캬웕톶 뗚第?1?8뻭卷뗚第?2웚期?쾵系춳统工릤程돌学톧报놨????ꎮ?????ꎮ?? ?军??四?쓪年?4캪月??J?O?U?R??N?A?Lꎮ ?O?F? ?S?Y?S?T?E?M?S ?E?N?G?I?r?伍?军?R?到??G????ꎮꎬ?????A~.， 2003 任王3믲或폐有要튪求쟳权좨的뗄定뚨价볛方랽法램及벰无컞套쳗利샻价볛格룱区쟸闰볤①ꋙ?쟘秦学톧志횾?1ꎬ，컢吴돥冲럦锋?2??(?1ꎮ듳.솬大샭连릤理工듳大톧学맜管샭理톧学풺院ꎬ，듳大솬连?1?1?6?0?2?4;ꎻ??2.ꎮ짏上몣海붻交춨通듳大톧学맜管샭理톧学풺院，ꎬ짏上몣海京??剧??'3?0?)?햪摘튪要ꎺz퓚在多뛠对쪱问볤段뛎的뗄拯뿲架볜下쿂，ꎬ닉采用폃完췪全좫套쳗期웚保놣健횵辱풭、샭理ꆢ쿟、탔线맦性规뮮划뛔对얼偶풭原샭理뫍和按샭理싛论룸给돶出쇋了믲或폐有튪要쟳求좨权뗄的싴卖랽方쳗套?샻科价볛格룱和뫍买싲方랽套쳗利샻价볛格룱的뗄计볆算쯣方랽法램，ꎬ分럖别뇰对뛔允퓊许탭证횤券좯卖싴空뿕、ꆢ现쿖金뷰借뷨贷듻和뫍不늻允퓊许탭证횤券좯卖싴空뿕、只ꆢ횻允퓊许탭绩쿖，뷰金뷨借듻贷뗄的쟩情?뿶况뷸进行탐了쇋研퇐究뺿.ꎮ쿠相펦应뗄的쳗套샻利볛价格룱和뫍元컞套쳗利샻价볛格룱区쟸间볤可뿉以틔通춨过맽递뗝推췆求쟳解뷢有폐限个쿞线룶，쿟注탔规맦划뮮问??题?得뗃到떽、ꎮ?맘关键볼琵듊:ꎺ鞍ꎻz쳗套科샻手ꎻ믲或폐有튪要쟳求좨权§ꎻ쿟线탔性맦规划뮮ꎻE폐有摩쿞证횤券좯쫐市场뎡?훐中춼圄分럖샠类号뫅:ꎺ?跑??到??컄文쿗献뇪挥쪶识码싫ꎺ:?A?컄文헂章뇠编号뫅ꎺ:?1?0?0?0ꆪ-?5?7?81??仪??黯??〉??但?ꆪ-0?1??5?9ꆪ-0?4????????????????????????????ꆤ????????????????????????Pricing method and arbi仕age-freeprice interval for ????????????????ωntingent claims Q?Iꆿ?N X??u?e?-?由??j?lꎬ，?WU?? ?C?h?O?I??电??缸?t???(?1?.ꎮ ?s?c?h?∞?，?1? ?o?f? M??a?n?a?g?e?m?e?ntꎬ, ?D?a?1?i?a?n? U?n??i?v?er??s?it?y?? ?o?f? ?T，??配h?1?1?01?，??吨野?，ꎬD?a?1?i?a?n ?1?1??6?0?2?4,ꎬ ?C?lø?n??a;ꎻ? 2?.ꎮ?Sc?h?∞?，??1 o??f M?a?n?a?g?e?m?e?n?t?ꎬ，?缉?部??增??强??iJ?i?副?秘??鸣???Un?i?v?e?r?si?t?y，ꎬS??h?an?g??ha?i? ?2?α?到?0?3?0，ꎬα??由?1?8)?????????ꎺ????????????????????????????????????ꎬ????????????????????????????????????????ꎬ???????Abs1ract: Under出，eframewo武ofmultiple 向他，this严perapplies perfect h哗昭principle，lin.倒?????????????????????????????????????????????????????????????????????????????ꆯ?????????????????progr恕nmu宅dua1ityprinciple and mar出事ùeme路uretheory to detennìning位sell匠，s arbitrage price ?????????ꆯ?????????????????????????????????????ꎮ????????????????????????ꎮ????????????????????????????and buyer’ s arbitrage price of ∞nti鸣:entcla担回sesare considered.臼1eis all侧i吨sh<珉se且鸣配??c?u?r?i?t?i??e?s??????????????????????????????????????ꎬ??????????????????????????????????????????????????and allO'响应gborrowing and lending侃S九四d出eother is not allowing short se监ng回curities?????????????????????????????????????ꎮ?????????????????????????????????ꆪ???????????????????????but allowing borrowing and lending臼站，咀learbi恼geprice and the arbi油ge-freeprice interval of由e????????????????????????????????????????????????????????????????????????????????????ꎮ?contingent cl也m岱nbe ob姐扫edby solving回'melinear p冀朝涩nmingproblems in把cursivefurm. ?????????ꎺ??????????ꎻ?????????ꎻ????????????????ꎻ?????????????ꎻ??????????????????????Key words: mar由tgale;arbitrnge; c刨出飞gentclainlS; line缸pr咿回归ng;finite security ma:rket 。?事틽!?言퇔?文컄采닉用폃线쿟性탔规맦划뮮对뛔偶얼原풭理샭、ꆢ鞍理샭论싛、ꆢ췪完좫全쳗套웚期保놣值횵?原풭理샭等뗈考뾼察달有폐眼쿞证횤券좯市쫐场뎡中훐或믲有폐要튪求쟳权좨的뗄定뚨价볛方랽?在퓚单떥时쪱间볤段뛎的뗄条쳵件볾下，쿂文ꎬ컄献쿗[?1?]?닉采폃用췪完좫全쳗套期웚?法램，ꎬ럡丰뢻富和뫍推췆广맣了쇋文컄献쿗[?1?]?的뗄结뷡论싛.ꎮ?保놣值횵与??时??e?c?t?h?e?d?j回??吨??〉풭原샭理뫍和쿟线탔性맦规뮮划랽方램法给룸出돶了쇋?有폐黑쿞证횤券좯市쫐场뎡(?f?in?i?t?e?毗???u?r?it?y?m?a?I?韭?e?t?)?中훐用폃两솽种훖证횤券좯?E? 方랽法램的뗄建붨立솢?〈?웤其훐中튻一훖种캪为컞无风럧险쿕债햮券좯)?对뛔或믲有폐要튪求쟳权좨(?∞??n?出??ꆪ?g?e?n?t? c?国??时?定뚨价볛的뗄方랽法램.ꎮ在퓚多뛠时쪱间볤段뛎的뗄在뿲架볜下쿂，ꎬ本놾?不늻失쪧一튻般냣性탔，ꎬ只횻考뾼虑싇两솽个룶时쪱间볤段뛎，ꎬ쫐市뎡场中훐证횤券좯?①ꋙ 收쫕稿룥日죕期웚:ꎺ2?(?X?}I?-ꆪ0?7? -ꆪ2?3?;ꎻ修탞订뚩吕죕朔웚:ꎺ2?0?0?2?-ꆪ0?9? -ꆪ1?3?.ꎮ ?基믹金뷰项쿮1쒿3:ꎺ国맺家볒杰뷜出돶青쟠年쓪科뿆学톧基믹뷰金资助훺项쿮目쒿仪???陇??5?3?0?3?)?;ꎻ画맺家볒自ퟔ然좻科뿆学톧基믹金뷰资助훺项쿮目쒿(?1?1世??顶??部?)??;ꎻ第뗚3?0?批엺中훐国맺薄늩士쪿后뫳科뿆研퇐基믹金뷰资助훺项쿮目.쒿?
캬웕톶 ???ꆮꆤ?ꆣ?쾵?춳?릤?돌?톧?놨?뗚??뻭?뗚?웚?1ω 系统工程学报第18卷第Z期ꆤꆤꆪꆪ뗄的볛价룱格ힴ状첬态뇤变뮯化죧如춼图?1쯹所쪾示.ꎮ??훖횤좯????ꎬ????ꎬꆭꎬ??랲?뗄돖폐춷듧ꎬ쪹웤릹?1种证券s(O)，s(l)，…，s(川的持有头寸，使其构놾本컄文랽方램法뗄的쮼思슷路쫇是:ꎺ닉采폃黑쓦逆쿲向뗝递췆撞뗄的랽方쪽式，ꎬ쫗首?돉뗄ퟩ뫏퓚?ꎺ?쪱뗄볛횵듳폚뗈폚믲폐튪쟳좨?成的组合在t= 2时的价筐大于等于或有要求权쿈先좷确뚨定?tꎺ=? 1룷各ힴ状첬态쿂下믲或폐有튪要쟳求좨权뗄的볛价횵值，ꎬ좻然뫳后퓙再?듋쪱뗄쿠펦볛횵ꎮ퓚헢퇹뗄풼쫸쳵볾쿂ꎬ붫뿉탐벯?此时的梧应价值.在这样的约束条件下，将可行集샻利폃用?tꎺ=? 1쪱时믲或폐有튪要쟳求좨权룷各ힴ状첬态뗄的볛价횵值좷确뚨定?t?=? 0?훐볛횵ퟮ킡뗄ퟩ뫏뛔펦뗄볛횵ퟷ캪믲폐튪쟳좨퓚? 中价值最小的组合对应的价值作为或有要求权在쪱时룃该믲或폐有튪要쟳求좨权뗄的볛价횵值ꎮ，볙假짨设쫐市뎡场짏上폐有랲π?+?1훖种횤证?ힴ状첬态?乓下쿂的뗄卖싴方랽套쳗利샻价볛格룱，ꎮ?좯券?氏?的??，ꎬ?抖??。?，ꎬꆭ…ꎬ?，s?(时?ꎬ，웤其훐中?s?(?O?)캪为컞无럧风쿕险햮债券좯，ꎬ?컞럧쿕샻싊짨캪?ꎬ?캪폐쿞헽헻쫽ꎮ?평由?马ꎺ=ꇆ~α뿚?i?(以?i?)튻-?so?( ?)?) ?+?石?。횪如，ꎬ?(??町뗈等?无风险利率设为O，n为有限正整数.볛份폚子??fꇭ随ß?Co?(P?.)? ꆾ~ S?.tꎮ. ꇆꎺ~? (?以?i)튻-?so?(i?))삲ai ?+ coꇝ ~? Ckꎬ?,k ꎺ=? 1ꎬ,2ꆯ?,3 ꇊ?ꎬ?ꎺ?ꎬꆭꎬ?ꎬ?ꇊ?l aiξR， i = 1，…，n，马ξRYmMaA 쿂쏦뾼달????훐뗄??폫룷횤좯닢뛈뿕볤?下面考察(P)中的言。与各证券鞍测度空间1瓦，뗄的맘关系쾵.ꎮ볇记?Y???ꎺ?ꎦ???튻?????ꎬ???뿚????????马(i)= Sk(i) -so( ),A = (a与;h叫π+1)rSk(j) , i ~ n 뿚a?Jg" ꎺ= ?{?-"ꎬ ?’J’ 'Jꎺ飞랲??ꆯꎬ，?zꎺ튻=? ?(?C1?ꎬꆯ，?C?〓ꆯꎬ??C?J)?Tll, j = n + 1 俨:0/=1 /=2 la"t ~ n q = (q., ,qn+.rr,qi =仁飞'좦回?1?솽商쪱时商볤훜周웚巍的뗄볛价룱格ힴ状첬态?뿚ꎺ?ꆣꎬꆭꎬ??ꎮꎬ?ꎬ???ꎺ??랲?ꆣ?l co, t = n + 1 ?1.ꎮ1?? ힴ按첬态?鸟下쿂或믲有폐要튪求쟳权좨퓚在?t?= ?1쪱屑뗄的싴卖랽方쳗套?퓲员过컊问쳢题?(?P.?)?뿉可볲简뮯化为캪??????샻和j볛价룱格?????ꆾ?rM??ꎮ???ꎮ???in ?qn?+1? 假볙设짨或믲有폐要튪求쟳权좨C?퓚在ힴ状첬态?马下쿂的뗄份볛值횵为캪?Ckꎬ，???ꇝ??(P){ s. t. Aq ;;量z2??퓚ힴ첬?쿂뗄볛횵캪????ꎬ????퓚ힴ첬??ꇊ??튻?n1 s(i)在状态马下的价值为Sk(i)，抖。在状态乓qεR+下쿂的뗄价볛值횵为캪s?o?(?仆??，ꎬ?i=? 0?,ꎬ ꆭ,ꎬn?ꎯ?;ꎻk? =? 1?,ꎬ2?,ꎬ3?.ꎮ? 旦쟒有폐?1?.ꎮ1?.ꎮ1?? 丸퓊许탭证횤券좯卖싴空뿕和뫍现쿖金뷰借뷨贷듻的뗄情况쟩，뿶?뚨샭??죴컊쳢????뗄ퟮ폅뷢듦퓚ꎬ퓲웤ퟮ?ꇝ?定噩1若间题(P，2乓)的最住解存在，员则号其最{볙畏짨设뷨借듻贷샻利싊率为캪O?.ꎮ为캪了쇋能쓜做ퟶ到떽对뛔C?的뗄完췪全좫???쳗웚놣횵ꎬ퓚?ꎺ?쪱ꎬ횤좯???뗄돖폐춷듧캪?폅횵??ꎺ??????C优恤值qιι;LL+d1=野r窍吕PkιC，ꎮꎬ웤훐ꎬ????ꎬ??ꎬ???ꎬ?套黯保值，在t= 1时，证券s(i)的持有头寸为α磊?〈듽待좷确定뚨)?，ꎬ웤其中훐a뿚i?>? 0?表뇭示쪾多뛠头춷头춷寸듧，ꎬ向??<?0?表뇭?ꎺ?φ=φ矶l门?.…ꆭ..?门?ꎮ캪횤좯???뛔펦뗄닢뛈?<Þn.<Þ.为证券s(i)对应的鞍调度示쪾空뿕头춷头춷寸듧，ꎬi?=ꎺO?，ꎬI?，ꎬ…ꆭ，ꎬn랲ꎻ在퓚t?=? 1?时쪱证횤券좯组ퟩ合뫏?햭볤ꎬ벴뛔죎틢?ꇊ?ꎬ폐?空间，即对任意pξ钱，有??的뗄价볛值횵为캪石。??=ꎺ~ꇆα뿚，?so?(?i)?，ꎬt?=?2?时쪱证횤券좯组ퟩ合뫏在퓚状ힴ?~ꇆP?内?(?i?)=?句?(?仆?，ꎬi?=? 1?,ꎬ ꆭ,ꎬ?n ???????态첬马?下쿂的뗄价볛盖횵为캪?횤쏷?????뗄뛔얼쿟탔맦뮮캪?证明(P)的对偶线性规划为2??rttitiMeb gL 百=ꎺ~ꇆ a뿚is?k(?i)?, ꎬk? =? 1?,ꎬ2?,ꎬ3? ???ꆿꆾ~ꇆC?内?????ꎮ???평췪좫쳗웚놣횵풭샭ꎬ뿉붨솢쿂쇐쒣탍?뾼???岛??<iittL由完全套期保值原理，可建立下列模型∞考ATu = ell+l 察달或믲有폐要튪쟳求좨权퓚在=??1?时쪱的뗄卖싴方랽套쳗科샻价볛格룱?u = ,( Ul.句，向)T~ 0 rr ( C) = Minco 웤훐ꎬ???캪뗚???룶풪쯘캪?ꆢ웤폠풪쯘캪?뗄?其中，e刊为第n+ 1个元素为1、其余元素为0的llrM??in?? ?Co 单떥位캻歹自쇐由쿲量솿.ꎮ即벴?(?P?)\??s?儿ꎮ，?ꎮ?言k三~ꇝ?C, ꎬk ?=? 1?,2ꎬ?,3ꎬ? K?ꆾ?a뿚.?ξꇊ?R(实?쪵数쫽)，?ꎬi?=? 0?,ꎬ1?, ꎬꆭ,ꎬn 랲?主튼机뿚ꆰ?=?{?:ꎺ?:f;ꎺ+1?ꆣ?闰컊题쳢〈?凹??的뗄含몬义틥为캪:ꎺ确좷定뚨有폐限쿞证횤券좯市쫐场뎡上짏n랲+??亦틠即벴?
캬웕톶 ?笨??黯?쓪年?4퓂月?쟘秦톧学횾志等뗈ꎺz믲或폐有튪要쟳求좨权的뗄뚨定价볛랽方法램벰及컞无쳗套利샻볛价格룱区쟸部볤?튻-?1?61? 튻-?证券s(i)对应的上鞍撞撞度空间，即对任意pε~ (Sk?(i)? 튻-?以????????ꎬꎮ?ꎮ?ꆢ횤좯????뛔펦뗄짏닢뛈뿕볤ꎬ벴뛔죎틢?ꇊ?i)?ꆮ??ꎬꆭꎬ?ꎬ?) Uk = 0 (i = 1,... , n) ꆫ?ꆣ?k=1 32M 泣，ꎬ폐有??????ꇆ~P??内?(i)?ꇜ运?以??i?)?(?i ?= ?1ꎬ，ꆭ…，ꎬ?叫?国틲듋此??ꎺ????횤证葫쏷??(?P??)的뗄뛔对얼偶쿟线탔性맦规划뮮为캪?3ꇆ2?以??i?)Ukꎺ=?以i?)?(?i?ꎺ= ?1ꎬ，ꆭ...ꎬ?，的??ꎺ??k=1 M值ꇆ~ç?内???矗ꎺ=1?ꇆ~?均=ꎺ1?ꎬ,? Uk注ꇝ?o?(k뫳 ꎺ= ?1?,2,ꎬ3??) ??????????뿚ꇜ??. AIuK=s;;o (D:3H :5孟벴即?U캪为运횤E券좯?S(??1)?，ꎬ?S(?纱??，ꎬꆭ…ꎬ，?S(??n)?뗄的轶事닢曾뛈度:ꎻ떱当컊问??????Alu = 1 쳢题(??乌??)ퟮ最폅优解뷢存듦在퓚时쪱，ꎬ由평线쿟性탔规맦iJ뮮j뛔对偶얼原풭理샭知횪?[2]?뿚u ?= ?(Ul?'ꎬ?句?，ꎬ?均??)T?;;:ꇝ::=?0 ????????????웤其中훐ꎬ，?A????ꎬ???ꎬ??为= (A,A) ，A캪?A뗄的잰前?n列쇐窍쿲量솿组ퟩ成돉的뗄?l 21q::+1 =如吕CkPkꎬ?뚨샭뗃횤ꎮ?횤뇏?뻘短阵헳ꎬ，?A2?=? ?(1?，ꎬ?lꎬ，?l)??T.ꎮ因틲듋此?定理得证.证毕定뚨샭理1?붫将鞍닢翻뛈度与폫或믲有폐要튪求쟳权좨的뗄뚨定볛价뷡结合뫏在퓚?ꇆ~? Uk ꎺ= ?1ꎬ，?乌兰ꇝO??k?=ꎺ1?? 튻一起웰，ꎬ폐有훺助폚于볓加짮深샭理뷢解짏上쫶述믲或폐者튪要쟳求좨权뚨定볛债方랽法램?뗄的本놾震훊.ꎮ쪵实볊际짏上ꎬ，헢这샯里뗄的鞍닢测뛈度쿠相떱当폚于믲或폐有튪要쟳求좨权?ꇆ~ (?S?k?(i)? -튻?句(?i)??)Ukꇜ运?O?퓚???룷ힴ첬쿂뗄떥캻볛횵뛔펦뗄???쪱뗄볛?&=1 在t= 2各状态下的单位价值对应的t= 1时的价쯹所以틔?值횵.ꆤ횻只쫇是쯹所쟳求뗄撤测닢度뛈满싺足ퟣ?q:?:+?1=????挥主???CkPkꎬ，?ꎬ?ꆣꇆ~ S?k(? i?)?uk?运ꇜ以???-i?)否럱期퓲存듦在퓚套쳗和샻I机믺会믡.ꎮ?벴I!P u뿚为캪s?(?1?)?，ꎬs?(?2?)?.ꎬ…ꆭ，ꎬS?(?时??的뗄上짏轶事닢毒度뛈;ꎻ떱当컊问쳢题?定뚨理샭I?可뿉转述쫶为캪?(??鸟??〉뗄的ퟮ最폅优뷢解듦存퓚在쪱时ꎬ，평由쿟线탔性맦规뮮划뛔对얼偶풭原샭理知횪?定뚨理샭l'??或믲有폐要튪求쟳权좨在퓚t?=? 1?时쪱的뗄싴卖方랽套쳗利샻?볛룱캪?좷n1l1?????(C) = max主~CkUk 价格为pE k=i 뛸???????1?.ꎮ2?? 状ힴ첬态马쒫下쿂或믲有폐要튪求쟳权좨在퓚t?=? 1?时쪱的뗄买싲方랽套쳗?吗(C)= m!l墓~CkPkP’=’P k=1 和샻i价볛格룱?웤훐ꎬ??ꇝ?ꎬ?ꎺ?ꎬ?ꎬ?ꎻꇆ?ꎺ?ꎮ?ꆢ?뗄뚨틥?1?.ꎮ2?.ꎮ1? 퓊允许탭证횤券좯卖싴室뿕和뫍现쿖金뷰借뷨贷듻动뗄情쟩况，뿶?其中，Pk法。，k= 1,2,3; ~Pk = 、φ的定义춬뚨샭?ꎮ?或믲有폐要튪求쟳权좨C?퓚在状ힴ态첬X?j?下쿂的뗄买싲方랽套쳗利샻价볛格룱?同定理1.?ꎮ?ꎮ??횻퓊탭쿖뷰뷨듻ꆢ늻퓊탭횤좯싴뿕뗄?均?(?C)?由평唁(?C?)?=? -튻1?哇(?-튻C?)?确좷定뚨[?1ꆧ]ꎮ则퓲有폐? 只允许现金借贷、不允许证券卖空的쟩뿶?뚨定理샭3?或믲有폐要튪求쟳权좨C?在퓚?t=? 1?时쪱的뗄状ힴ态첬?X?쿂下?j情况샠쯆폚????ꎬ뾼달싴랽쳗샻볛룱뛸??????的뗄싲买랽方쳗套利샻价볛格룱为캪?类似于(鸟)，考察卖方套和j价格吨1(C) = M?i?n言??。뗄的쒣模탍型캪为?琦(?C?)?=?????????ꎬ约旦CkPk?M??in ?????rqn+1 웤其中훐，ꎬp?εꇊ?φ，ꎬp?、ꆢ?φ的뗄定뚨义틥同춬定뚨理샭1.?ꎮ?(?P?3?)?~? A?q? ;ꇝ;:::= z? 1?.ꎮ2?.ꎮ2?? 只횻允퓊许탭现쿖，뷰金뷨借듻贷ꆢ、늻不퓊允탭许횤证좯券싴卖空뿕的뗄?l? q?;? ;ꇝ;:::= 0? (?i? =? 1?，ꎬꆭ…，ꎬπ?)?，ꎬ q?n?+?1?εꇊR? ?情쟩况뿶?则퓲有폐?ꎮ?或믲有폐要튪求쟳权좨C?在퓚状ힴ态첬?X下쿂的뗄买싲方랽套쳗科샻价볛格룱?j定뚨理샭2??若죴问컊题쳢(?P?3?)?存듦在퓚最ퟮ优폅解뷢，ꎬ퓲则믲或有폐要튪?1?ftꇫl (? C?)?由평1f?t?l(? C?)? =? -튻1ꎬ[?’"0’1 (?-튻C?)?确좷定뚨，ꎬ놴黯?有폐?求쟳权좨C?在퓚t?=? 1?时쪱的뗄卖싴方랽套쳗利샻价볛格룱为캪?定뚨理샭4??或믲者폐要튪求쟳权좨C?在퓚t?=? 1?弱쪱的뗄状ힴ态첬月?二?????下쿂的뗄买싲方랽套쳗科샻价볛格룱为캪?均1〈C〉=75三矶웤훐ꎬ??ꎻ???ꎬ???????ꎬ?ꎺ???ꆭ??ꎬ??캪??ꇫ???????1ft1 (C) =巨BECKPK其中，p= (Pl>P2，P3严，善=善1n…n~泣，ø;为???ꆮ??
캬웕톶 ꆤ?ꆤꆪꆪ-?1?6?2一ꆤ?ꆪꆪ?쾵系?统춳?工릤?程돌?学톧?报놨?第뗚1?8?卷뻭?第뗚?2웚期?웤훐ꎬ?ꇊ?ꎬ?뗄뚨틥춬뚨샭?ꎮ?为캪(?1?.ꎮ0?8?8?，ꎬ1?.ꎮ?1?71??)ꎮ웤.其훐中ꎬ，닉采폃用M?a?t?l?a?b编뇠程돌计볆算쯣担쿠?其中，pε善，p、善的定义同定理2.평컊쳢????뫍????벰싲랽쳗샻볛룱뫍싴랽쳗?应펦的뗄线쿟性탔规맦划뮮问컊题쳢，ꎮ?盘问题(P)和(P)及买方套和价格和卖方套13샻볛룱뗄맘쾵뿉횪?????ꇜ뛸????믲?襄맼E??或믲有폐튪要求쟳权좨?C和뫍证횤좯势s?川??、?ꆢs?(?l?)?퓚在ힴ状첬态马??下쿂的뗄价볛筐횵?和j价格的关系可知均(C)运1fÔ(C)(或1r?gl? (?C?)? =ꇜ=:; 1뛸f l? (?C?)?)?;ꎻ另쇭外췢，ꎬ在퓚区쟸间볤收?红?的??，?ꎬ?ힴ첬????????????????????????????????????ꎮ????ꎮ??????????????ꎮ????ꎮ???’1뛸f ( ?C?)?)?(?或믲(1?r?g?l?(?C)?，ꎬ1췫f在1?( C??) )??)쓚内뗄的죎任뫎何볛价룱格对뛔???????????????ꎮ????ꎮ?????????ꎮ????ꎮ?????????ꎮ???或믲有폐要튪求쟳权좨的뗄买싲卖싴主쮫立方랽均뻹不늻产닺生짺套쳗和~샻ꎻ;죴若볛价룱格뗍低???????ꎮ??????????????ꎮ????????ꇞ??ꎮ????ꎮꇞ??????폚??????믲???????ꎬ싲랽듦퓚쳗샻믺믡ꎻ죴볛?맼襄?-于动(C)(或πgl(C刀，买方存在套利机会;若价句횤证좯?券一??{?8?}iꆢ7-? ?{?›?}퓚›在ힴ一精’-A-III-ij 첬?元?，쿂一下뗄的寸볛一份횵一值s-s-a、-?룱듳폚뛸????믲잽????ꎬ싴랽듦퓚쳗샻믺믡ꎮ?τ-v格大于1fÔ(C)(或1fÔl(C片，卖方存在套和j机会，ힴ첬??뿖?1吐句即벴폐有???????????ꎮ????????定뚨샭理5?若죴或믲有폐要튪求쟳权좨C?在퓚t???1时쪱的뗄ힴ状态첬???????ꎬ????ꎮ????ꎮ캻?乓쒫下쿂的뗄卖싴方랽套쳗科샻价볛格룱为캪矿??(?C)?和뫍싲买랽方套쳗科샻价볛格룱为캪?πb(? ?C)?ꎬ，则퓲该룃状ힴ态첬下쿂的뗄无컞套쳗利샻价볛格룱区쟸闰볤为캪?맼?믲폐튪쟳좨뗄볛룱?(?泸(?C?)?ꎬ，?矿(?C?刀??，ꎮ?싴랽쳗샻볛룱?싲랽쳗샻볛룱??퓊탭싴뿕?늻퓊탭싴뿕?퓊탭싴뿕?늻퓊탭싴뿕?撞췆诠싛E??若죴벯集合뫏?φ〈?믲或?善?〉훐中횻只듦存퓚在캩锥튻一鞍닢测??ꎮ????ꎮ????ꎮ?????ꎮ???度뛈，ꎬ퓲则?动??(?C)?=? 1뛸f ( ??C)?(?或믲1?rg??l?(?C)??= 1뛸f l?(?C?)?)?,ꎬ벴ep? 此듋时쪱，ꎬ믲或폐有튪要求쟳权좨的뗄份볛格룱惟캩一튻.ꎮ?4?? 结뷡쫸束语폯?2? ?t? =? ?0时쪱믲或폐有要튪求쟳权좨的뗄套쳗利샻价볛格룱??(?1?놾)컄本뾼文달考察쇋了폐有쿞眼횤证좯券쫐市뎡场믲或폐有튪要쟳求좨权的뗄?定뚨价볛方랽法램，ꎮ뛔对폚于쪱时볤间뛎段不늻为캪2?和뫍/ꎯ:믲或ힴ状첬态쫽数늻不캪为3??用폃第뗚1?节뷚的뗄方랽法램뿉可以틔뗃得到떽믲或有폐要튪求쟳权좨在퓚状ힴ态첬?的뗄쟩情뿶况횻只탨需붫将짏上쫶述랽方램法볲简떥单탞修헽正即벴可뿉得뗃到떽裙쿠关맘?2쒫5쿂下的뗄套쳗利샻价볛格룱，ꎬ볇远캪为乌?ꆺ(?j?ꎬ?= 1?，ꎬ2?，ꎬ?到?ꎻ;붫将?鸟?쫓视为캪?结뷡论싛:ꎻ?튻一个룶"ꆰ탂新ꆱ"뗄的믲或폐有튪要쟳求좨权퓚在ힴ状态첬t?=? ?1的뗄ힴ状첬态乓훃下쿂??(?2)?퓚在上짏述쫶分럖析컶中훐，ꎬ캪为了쇋简볲单떥，ꎬ볙摆짨设컞无럧风撞쿕利샻?的뗄价볛值횵，ꎬ닉采폃用폫与第뗚1?节뷚完췪全좫一튻致훂的뗄方랽法램，ꎬ뿉可以틔뗃得到떽?率싊为캪?0ꎬ，헢这튲也쫇是탭许뛠多컄文献쿗的뗄习쾰惯맟性탔假볙设짨，ꎬ一튻方랽面쏦，ꎬ?该룃或믲有폐要튪求쟳权좨在퓚?t=? 0?쪱时的뗄쳗套샻科볛价룱格和뫍无컞套쳗利샻价볛?这헢样퇹处뒦理샭讨쳖论싛较뷏方랽便뇣:ꎻ另쇭一튻方랽面쏦，ꎬ뛔对뷡结싛论늻不듦存퓚在놾本?格룱区쟸间볤，ꎬ룃该볛份룱格뫍和컞无쳗套샻利볛价룱格쟸区볤间벴即캪为믲或폐有要튪求쟳?质훊탔性的뗄影펰畹쿬;ꎻ틲因캪为헢这퇹样뒦处샭理뿉可샭理뷢解캪为ꋙ①对뛔真헦实쪵的뗄?权좨C?在퓚t??= ?0时쪱的뗄价볛格룱和뫍无컞套쳗利샻价볛格룱区쟸间볤.ꎮ?经뺭济볃系쾵统춳经뺭无컞风럧险쿕利샻率싊折헛现쿖，ꎬ形탎成돉新탂的뗄经뺭济볃系쾵统춳:ꎻ?②ꋚ对뛔薪탂的뗄经뺭济볃系쾵统춳进뷸行탐担쿠应펦的뗄分럖析컶和뫍讨쳖论싛，ꎮ当떱?3? ?示쪾倒샽?然좻，ꎬ퇏严룱格뗘地붲讲ꎬ，쯤虽좻然춨通뎣常볙假짨设无컞风럧险쿕利샻率싊为캪常뎣数쫽，ꎬ?但떫实쪵际볊짏上컞无럧风险쿕不늻一튻定뚨为캪常뎣数쫽，ꎬ틲因듋此헢这튻一샠类ퟷ作法램?假볙设짨市쫐场뎡有폐?2种훖证횤券좯s?(?O?)?，ꆢ?s(??1)?，ꎬ无컞风럧险쿕利샻率싊?存듦在퓚着ퟅ共릲同춬的뗄缺좱陷쿝，ꎮ这헢已틑超뎬出돶了쇋本놾文컄的뗄讨쳖论싛范랶围캧，ꎬ?为캪?O.ꎮ或믲폐有要튪求쟳权좨C?뫍和횤证券좯抖??的??、ꆢ?抖??。?퓚在ힴ状态첬?ljk不늻再퓙论싛及벰，ꎮ?下쿂的뗄价볛值횵及벰证횤券좯?s(?O?)?，ꆢ?s(?1?)?在퓚状ힴ첬态乓쒫下쿂的뗄价볛值횵由평??(?3?쇭)췢另外ꎬ퓚，룼在튻更一냣般뗄的쳵条볾件쿂下，ꎬ죧如ꎬ，듦存퓚在붻交틗易?表뇭1?和뫍뇭表2?给룸出돶.ꎮ볆计쯣算뷡结맻果볻见뇭表?3.ꎮ?成돉本놾、ꆢ붻交틗易춷头듧寸풼约쫸束짵甚훁至샻利폃用쒣模뫽糯벯集뫏合살来쏨描述쫶或믲?允퓊탭许싴卖空뿕时쪱的뗄无컞套쳗科샻价볛格룱区쟸闰볤为캪?者폐튪要쟳求좨权的뗄늻不좷确定뚨性탔等뗈，ꎬ뿉可틔以뛔对놾本컄文뗄的랽方램法뷸进行탐?(?1?.ꎮ?1?2?2,ꎬ1?.ꎮ1??7?2)? ，ꎬ늻不퓊允탭许싴卖뿕空쪱时뗄的컞无쳗套샻科볛椅룱格区쟸间볤?适쫊当떱的뗄扩삩展햹来살讨쳖论싛，ꎬ部늿分럖结뷡果맻可뿉参닎见볻文컄献쿗口，??剖ꎬ?，?ꎮ?参닎考뾼文컄献쿗:ꎺ???????[1] M凶?i?el?a??M，ꎬ?跑?跑??侧?s??k?M?.ꎮ M?a??r??位?职?l?e?M??e?tho??d?s ?????????????????ꎺ??????????????????????ꎮ?????ꎬ?????????ꎬ????in Financ姐lModelling:Th回'ry8I对A冉蓝佣后on[岖.Berlin, Heidelhe哩，NewY?o?r?k:ꎺ输??也?伊咽血???事?，?ꎬ?1势???7.ꎮ部??.ꆪ-f?T?l?{?쿂下辛苦뗚第1??7?6页튳〉??
캬웕톶 ꆤ??ꆪꆪ???ꆤ?ꆪꆪ?系쾵?统춳.ꎮ릤工?돌程?学톧?报놨?第뗚?1?8卷뻭?第뗚?2期웚?-176一参닎考뾼文컄献쿗:ꎺ?[?1?]?H?e?r?r?er?a?言?，ꎬ?He??rr?e?ra-?V??i??~ꎮ? E?ꎬ, V?，??但?也??ga?y??J? ?L?.ꎮ ?A? ?li?r明???白?c??d?e?c?i?si?o?n?阳????耀????m??伊??1?p??d??ec?i?si?o?n ?pr?配??幡????in?g?r?m?.?写?fl?de?c?i?s?io?n?脑??网??[?后??，?ꎮ?G?r?o?t?罢?p?D?l??到?si?o?n?N?唔晦??a?t?ion，ꎬ'?1现??汤?，ꎬ(?5?)?:ꎺ1?6??5??-1??7?6? ?[?2?]?M配??i?m?in??V? M?，ꎬ?出?恤?1?0??1,ꎬ T??a?m?u?r?a ?H?.ꎮ L?i?n?醉?自?岳c???I?a?h?e?l??s如?假严뎰四?吨?缸r?L??Y??严??哩?f??e?r?e?n?c?e?r?e??la?1?i?on?s?? ?i?n?缸?呵?g?r??m?.?I?P??企??CI?由?拥?皿??岳?吨?[??J?]??.ꎮ????ꆪIEEꆪE?ꎮ T?r?a?n?s??削??侧??但???每?酷??嚣?，?施ꎬ应??，?ꎬa?n??d ?C?y?b?e?n?四???倍?P?a?r?t?B?:ꎺ C?y?b?e??n建??烛??，ꎬ?1鳞??，?ꎬ2??8?(?2?):ꎺ 2??0?5ꆪ-ꎮ2?1?8?? [?3?]? ?He??rr?e?ra ?F?,ꎬ H?e?rrera?吊??e?d?ma??E?,ꎬ? Ver由自'f1yJ? ??L.ꎮ?臼?r?ec?t???a?pp?r?时????E?阳?回???s??e?s?i?n?罗??u?u??p?缸???i回??拥阻??捡?喀??四??吨?均??.?ñ??s??t??i?c???O?WA???等??四??百?阳???[?1??].ꎮ ?F出??z??y?S?t?堕?s?a?n??d?句??跑?到圃?，ꎬ1?现??汤?，ꎬ7?8?:ꎺ?7?3ꆪ-8?7?? [??4]??He??rr?e?ra F?,ꎬ H?e?rrem?-V?i?e?d?m?a E?,ꎬ Vꆢꎬe?r?曲事'f1yJ?? L?.ꎮ A?? r?nt?io??n??a?I??∞?翻??回?U?SI??D?(??副?部?箩??u??u?p?de?c?i?si?∞??皿?挝?电?部??啤?坠??耶?.?ú?s??l?i?c춧811配?回回嘘쓄[1ꆾ]??.ꎮ?F?t?J?Z?:?i?!?亨?&?也?a??n?d?句??就?ꆮems，ꎬ1??好?几?ꎬ8?8?:ꎺ3??1ꆪ-4?9?? [?5?]? H?e?r?r?e?ra? ?F,ꎬ H??er?re??m?-?V?ie??d?m?a? ?E.ꎮ ?L?i?略??部c??勘???:?O?Oo?n?皿??a?l?同??s:ꎺs?t?ep?s? ?f?i由型?运回可???;?d?e?c?i?到?m??严??ub?l?钮?I?S?u?n??d?e?r ??li?r伊???sb?C??in?fo?n?n?a出???1[??币?，ꎮ??F???????????????ꎬ????ꎬ???ꎺ??ꆪ???llrLY st也and句瑛em酶，2α泊，115: 67-82 [??6]?刘쇵学톧爱낮，ꎬ샮李永폀畴쏷，ꎬ쪷史훒忠뿆科.ꎮ튻一훖种믹基폚于폯语퇔言变뇤솿量的뗄M?∞??M?问컊题쳢的뗄决뻶策닟方랽法램[?且??eꎮ系쾵统춳工릤程돌，ꎬ?20?0?1?ꎬ, 1??9?(?5?):ꎺ ?2?8ꆪ-3?2?? [?7?]?胡뫺应펦子욽基ꎮ믹于模폚糊쒣语뫽言폯群퇔体좺决쳥策뻶的닟一뗄致튻性훂梅탔词킭技뗷术벼[쫵1?]??ꎮ.쾵系춳统工릤程돌学톧报놨，ꎬ2?邸??，?ꎬ1??5?(?2?):ꎺ ?1?4?8ꆪ-1?5?2?? [?8?]?H?e?r?r?e?r?a? ?F?,ꎬ 1?如??r?e?m-?V?i?e?d?m?a??E,ꎬ Vꆢꎬe?r?曲事.y?J ??L.ꎮ C?h?o?i?c?e?阳????剧?????f?or??即????阳???n?og?en?e?o?凶????严??p???邮???si?on?m?a同??inl??ir?耶???邸?c??蜡????E恕[?1?]?.ꎮ? F?凶??町???S??也??a??n?d?句??磁??层ns，ꎬ惯??法??，ꎬ?94?:ꎺ笃??7?一?立法?[??9]?H?e??rr?er?a ?F?,ꎬ H?e?r?r?er?a?-V??ie??d?m?a? ?E.ꎮ A?m?ꎮ唱?阳??等???四???幽??'1?5?岛?r?坠??明???白C??w?e?i?g?l?叫?她??口??国???阳?[??1?]ꆾ?.?ꎮI?ꆪE?Eꆪ?Eꎮ ?TI回??国??血??牺????o?n?每?ꎬꎬ?班?础，ꎬ?施?n?，ꎬ?a??n?d? C?y?I?Je?n?v?;?现?臼-?P?a?r?t?A?:ꎺ句??뎰磁e얦msa??n?d? ?Hu?n?四?毡?，ꎬ1??野??7，ꎬ?2?7?(?5?):ꎺ 6?4??(?卜-??65??6?作ퟷ者헟篝볲介뷩:ꎺ?王췵政타荣죙(?1?9?7?7?一튻)?ꎬ，얮女ꎬ，뫓河놱北쟘秦믊皇岛떺入죋，ꎬ늩博士쪿生짺.ꎮ퇐研뺿究方랽向쿲zꎺ决뻶策닟理샭论싛与폫应펦用폃.ꎮ?樊랮治훎平욽(?1??96?1?一튻)?ꎬ，쓐男ꎬ，붭江쯕苏헲镇江붭人죋，ꎬ博늩士쪿，ꎬ뷌教쫚蟹，ꎬ늩需쪿士짺生떼导师쪦，ꎮ퇐研뺿究랽方向쿲zꎺ뻶决策닟理샭论싛与폫应펦用폃、ꆢ信탅息쾢技벼术쫵与폫管맜理샭等뗈.ꎮ?{?짏上뷓接뗚第?1?6?2页튳〉??[?2]?쳆唐焕므文컄，ꎬ쟘秦톧学忘횾.ꎮ쪵实F폃目ퟮ最폅优뮯住方랽法램[??岖?，ꎮ大듳连솬:ꎺ大듳连솬理샭工릤大듳学톧出版돶社냦，짧立ꎬ?泪??。??[?3?]? ?Wu? ?C?h?o?n?g?-?f?i吨??，?ꎬQ?i?n? ?Xu?←???也??ꎮF?l?l?r?L?Y?c?r?e??di?hl??e?峙???世???pr?i?CÍ?I喀??酣??也?o?d??f?o?r ??c?o?n?由?伊??酋??c?l?a?i?m?i?n? ?fi?ni?也??m???如?????wi?也??始??回???r?p?啤?阻뻗四ꋲ??吨ꆿ??[?A??].ꎮ I?n?D??Li,ꎬ X??Q??也??i?ꎬ，?e?t al e??dꎮ, p?m?<??精??通?n?g?so?f?t?h?e??沪??h?阳??回??t?io??n?a?I?也??nf??e?re?n?c?e?o??n? Ü?J?:?现?m??础?。?n?:??Te?c?h?r?ú?申???晤???时????A萨????c?a?b?晒???[ꆾC??].ꎮ H?o?ng? ??K?on?gꎺ:?臼??l?t??eI??耶?路??巧?D??e?v?d??啊???附???臼???叩??n?y?，ꎬ2??0?0?1ꎮ.1??2?5?3?-1?2?6?1? ?[4?]?쟘秦学톧志횾，ꎬ컢吴돥冲럦锋基ꎮ믹于鞍폚幸日뫍线쿟性탔规맦划뮮对뛔偶얼原풭理샭的뗄或믲有要폐求튪权쟳的좨定뗄价뚨方볛法랽[램1?]??.ꎮ控뿘和훆i与폫决뻶策닟，ꎬ?2?00?1?，ꎬ?(퓶增刊뾯)?:ꎺ8?4?←??割???8?作ퟷ者헟简볲介뷩:ꎺ?쟘秦学톧志횾(?1?9?6?5?一튻)?ꎬ，쓐男ꎬ쇉，辽쓾宁듳大솬连죋入ꎬ늩，薄쪿士ꎬ뢱，뷌副쫚教授ꎮ，퇐研뺿究랽方쿲向ꎺ:뷰金죚融릤工돌程폫与쾵系춳统릤工돌程eꎮ?컢吴冲돥锋럦?(1??9?6?2一튻)?ꎬ，쓐男ꎬ，헣浙붭江컂温훝州죋入ꎬ，늩博쪿士ꎬ，뷌教쫚授ꎬ늩，博쪿士짺生떼导쪦师ꎮ.퇐研뺿究랽方向쿲zꎺ金뷰融죚工릤程돌与폫系쾵统춳工릤程돌.ꎮ?
