount.BoyleGuthrie[2]donotconsiderhoweverthedividenddistributionpolicy.Theoutlineofthepaperisasfollows.Section2describesthemodelanalysessomeusefulbenchmarksprovidesafmulati

13、onofourproblembasedonthedynamicprogrammingprinciplederivesanecessarysufficientconditionfthegrowthoptiontobewthless.Section3statesprovesourmaintheemderivestheoptimaldividendinvestmentpolicypresentsfinancialimplications.Se

14、ction4concludes.Inthispaperweconsidertheimplicationsofliquidityfthedividendinvestmentpolicyofafirmthatownstheperpetualrighttoinvestinanewprofitrateincreasingtechnology.Themathematicalfmulationofourproblemleadstoamixedsin

15、gularcontroloptimalstoppingproblemthatwesolvequasiexplicitlybyusingaconnectionwithanauxiliarystoppingproblem.Adetailedanalysisbasedonthepropertiesoflocaltimegivesthepreciseoptimaldividendinvestmentpolicy.Thistypeofproble

16、misnonstarddoesnotseemtohaveattractedmuchattentioninthecpatefinanceliterature.OuranalysisfollowsthelinesofstochasticcontrolreliesonthechoiceofadriftedBrownianmotionfthecashreserveprocessintheabsenceofdividenddistribution

17、.Thismodellingassumptionguaranteesthequasiexplicitnatureofthevaluefunction.WeusethisfeaturefinstanceinProposition3.4whereweshowthatisasupersolution.FurthermethepropertyofindependentincrementsfBrownianmotionplaysacentralr

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