뗚28뻭뗚6웚뫢퇴쪦랶톧풺톧놨쓪12퓂JournalofHengyangNormalUniversityDec12007폐붻틗럑뫍싲싴볛닮뗄컞쳗샻쫐뎡쒣탍틗퇞뒺,컢탛(뫢퇴쪦랶톧풺쫽톧쾵,뫾쓏뫢퇴ꆡ421008)햪ꆡ튪:룸돶튻훖폐붻틗럑뫍싲뷸싴돶볛닮솽훖쒦닁뗄뛠훜웚뷰죚쫐뎡쒣탍,퓚헢훖쒣탍쿂뷸탐쫐뎡뗄컞쳗샻뿌뮭ꆣ맘볼듊:컞쳗샻;붻틗럑;싲싴볛닮훐춼럖샠뫅:O21119컄쿗뇪쪶싫:A컄헂뇠뫅:1673ꆪ0313(2007)06ꆪ0017ꆪ021ꆡ틽ꆡ퇔ꛈ=(ꛈn)0ꇜnꇜT,ꆡꆡꛈn=(ꛈ1n,ꆭ,ꛈdn)웤훐ꛈin뇭쪱뿌n춶폚뗚i훖닺뗄럝뛮,죴ꛈinꇝ0퓲뇭춶뛔폐쒦닁뗄뷰죚쫐뎡뷸탐쳖싛쫇쫽샭뷰죚뷼쓪살퇐뺿헟퓚쪱뿌n싲뷸ꛈin럝뗚i훖닺,죴ꛈinꇜ0퓲뇭춶헟퓚뗄죈뗣ꆣ컄쿗[124]뗈뛔뻟폐붻틗럑쒦닁뗄뷰죚쫐뎡쒣탍뗄쪱뿌n싴돶-ꛈin럝뗚i훖닺ꆣ컞쳗샻뷸탐쇋퇐뺿ꆣ죎뫎튻훖쒦닁뚼뿉쓜쪹뗃컊쳢뢴퓓,컄짨쪱뿌n떥캻닺i퓚ힴ첬ꛘj뗄쫕틦싊캪Rin(ꛘj)1ꇜi쿗[5]뛔뻟폐붻틗럑뫍싲싴볛닮솽훖쒦닁뗄떥훜웚샫즢쪱볤ꇜd,0ꇜnꇜT,1ꇜijꇜkꆣgn(ꛘj)=Rin(ꛘj)ꛈin,쯼뇭쪱뿌n뗚i뷰죚쫐뎡쒣탍뗄컞쳗샻뷸탐쇋퇐뺿ꆣ놾컄붫퓚폐붻틗럑뫍훖닺퓚ힴ첬ꛘj뗄쫕틦ꆣgn(ꛘj)=ꇆdgin(ꛘj),쯼뇭쪱뿌n싲뷸싴돶볛닮솽훖쒦닁뗄뛠훜웚뷰죚쫐뎡쒣탍쿂,뷸탐쫐뎡i=1뗄컞쳗샻뿌뮭ꆣ춶ퟩ뫏퓚ힴ첬ꛘj뗄쫕틦ꆣ볇gn=(gn(ꛘ1),ꆭ,gn(ꛘk))ꆣ컒쏇뚨틥R짏뗄쿟탔몯쫽:i2ꆡ쫐뎡쒣탍(1+ꛋin)Biꛈnnꆡꛈin>0ifn(ꛈ)=(1-uin)Aiꛈinnꆡꛈinꇜ0뾼싇튻룶룅싊뿕볤(ꚸ,F,P)벰웤짏튻뗝퓶뗄ꛒ듺쫽쇷ꆡꆡ1ꇜiꇜd,ꆡ0ꇜnꇜT(Fn):F0ΑF1ΑꆭΑFT,T<ꇞꆣꚸ={ꛘ1,ꆭ,ꛘk}듺뇭쯹폐d뿉쓜뗄ퟔ좻ힴ첬,Fn듺뇭떽쪱뿌n캪횹쫐뎡뗄좫늿탅쾢ꆣ쇮fn(ꛈ)=ꇆifn(ꛈ),퓲fn(ꛈ)뇭쪱뿌n냼삨붻틗럑퓚쓚뗄i=1뾼싇튻룶놾쫐뎡,쯼평d훖닺ퟩ돉,닺뗄릺싲볛춶ퟩ뫏뗄ퟜ돉놾,fn(ꛈ)=0뇭쪱뿌n쎻폐죎뫎돉놾,fn(ꛈ)룱맽돌캪튻럇뢺뗄쫊펦맽돌:<0뇭춶ퟩ뫏퓚쪱뿌n닺짺쇋헽뗄쿖뷰쇷ꆣB=(Bn)0ꇜnꇜT,ꆡꆡBn=(B1n,ꆭ,Bdn)ꆣd웤훐쇮<n(ꛈ)=ꇆ(1+ꛋin)Bin(ꛈin-ꛈin-1),ꛈin>0,1ꇜnꇜTꆣBin듺뇭쪱뿌n릺싲뗚i훖닺뗄볛룱ꆣi=1닺뗄돶쫛볛룱맽돌캪튻럇뢺뗄쫊펦맽돌d:쇮ꛕn(ꛈ)=ꇆ(1-uin)Ain(ꛈin-ꛈin-1),ꛈ1nꇜ0,1ꇜnꇜTꆣA=(An)0ꇜnꇜT,ꆡꆡAn=(A1n,ꆭ,Adn)ꆣi=1웤훐Ain듺뇭쪱뿌볙짨쫐뎡볈쎻폐뷰쇷죫,튲쎻폐뷰쇷돶ꆣ춶헟퓚n돶쫛뗚i훖닺뗄볛룱ꆣ놾컄짨돶쫛볛룱싔뗍폚릺싲볛룱ꆣ돵쪼쪱뿌틔뫳뗄붻틗죕캪쇋릺싲튻킩닺,쯻뇘탫싴뗴튻킩짨퓚쪱뿌닺ꆣ컒쏇뚨틥ퟔ죚붻틗닟싔죧쿂:n(0ꇜnꇜT)릺싲떥캻닺i뗄붻틗럑폃캪ꛋin,돶쫛떥캻닺i뗄붻틗럑폃캪뚨틥1ꆡ죴<n(ꛈ)ꇜꛕn(ꛈ),1ꇜnꇜT,퓲돆쫐뎡쫇ퟔ죚uin,1ꇜiꇜdꆣ튻춶헟뗄붻틗닟싔믲춶ퟩ뫏캪튻뿉쇏맽돌ꆣퟔ죚붻틗닟싔뗄좫쳥볇캪SFꆣ:쫕룥죕웚:2007ꆪ09ꆪ20ퟷ헟볲뷩:틗퇞뒺(1975ꆪ),얮,뫾쓏뎣쓾죋,뫢퇴쪦랶톧풺쫽톧쾵붲쪦,쮶쪿,퇐뺿랽쿲:쯦믺럖컶ꆢ뺭볃럖컶폫뷰죚1
1ꆡ8뫢퇴쪦랶톧풺톧놨2007쓪뗚28뻭3ꆡ컞쳗샻뗄뿌뮭횤쏷ꆡ쿈횤돤럖탔ꆣ쇮ꛈꇊSF,쪹뗃(-f0(ꛈ),gT)ꇝ0ꆣ퓲ꛈ쫇폅뮯컊쳢뗄뿉탐뷢,폖틲캪ퟮ폅횵캪0,뚨틥2ꆡ돆쫐뎡쫇컞쳗샻뗄,죴늻듦퓚춶ퟩ뫏ꛈꇊSF폐f0(ꛈ)ꇝ0ꆣ쪹뗃듓뛸폐f0(ꛈ)=0,헢쮵쏷ꛈ쫇컊쳢뗄ퟮ폅뷢ꆣ:g평폚컊쳢뗄쎿튻룶ퟮ폅뷢쪹풼쫸쳵볾돉캪뗈쪽,Tꇝ0,f0(ꛈ)ꇜ0,gTꇙ0,f0(ꛈ)ꇙ0ꆣ뚨틥Rk+1훐뗄튻룶벯뫏폐gT=0ꆣ:H=듓뛸(-f0(ꛈ),gT)=0,폚쫇늻듦퓚춶ퟩ뫏ꛈꇊSF쪹{x=(x0,x1,ꆭ,xk):ꛈꇊSF,뗃(1)돉솢ꆣx0ꇜ-f0(ꛈ),(x1,ꆭ,xk)=gT}ꆣꆡꆡ뚨샭1ꆡ쫐뎡쫇컞쳗샻뗄ΖHꇉRk+1+={0}ꆣ쯹틔뻝뚨틥2횪쫐뎡쫇컞쳗샻뗄ꆣ횤쏷ꆡHꇉRk+1웤듎횤뇘튪탔ꆣ짨쫐뎡쫇컞쳗샻뗄ꆣ+ꇙ{0}Ζϖy,yꇙ0,yꇊRk+1+ꇉHΖϖyꇊRk+1+,ꛈꇊSF쪹뗃0<yꇜ퓲뛔죎틢싺ퟣgTꇝ0뗄ꛈꇊSF,뇘폐f0(ꛈ)ꇝ0ꆣ(-f0(ꛈ),gT)Ζ듦퓚쳗샻믺믡ꆣ듓뛸쮵쏷컊쳢뗄뿉탐뷢뗄쒿뇪횵뻹럇뢺ꆣ뚨샭폖틲캪ꛈ=0쫇컊쳢뗄뿉탐뷢,웤쒿뇪횵캪0ꆣ2죴듦퓚헽뗄q=(q1,ꆭ,qTk)쪹뗃:ΠꛈꇊSF,폐k틲듋컊쳢뗄ퟮ폅횵캪0뗃횤ꆣꛈiTꇆRiT(ꛘj)qjꇜif0(ꛈ)=(1+ꛋi0)Bi0ꛈi0,퓲쫐뎡쫇컞죴ꛈꇤ쫇컊쳢뗄튻룶ퟮ폅뷢,퓲f0(ꛈꇤ)=0,쟒gꇤTꇝ0,j=1(1-ui0)Ai0ꛈi0틲듋gꇤ(T)=0,럱퓲쫐뎡쫇쳗샻뗄ꆣ쳗샻뗄ꆣ틲듋쎿룶ퟮ폅뷢ꛈꇤ쪹풼쫸쳵볾돉캪뗈쪽뗃횤ꆣ횤쏷ꆡ랴짨쫐뎡쫇폐쳗샻뗄,듋뚨샭뇭쏷:죴쫐뎡컞쳗샻믺믡,퓲캪퓚붻틗쒩웚쎿튻퓲뻝뚨틥2횪:듦퓚ꛈꇊSF,쪹뗃:룶ퟔ좻ힴ첬닺짺럇뢺쫕틦뛸ퟶ춶ퟩ뫏뗷헻쯹탨뗄ퟮ짙돵-f0(ꛈ)+gTq>0ꆣ(1)쪼춶뛮캪쇣ꆣ틲틑횪kiꛈ0ꛈi0ꛈi0>0ii닎뾼컄쿗:TꇆRT(ꛘj)qjꇜ(1+ꛋi0)Bif0(ꛈ)=j=1(1-ui0)Ai0ꛈi0ꛈꆣi0ꇜ0[1]JouiniandKallal1Martingalesandarbitrageinsecurities듓뛸뗃marketswithtransactioncosts[J]1J1Econ1Theory,1995ddkii(66):17821971f0(ꛈ)=ꇆif0(ꛈ)ꇝꇆꛈTꇆRT(ꛘj)qj=gTq,i=1i=1j=1듓뛸뗃[2]Kabanov,Yu,Stricker1C1TheHarrison2Krepsarbitragepricingtheoremundertransactioncosts[J].-f0(ꛈ)+gTqꇜ0ꆣ(2)듓뛸(1)폫(2)닺짺쎬뛜ꆣEcon,2001,35:18521961뚨샭[3]ShunmingZhang,ChunleiXu,XiaotieDeng1Dynamic3ꆡ죴듦퓚헽뗄q=(q1,ꆭ,qTk)쪹뗃죧쿂컞풼쫸폅뮯컊쳢arbitragefreeofassetpricingwithproportionaltransac2minf0(ꛈ)-gTq,ꛈꇊSF,뗄ퟮ폅횵캪0,퓲쫐뎡쫇컞쳗샻뗄ꆣtioncost[J]1Math1Finance,2002,12(1):892971횤쏷ꆡ틲캪죴짨쫐뎡쫇폐쳗샻뗄,퓲[4]샮뎿,돂샶욼,훜폱풪1폐붻틗럑뗄컞쳗샻쫐뎡쒣탍[J].f0(ꛈ)-gTq<0,폫틑횪뫾쓏얩튵듳톧톧놨(ퟔ좻뿆톧냦),2006,32(3):32723291minf0(ꛈ)-gTqꛈ,ꇊSF,뗄ퟮ폅횵캪0쎬뛜ꆣ[5]샮훙량,췴쫙퇴,뗋킡쳺1폐쒦닁뷰죚쫐뎡훐잿컞쳗샻뚨샭4ꆡ쫐뎡컞쳗샻떱쟒뷶떱폅뮯컊쳢minf0(ꛈ)뗄뿌뮭[J]1쾵춳릤돌샭싛폫쪵볹,2002,(10):602651gTꇝ,Πꛈ0ꇊ[6]붯뒺뢣,듷폀슡1튻냣M2V쒣탍훐뗄폐킧횤좯ퟩ뫏벰SF뗄ퟮ폅횵캪0,쟒웤쎿룶ퟮ폅뷢ꛈꇤ쪹풼쫸쳵볾돉캪뗈쪽ꆣ컞쳗샻럖컶[J]1펦폃룅싊춳볆,2007,23(2):312411TheMarketModelofNo2ArbitragewithTransactionandAsk2BidSpreadsYIYan2chun,WUXiong2tao(DepartmentofMathematics,HengyangNormalUniversity,HengyangHunan421008,China)Abstract:Thebackgroundofthispaperisthemulti2timefinancialmarketmodelwithtransactionandask2bidspreads1Inthispaper,wegivethecharacterizationofno2arbitrage1Keywords:no2arbitrage;equivalentmartingalemeasure;financialmarket
