2007 11 h p Vol. 10, No. 4, Nov 2007 žç Êu Š»! http://cmr.ba.ouhk.edu.hk
Š Òš 1 žç Êu Š»! såžk Black and Scholes1973 à u Rubinstein and Leland1981²kÄÇ Ê}pÄqåžgukà ÊOption-Based Portfolio Insurance, OBPI uh½ ç Rough Set TheoryFuzzy Theory ž Grey SystemÔ ÊContingent Portfolio Insurance Ð à Äq~Â Ê}Ä q~ ÂÌ Ê ³ isåžkp w m ÄØ àåžváåžà 1992 1 h 2003 12 h ÊÊç Š»! vpæ ž! vpæ ž
Š Òš 2 õé Ê}pà Ád s² àgk Êáfh ð ð }n uåž} w sõ ÊÌ~ }qâ Êʹ qâ Í Ê v s} }à~¹ zê}äq~oùýêj} ïš 1999ukà Ê ½Ì à Äq~ ÂØ Ê í Áw si³e lâ~sd½ ³i páw s ïé Á îd}ì Á Øks à såžkpäqàåž Ê}pÄ qn ³Ê} såžukà Ê dºkeç u Êkh½½Ì à Äq~ ÂØkÄq }Äq~ ~h ÂÌ ÊÁ kïšáp Ê såžvá 1 l Ê 2 ih½½ìl1999 Ê Ð Ê 3 ÊÁ} såžzdààgàåžh½ dº½ç ½à¹ u
Š Òš 3 Áh½i Ê dº½ç ½ke½Ì³ke Á ÕàsåžÁÔ ³ Ê àšqkán à Ê Á Rubinstein & Leland1981lÁ²u ʳReserve Asset~ÇÙ Áðð ³Active Asset~Ääi k ʳ éáêm nu Black & Scholes Á q ÃÁ rt S + P = C + X e rt 1 = S N( d ) + Xe N( d ) = ϖ S + 1 ϖ 2 X e rt 2 SP ŒàʳÁÐ êk Á Ô änk u 1N (d1) ÁÄe21-N(d2) sòà X e rt à r Áðóʳ¹ä{Á k ä{áê¹ pïù ³¼ (1) 1 e2 É ò ÙÄe h ÁÄeð eä ÁÙì }yˆóúä Är 1 ðá 2 (2) Á r¼zì 1 š Ê 2 š ìêôkš äá X
Š Òš 4 3 ÁÄ}ʽ³ 4 Êð r 5 š Á½Ì ½Ì ½Ì àul }Äq½k Á½Ì láá h ½ láçâ½ìe láç½ìk ½Ìh½ ñkìæö Ä y i K%Œ Ä Ú Á Ì ÄàÇgo long i K%Œ} Äu Á Äl}jÌ ÁÁ K%ÌÄ Œlõs Ä ò Âw Â Ä h}ejì Š K%zÄ }Âw òä àâgo short ½Ì } Š K%ÁÄÌ à Œ K%Ç/½Ì} Á li ìä{ åž}áì àá Ãä{Á½ ñæö Ä yš i K%Œ Ä Ú Á Ì ÄàÇ Äl}jÌ ÁÁ K%ÌÄ Œlõs Ä Çð  Äh}ejÌ Š K%zÄ
Š Òš 5 ½Ì } Š K%ÁÄÌ à Œ K%Ç½Ì }såžuç½ì dº½ç ½k l Ê ž dº žgrey theoryùuàæ 1982 ÆÁ }Éþ zá½ àu }ÉþkÁ½à ŒkÆ ÉþÁ z zážà žgrey system žláõešh }ÉþkÀn žás léþ žá Àdu žájìåžûdà u dº žô še ž 1996k dº Á dºás²ùä³á dºqù z Á ˆ ÀÁä Ô ËÙŒdgÁÙÔÁ à Ô ÙÔÁíé1993 dºá ~ izª z X 0 = ( X 0 (k) k=1,2,,n ) à zàsz X i = ( X i (k) k=1,2,,n ) àizàz i=1,2,.m Ìh½m Æòd X( k ) X ' ( k ) = X( 1) òd X( k ) X ' ( k ) = max X ( k )
Š Òš 6 òd X( k ) X ' ( k ) = min X ( k ) qòd X ' ( k ) = X( k ) X( k ) òd X ' ( k X( k ) min X ( k ) ) = max X ( k ) min X( k ) zizáü z } o ( k ) = x ( k ) x ( k ) Δ 0 ü z i=1,2,m, k=1,2,n i i lüò = maxi maxk Δoi ( k ) üò = mini mink Δ oi ( k ) ìë u r oi min min Δoi ( k ) + ρ max max Δoi ( k ) ( k ) = Δo ( k ) + ρ max max Δo ( k ) i i àdž 0.5 ìô n 1 roi ( k ) = roi ( k ) n k u l fuzzy theoryùuçm ÜŠdÁsL.A. Zadeh 1965 lákl fuzzy setsá²k íuþ À³ÁkÐ í Á Á²æk± ÁËï kòbinary logic í ÀÁ
Š Òš 7 Ð Á uãá {}ägl~ {Á }~u Á h zp 1 Ð ÐÁ nuó{a,b,c} mkš x a c x Trangle(x;a,b) = max (min(, )) b a c b Ð Ð nupó mkš x a d x Trapezoid(x;a,b,c,d)=max(min(, 1,, 0 )) b a d c 3 Ð Ð ~ gaussian(x,σ,c)= e x c 2 ( σ ) 4 {Ð Ð ~ 1 Bell(x;a,b,c)= x - c 1+ ( ) a 2b Áì } ³ n uãj wnuì½ nòûuˆh ÁõÌÙì h íps p qf Á ~ S Ðe π Ð š Á ÂýÊÁ̪ Á lánàù½ìá kàuá
Š Òš 8 1 Mamdani Mamdani Ù u½ lžlòjlòzmkdn Áò 2 Sugeno Sugeno Ùk~ Áh Æv ÌÁ kmq½ìh kžõlòu là~ Ù zád 3 Tsukamoto Tsukamoto ÁÌÙ k Ævj ÌÁlãÙuÌÁò uáòžõlìù ÌÁlòm q Ž ÁlÁ òcrisp value àddefuzzificationdáh½ Ô~ h½ Ç{mkuàuÁ z ïg½center of gravity ïg½center of area, CoA ½Ù ¹~ ïáïg ïgá òùõ Álò ªïg½center of sums defuzzification ½ïg½ä{ Áü } ïáìïì ïg½âìl Áïg ªïg½ÌÙó ì qò½mean of maximum defuzzification ÔòàdÁlòê{ ~Ô òì qò ïg½center of largest area defuzzification ½àìï ïáy gœàdálò
Š Òš 9 ç k ç Ás²Ãê ìn g Pawlak 1982 1ž IS Information System IS = ( U, A) U A³ f a :{ U V, a A} a Va³ò 2n ËIndiscernibility relation ³ B Aón Ë Ind(B) ~ óàx x i ª x j } ³ B Ùn Á~¹ b( x ) = b( x ), b Bó Ind (B) òàn Ë i j 3çªçLower and upper approximations ó X m U ( X U ) j X }³ B ( B A) à BX ç à BX Áç BX BX = { xi U [ xi ] Ind B) ( X = { xi U [ xi ] Ind B) X } ( 0} 4òAccuracy of approximation } X } B j B m ³ A ( B A) μb ( X ) = card( BX ) / card( BX ) 5v³Independence of attributes Ì X Áò ~¹ Ind( A) = Ind( A ai ) Ì a ÙrìÁ ò a } AÙv³ i i
Š Òš 10 6gªd³Core and reduct of attributes ~¹v³ a i ždná³ Ì n àd³~d³rnfá³ àg³ 7dClassification F = { X1, X 2, L, X n}, X i UÙ U Áó j F ï x X i X j = φ j X i = U, i = 1,2, L, nì F àu Ád X i à Classes çdlower approximations of F B F) = { B( X ), B( X ), L, B( X )} ( 1 2 n çdupper approximations of F B F) = { B( X ), B( X ), L, B( X )} F dî η = card( B( X )) / card( U ) B F dò β = card B( X )) / card( B( X )) B i ( i i 8šÆDecision table ( 1 2 n óž IS Æm³ Aeš D òàšæ 9D-~³D-superfluous attributes ³ a i B, B A~¹ POSB ( D) = POS ( B a ) ( D) Ì a i Ù D-~³ 10šÌDecision rules šìnkæv~ ak i d j ak س a i k iòj Ø«d j Øš d jò äåž ÊÁ²Ç }pâàð âáï Ù} 1980 kkõäág ~ÈÕÙ }l SPO B&H Ù uá Ê i
Š Òš 11 } syvìp SPO Áäåž ì³á š Zhu Kavee1988 u}n½ SPOSPQe«i CPPI ÊÁi¹q½³ SPO w sj CPPI ÌäŠFischer Jones 1987Ág CPPI e SPO ʪ B&H Á i¹qù eá½ u SPOq Ùe ïì u CPPI Perold & Sharpe1988 Á ip{b&hb&h«cppi e Á ʹ ~ Ênkm êá½ìæ ÙüGarcia and Gould1987i {ìêô Ê kó1.} w sìêôš q~ B&H 2.ê w sìæ B&H 3. Ê}Ânk u }~~ B&H 1999kà ÊOption-Based Portfolio Insurance, OBPI½Ì à Äq~Â Ê SPO ª B&H i kpó 1.}~k B&H 2.}ÂSPO Á Êe B&H3.}SPO Áà üã Ê}w sõ nš B&H4.} Ê Áw s ïé Áº1992ˆ i SPOCPPI e³ ÊTIPP ÊÁ¹} àä{æêôçqsk SPO CPPI TIPP à 1991 SPO e³û åž Ê Äi Á ³ SPO Ìu ~ 1990 u Zhu & Kavee Áåžh½ SPO CPPI ˆ¹q ã~ B&H
Š Òš 12 m1996u CPPI SPO}çpÄqÁÊ ¹vCPPI SPOjìÊÔç pìêôšìe1997kpäø à¹v straddle ðá ³} ³hïk³ Á ³ p Êäåžnk Á³{ uáä{ Ê}Ânk u e~ B&H f }q w sá Áòuä È æ såž åžsàp w mäøåž à 1992 1 h 2003 12 h uámø ÁÄØ w Äw g w Þ ä pý~ kôkà Ê h½ dºç u ½Ì Êk h½ íåž dº½ u qkàjáá~ˆr «Áh ûâ Áh àhùnuu } Á s u Á Ùäu Áh½ Ái lqkk MA Æv kæœnmk s l dºh½œù u q l Áþ š s N há { ½Ì ÁÄ ÃÁÂÙé ÁufÁw ïšw sk Á ~ 3-1 dº½åžþ sh½ùk½ì dºkk Ævà jì eh½ ~
Š Òš 13 sh½y u½ì Äq~  zu dº š s N há} dº}m w eä ¹k Ì àhé GRG } ydºüüw eäüüd ìl M háq Õ Ì x - min X x ' = max X - min X min X àz X Áòmax X àz X Áòx àz X Á Ú~ 01 Ôv Ð GRG dºáôäû ì s ŒÙ z Ù u GRG ä ÔÁiÉ
Š Òš 14 Æ dì Ä ½Ì { ½Ì Á dº É {½Ì Á ÐÐ Œ w Œ 3-1 Ù ìòw s äæ È q 3-2 GRG ¾ù ˆ 200246ð
Š Òš 15 u iá Ðì y l ~ 3-2 v pkæ à ÐkepkÆà Ðzm óqð~ z Ð MA GRG dº ä ÔÁ ÐŒnkÆ MA Á ~ nu z s Á u }Ì M hqzá 01 } }Ôvó GRG Ð ÐÁw } 01 khé pæ d } u Black & Scholes Á k Æ ów hàç ʳÄeÇ y GRG dº Á uìí½ì Äq~  ê i Ì GRG dº1. yš GRG dº uáe t ó } MA GRG dº ä Ô ÐŒnkÆ} MA Á 2. u dº} w keäó }Ù} GRG dºõ ó u~ š ~ ódº} GRG dºõá Ðà óà Ì à3. ê GRG dºõàà½ìä{ Ì Äq~ ï ÁÇÄk h 4. eê GRG dºõ¹½ìä½ èìàù õ ÇÄ yˆ GRG dº e~¹ i w GRG dº1. GRG dºh ½~{Ìí GRG dº¹áä½½ìä{ì Äq ï Ì ÊÁ ïìl Ä Ç ÌÁÄÇ k
Š Òš 16 ÊÁ¹2. ê Ãä½ä{Ìà õ ÇÄ yˆ êä}i ÌàÆvÄq õ ~  õ ~ ÂÁ ½ÌŒê~ êâ Ê ìsòw s ç ½ Áh½ Ô~ u~e{ MA Áz½ ŒàÉÁh½êeÁ MA }eá MA Ìn à~ze àâzç ½ŒÙy u nk±á mw keäu Áqz þ ìôvnuá fuzzy rule ç km Ô s½ì ÁÄ ~Â~ ~Âq ÌíóÁ MA zu ÁìÕzls n h нÌÁÂÙé Ákf½Ì}Áw ïš Á såžh½ùk½ìkeç à jìdº eh½ndàôvìýç ½Ì d~ 3-3 v
Š Òš 17 Æ dì Ä o Ì { ½Ì Á ½Ì É Fuzzy Ì {½Ì Á Æ Fuzzy Rule Rough Set d Rule Fuzzy Rule 3-3 Œ ìòw s f æ þ ö u ìôvìý òìná lnuáìôvì ýz uç Ìý jì ~ w Œ Ù }Ôvýy unk±ámw keäó
Š Òš 18 Ì n päqàâ z n ól ó Á óu qma Áz nu 3MA/12MA Á à Á ~ P_ma K i = mean i Á i K hqz ê P_ma K 1 >= P_ma K 2ÌÚ}àp_trend = 1 K 1 < K 2 eàp_trend = -1 } n p_trend Áò ÚÁ k kwù~ Á n ókæáà~æ 3-1 ̹ v ð 3-1 õã h h w 1 810104 810130 1 1 1 1 1 2 810207 810218-1 -1 1-1 1 3 810219 810302 1 1 1 1 1 4 810317 810502-1 -1-1 -1 1 ÔvÌý ÔvÌfuzzy ruleýì uìá¹ ó kôv Á fuzzy rules Rank = há há/e if rank >= 30then rule = 1 if else 0 <= rank < 30then rule = 2 if else -30 <= rank < 0then rule = 3 else -30 < rank then rule = 4
Š Òš 19 êùúàl ruleìæv fuzzy rule pz } MA võïìâ yˆóä{à}{á rule ~ Æ væ Á fuzzy rule Ôv ~Æ 3-2 v ð 3-2 ð fuzzy rule Î h h w rule 1 810104 810130 1 1 1 1 1 1 2 810207 810218-1 -1 1-1 1 4 3 810219 810302-1 1 1 1 1 2 4 810317 810502-1 -1-1 -1 1 3 p uç dì êæ 3-3 ào ÔvÁ fuzzy rulešæ z 10 ók u x1 ~ x10d kæ 1 10ó³a1a2a3 keu Ìku ÆvÁšÆç dìá² ~ ð 3-3 ÎÄð U a1 a2 a3 Ì U a1 a2 a3 Ì 1 2 1 3 1 6 1 1 2 3 2 3 2 1 2 7 3 2 1 2 3 2 1 3 1 8 1 1 4 3 4 2 2 3 2 9 2 1 3 1 5 1 1 4 3 10 3 2 1 2 ÔvÆ ðyyôvóæ ÆûÀx x i ªx³ a j ÁËê b( xi ) = b( x j ), b BÌ x i ª x j àn Ë 2.5.1 2Ì {ó set~æ 3-4 x 1 x 3 e x 9 } ³ a 1 Áòà 2 ³ a 2 Áòà 1ke³ a 3 Áòà 3Ìn{ x 1, x 3, x 9 } à{
Š Òš 20 ð 3-4 Œð U a1 a2 a3 { x 1, x 3, x 9 } 2 1 3 { x 2, x 7, x 10 } 3 2 1 { x 4 } 2 2 3 {x 5, x 8 } 1 1 4 x { 6 } 1 1 2 Ôvn Ë àì ² ÁËr lg³} yôv ón Ë~Æ 3-5 }*Æv 1 ª 3 a2 óx³ üù½³ a a 1 3 1 ª 3 Áü kk ð 3-5 ô 1 2 3 4 5 1 2 a 1, a 2, a 3 3 a 2 * a 1, a 3 4 a 1, a 3 a 1, a 2, a 3 a 1, a 2, a 3 5 a 1, a 3 a 1, a 2, a 3 a 1, a 2, a 3 a 3 š gcore³ 2.5.1 5 e 6 Án ËÁò zuqºkádh½ g³ a 2 a 3 ~ f ( A) = (a + 1+ a2 + a3 )a2 (a1 + a3 )(a1 + a3 )(a1 + a3 )(a1 + a2 + a3 )(a1 + a2 + a3 )(a1 + a2 + a3 )(a1 + a2 a3 ) a3 f ( A = a 2 a 3, í ) Ævn Ë d~³ } lg³õ ÙŒ} ³~Á³Ù ³Á} Á ² Ä
Š Òš 21 Á Ù}³ a1 Õ~Æ 3-6 vn õy Á g³rênn ð 3-6 ŽþëŒð U/A a2 a3 { x 1, x 3, x 9 } 1 3 { x 2, x 7, x 10 } 2 1 { x 4 } 2 3 {x 5, x 8 } 1 4 { x 6 } 1 2 d d~³õsåžz d d yáx³òª ÙŒ ~ÁndÁ³ dry l iág³œôv f i (A) Ë ½ í 3 i Áò~ nzó f ( A = a + a a a a = a a 1 ) ( 2 3) 2 3 3 2 3 f ( A = a + a a a + a a + a = a 2 ) ( 2 3) 3( 2 3)( 2 3) 3 f = 3( A ) = a2a3( a2 + a3 )( a2 + a3 ) a2a3 f = 4( A ) = a3( a2 + a3 )( a2 + a3 )a3 a3 f ( A = a a + a a + a a + a a = a 5 ) 3( 2 3)( 2 3)( 2 3) ïó nklõdá¹~æ 3-7 v ì êùáqz 3 h 12 hðyì l n óá óqüáqò u n óqò lòòk ma(3-12) maxe ma(3-12) m in ÆvÕzd ÔvÁ~ 3-4Á ~ 3-5 ab àçj cd wà Ç ä{áh½zd Ôvl Á 3 3
1.5 0 Š Òš 22 ð 3-7 Žþ Œð U/A A2 a3 Ì { x 1, x 3, x 9 } 1 3 1 { x 2, x 7, x 10 } * 1 2 { x 4 } 2 3 2 {x 5, x 8 } * 4 3 x { 6 } * 2 3 *Æv} a ma(3-12) b 3-4 ˆ«ëÐ ÃŽª 3-5 ˆ«ëÐ ðy fuzzy rule ïòkeá ïòd ìà 1006734ke 0 êù fuzzy rule s ÁÌ Ìïòà 50z duïg½center of gravity Õ Á¹ŒÙÁÔò æþ Á ó yu fuzzy rule ~ˆ½Ì ~ Æ d c d ma(3-12) 1.5 0 a } u Black & Scholes Á k Æ ów há àç ʳÄeÇ y b ma(3-12) c d ma(3-12)
Š Òš 23 Ì Á UÔu 6080 Áò i Ì Ì1. fuzzy rule dº} ìáquáõkôv~á Á¹Œà }~eâáô2.â } ~eâôôv~á fuzzy rule } w Ùu min ½ u ( x ) min( u ( x ),u ( x ))) A B = A B ( X ) = Ùu max ½ u max( u A( x ),u B ( x )) 3.} d uïg½ ìõ Á¹ŒÙÁÔò4.ê ò UÆv ÌÁä½½Ìä{Ì Äq~ ï ÁÇÄk h êò UÌà õ ÇÄ yˆ Ì e~¹ i DÔ D ò 2040 Áò Ì1. ÌÁh½~{Ìí ïg½ ìláò D òæv Ì Áä½½Ìä{Ì Äq ï Ì ÊÁ ïìl ÄÇ ÌÁÄÇ Á k ÊÁ¹2.êò DÌà õ ÇÄ yˆ p êä}i ÌàÆvÄq õ ~  õ ~ ÂÁ ½ÌŒê~ êâ Ê ìsòw s A B
Š Òš 24 Èãä }s Ê ½Ì Ê à l1999³ ið y{ i Äq~ {q i}ihï u 1%2%3%5%e 8%{i³Ìu ü½z dà k dï³overlappingsåžà ¹Ç q Ù w sá½ Æ òà 100 Š ³ë Æ 4-1 Æ 4-4 d våž Ê³ } { ink k Á } { Á¹äé Ê Á Á ³ GRG dº½ç ½ ÁÇ Á Á ³j ½Ì GRG dº½ç ½ ÊÁi GRG dº½} à ç ½v GRG dº½ u}à Á ç ½} à kh½ævç ½u}Ç Á Êä{i ½Ì ÊÁw sæv Áw s såž GRG dº½ç Ì ŠÁw s Ævsåžh½ s Äee~ké w sôé Á
Š Òš 25 Á ç ½} à 72.3%Á Ám Á q ïáv Ç ð 4-1 Á Š Á ó äð Ê ³ ì GRG dº ç ½Ì ð 4-2 (2%) (1%, 31-71) (3%) (8%) q 1,205,398 1,193,801.0 1,150,037 1,073,129 1,065,030 20.5% 19.4% 15.0% 7.3% 6.5% w s 20,575 16,858 36,692 8,348 6,797 ò 880,510 850,226 920,571 881,296 538,043 ò 1,898,244 1,994,944 1,846,412 1,169,461 1,800,295 ü 299,284 324,196 272,331 213,220 361,875 ÁÏ Š Á ó äð Ê ³ ì GRG dº ç ½Ì (1%) (1%40-60) (5%) (8%) q 1,216,453 1,198,593 1,215,432 1,037,813 1,098,346 21.6% 19.8% 21.5% 3.8% 9.8% w s 38,674 37,977 30,706 13,799 7,250 ò 797,375 852,228 783,370 828,860 630,250 ò 1,754,783 2,138,821 2,034,251 1,899,498 2,112,901 ü 325,323 368,485 330,939 338,385 425,717
Š Òš 26 ð 4-3 ð 4-4 Á Š Á ó äð Ê ³ ì GRG dº ç ½Ì (2%) (1%30-71) (5%) (8%) q 1,292,629 1,378,017 1,164,921 995,264 1,165,318 29.3% 37.8% 16.5% -0.47% 16.5% w s 97,022 56,053 58,848 21,614 8,091 ò 854,078 771,921 711,907 730,064 542,515 ò 2,027,586 2,025,372 1,647,996 2,167,658 2,428,031 ü 408,601 408,969 424,962 284,677 579,695 Á Š Á ó äð Ê ³ ì GRG dº ç ½Ì (3%) (8%40-60) (3%) (8%) q 1,438,731 1,723,032 1,430,462 858,296 1,141,944 43.9% 72.3% 43.0% -14.2% 14.2% w s 84,984 39,540 192,784 31,133 9,044 ò 839,866 1,234,353 995,373 597,951 912,642 ò 1,986,311 2,254,549 1,844,516 1,162,269 1,320,426 ü 574,941 511,445 424,962 284,677 208,588 Š í à Ê}{qÀ½k Äq~Âe ³ e i ÊÁ dºi uá¹~æ 4-5Æ 4-7 v¹ } ~ Êe³Áã~ ʳÌ}{ ½Ì {¹
Š Òš 27 }ÂGRG dº½½ì Ê ³ e hðá ç ½ Ê ³ Ì}{½Ì {¹u Êe³ }Ä ÊÁ } ä Á }Äq ³säŠ Ê Á äiì Áü³}åž{ {Á¹ } Áw sì i l~ ð 4-5 Š ð 85/3/9 ì Ê GRG dº ç ½Ì ³ (1%, 10, 10) (3%40-60) (3%) (8%) q 1,518,829 1,814,355 1,713,292 1,852,450 2,051,162 51.9% 81.4% 71.3% 85.2% 105% 86/7/28 w s 12028 11,116 13,314 10,998 10,542 88/2/22 q 1,594,119 1,479,710 1,509,000 1,412,868 1,584,777 59.4% 48% 50.9% 41.3% 58.5% 89/2/16 w s 13095 10,215 14,104 9,730 8,469
Š Òš 28 ð 4-6 ìš ð Ê ì GRG dº ç ½Ì 83/12/14 ³ (3%, 3, 11) (1%, 30-71) (1%) (3%) q 923,480 1,043,524 1,021,285 914,862 706,900-7.65% 4.35% 2.13% -8.51% -29.31% 85/2/28 w s 22,098 16,114 195,921 5,876 4,567 91/4/24 q 929,949 811,590 945,461 905,900 636,264-7.01% -18.84% -5.45% -9.41% -36.37% 91/10/15 w s 18,854 5,009 77,874 3,071 4,253 ð 4-7 Š ð Ê ì GRG dº ç ½Ì 82/7/12 ³ (1%, 10, 10) (1%, 40-60) (3%) (8%) q 1,026,515 1,008,727 1,013,861 985,424 1,000,232 2.65% 0.87% 1.39% -1.46% 0.02% 82/10/27 w s 8791.4 8,799 8,838 9,193 5,871 88/6/7 q 1,062,436 1,089,413 1,113,890 935,958 991,642 6.24% 8.94% 11.39% -6.40% -0.84% 88/12/20 w s 19715 14,871 22,781 11,261 5,833
Š Òš 29 þ Ô dº½ç ½ ½Ì dº½ ç ½ Ç ÊÁ Á ³ ä{i ½Ì ÊÁw s Æv Áw s såž dº½ ç Ì ŠÁw s }~k Ê ³Ì}{½Ì {¹ }Âu Êe³}Ä ÊÁ } ä Ì Á }Äq ³Æü Á ü³}åž{ {¹ } Áw sì i l~ GRG dº½ ÕÁãk~š u } s {ÁÔšnk u dh½ }Áïò ç ½ÔvÌýÙu 1992 1995 24 ó Ákédº n slá½ u Í mìý~ Áš n n ÔÁmdºÔl nôv Á sgk w h shá ê u Ä dº Çq w À½
Š Òš 30 1999 Ê}pÁuvmy åž slàg º1992 ʽÌp ð 131 1991 Êåžô³ûu vø¾ åž slàg 1990 ʈåžvp åž slàg m1996äq ʹåžvm yåž slàg 1997Strap Strip }päquvm yåž slàg ˆ 2002pÄ ³åžvpæ žslàg 1987 žsh½làâ Ý1996 õuzæ ïo íé(1993) žh½¹mºlàâ Black, Fisher, & Myron Scholes (May/Jun 1973). The pricing of options and corporateliabilities. Journal of Political Economy, 637-659. Black, Fischer, & Robert Jones (1987). Simplifying portfolio insurance. Journal of Portfolio Management, 48-51. Fama, Eugene F., & Blume, Marshall E. (Jan 1966). Filter rules and stock market trading. Journal of Business, 39, 226-241.
Š Òš 31 Garcia, C. B., & Gould, F. J. (July-Aug 1987). An empirical study of portfolio insurance. Financial Analysts Journal, 44-54. Pawlak Z. (1982). Rough sets. International Journal of Computer Science, 11, 341 356. Perold, A. F., & Sharpeu, W. F. (Jan/Feb 1988). Dynamic strategies for asset allocation. Financial Analysts Journal, 16-26. Rubinstein, Mark, & Leland, Hayne E. (Jul/Aug 1981). Replicating options with positions in stock and cash. Financial Analysts Journal, 63-71. Zhu, Yu, & Kavee, Robert C. (Spring 1988). Performance of portfolio insurance. Journal of Portfolio Management, 48-54. Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8, 338-353.