• 沒有找到結果。

Combinatorial Methods for Double-Barrier Option Pricing

N/A
N/A
Protected

Academic year: 2021

Share "Combinatorial Methods for Double-Barrier Option Pricing"

Copied!
25
0
0

加載中.... (立即查看全文)

全文

(1)    

(2)      

(3)     " ! #

(4)

(5) $

(6) % &   '

(7) )(* +. ., -/0213-546/$7"85469 :<;>=?4A@CBEDF;>/GBH96IJ7"9KDF=5-BL;>@NMOQPR;>/OQ; 46/SUTV/)IW96@LDX4ABEPY96/XZ[/)\GPY/);Q;Q@EPR/)\ ]<4ABEPY9K/546^`_a46PcbH46/ d</PceK;>@LfCPcBhg.

(8)  i j k lnmAoqpCrGstvuwoCxyrAm z|{}z ~€2‚„ƒw ‡†‰ˆŠƒw‹Œ‹‚ {Ž{a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ z|{ ‘Šƒw’“’•”–h’˜—𙁀2”Œ›| ‡‚ {Ž{a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ z|{œ žš›|‡Ÿ‡‹Œ–¡ ¢‘Šƒw’•’“”–h’—𙁀2”Œ›| ‡‚£{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ z|{¥¤ ¦Q€2’“‡§h€•‡’•–a›w¨©ª‡”Œ‚„©ª–n‚•”Œ‚«{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ¬ ­KrA®°¯²±[³´uLµ6¶ApCrAtvmsv· >{}z ©ª‡–J‘`‹¹ƒE§»º¼ ½¦>§»ª‡›|‹Œ–n‚¾—𙁀2”Œ›| ¿~’•”§h” ‡ÀÂÁ¿›>†‡–h‹Ã{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ >{ ©ª‡–ŽÁ<–n’W€2›| <‘Šƒw’“’•”Œ–n’„—𙁀2”Œ›| ¿~’•”§h” ‡ÀÂÁ¿›>†‡–h‹*{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ >{œ ©ª‡–£ÆÇ”–h ‡–n’„~’•›Q§n–h‚•‚{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ >{¥¤ ©ª‡–J‘`” ›|È"”ƒw‹6Á<›>†–n‹É{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ Ë ÌŽrÍ®.ÎxRmϳoqrÐpLxy³´ÑÓÒU¯¼oCÔÏrGsv· œ{}z ©ª‡–J‘`” ›|È"”ƒw‹A©’“–n–ÖÁ<–h€•ª‡›>†Ø×˜”Œ€•ª¿‘Šƒw§»º¼×ŠƒE’•†‰Ù¢ †‡‡§h€•”›| {Ž{J{a{Ž{J{Ž{J{J{ œ{ ©ª‡–Jۄ–¡Ü´–n§¡€2”Œ›| ‰~’“” ‡§h”™‡‹Œ–Ý{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ œ{œ ©ª‡–aÙ¢†‡–߃à›w¨)ˆ`›|È[Ÿ‡”Œ ´ƒE€•›|’•”ƒw‹GÁ<–¡€2ª‡›Q†‡‚H{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ á ̎rÍ® âtGoq³oCxyrAmv³‡ÑÓãH¯Q·ßtvÑyoq· ¤‡{}z ˆ`›| ¼ä|–h’•À|–h ‡§n–[ˆ`›|È"™‡ƒw’•”Œ‚•›| {Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ¤‡{ åš´ƒw†‡’•ƒE€2”Œ§£Û„ ‡ ‡” À©”ŒÈ"–h‚{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ¤‡{œ Á<›|’“–Žžš”Œ‚•§h‡‚•‚“”›| ‡‚æ{a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ¸ ̎rÍmvu¼Ñct·ßxyrAmF³´mvsXèÏtÏoCtÏpC¯‰éêrApCµ ±3xyÎÑcxcrжÐpC³‡âÔÍì. ”. k ¸. z . ¤. œ Å. Å Ê. Ä. Õ Ú zqÞ z|z k¼á zߤ zCÊ zqç ¬´ë ¬Gk.

(9) í )<   î +

(10) jê z|{}z z|{ z|{œ z|{¥¤ >{}z œ{}z œ{ œ{œ œ{¥¤ ¤‡{}z ¤‡{ ¤‡{œ ¤‡{¥¤ ¤‡{Ä ¤‡{Å ¤‡{Ê. ˆŠƒw‹‹G—£™>€2”›w K{¾{J{J{Ž{a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ~€ï—£™>€2”›w K{<{J{J{Ž{a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ žš›qט > ½ƒw †> ¢Ù¢ <ˆŠƒw‹Œ‹Gƒw ‡†<‘`” ›|È"”ƒw‹A©’“–n–w{?{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ žš›|‡Ÿ‡‹Œ–¡ ¢‘Šƒw’•’“”–h’—𙁀2”Œ›| ¿ƒw ‡†¿‘`”Œ ‡›|È”¹ƒw‹A©’“–n–E{°{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ‘`” ›|È"”ƒw‹6Á<›>†–n‹Y{ {a{J{Ž{J{Ž{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ‘Šƒw§»º¼×`ƒw’•†<Ù¢ ‡†‡‡§¡€2”›w بy›w’˜€•ª‡–J‘`” ›|È"”ƒw‹ÍÁ<›Q†‡–n‹R{{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ©ª‡–Jۄ–¡Ü´–n§¡€2”Œ›| ‰~’“” ‡§h”™‡‹Œ–ï¨y›|’˜‘`”Œ ‡›|È”¹ƒw‹ÍÛ¾ƒE ‡†‡›|ÈÉÆjƒw‹Œºð‚n{v{Ž{J{a{Ž{J{Ž{J{J{ ۄ–h™Í–nƒE€2–h†<ñ¾™‡™‡‹Œ”§ßƒL€2”›w ‡‚Š›w¨v€2ª‡–Jۘ–hÜ´–h§h€•”›| ¿~’•”Œ ‡§n”Œ™‡‹–E{J{J{J{Ž{J{a{Ž{J{Ž{J{J{ ‘Šƒw’“’•”–h’˜ˆŠƒw‹Œ‹Ï—𙁀2”Œ›| Nט”Œ€2ªØ©Š×ӛH‘ŠƒE’•’•”Œ–n’“‚‡ ‡†‡–h’¾‘Ó” ‡›|È”¹ƒE‹KÁ<›Q†‡–h‹Y{Ø{Ž{J{J{ ¦>” À|‹–V ½‘Šƒw’“’•”Œ–n’ˆŠƒE‹‹Íט”}€2ª‰ˆ`›|È[Ÿ‡”Œ ´ƒE€•›|’•”ƒw‹KÁ¿–h€2ª›>†‡‚h{´{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ žš›|‡Ÿ‡‹Œ–¡ ¢‘Šƒw’•’“”–h’ˆŠƒw‹Œ‹6ט”Œ€•ª‰ˆ`›wÈ[Ÿ‡” ‡ƒE€2›|’“”¹ƒw‹6Á<–¡€2ª‡›Q†‡‚n{N{J{J{Ž{J{a{Ž{J{Ž{J{J{ žš›|‡Ÿ‡‹Œ–¡ ¢‘Šƒw’•’“”–h’ˆŠƒw‹Œ‹6ט”Œ€•ª‰ˆ`›wÈ[Ÿ‡” ‡ƒE€2›|’“”¹ƒw‹6Á<–¡€2ª‡›Q†‡‚ÖòYÁ‰ƒwÀw ‡”Œó´–h†Ðô¡{ {Ž{J{J{ žš›|‡Ÿ‡‹Œ–£‘Šƒw’“’•”Œ–n’W ½ˆŠƒw‹‹Aט”Œ€•ª<‘`ƒw§»º¼×Šƒw’“†‰Ù¢ ‡†‡§h€•”›| K{à{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ žš›|‡Ÿ‡‹Œ–¡ ¢‘Šƒw’•’“”–h’ˆŠƒw‹Œ‹6ט”Œ€•ª<‘`ƒw§»º¼×Šƒw’“†‰Ù¢ ‡†‡§h€•”›| °òYÁ<›Q†‡”}ó´–n†ÐôV{G{a{Ž{J{Ž{J{J{ åš´ƒw†‡’•ƒE€2”Œ§£Û„ ‡ ‡” À©”ŒÈ"–h‚n{š{J{J{Ž{J{Ž{J{a{Ž{J{J{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{ ©ª‡–J~–h’“¨y›|’“Èõƒw §n–£×˜”Œ€•ª<‘`ƒw§»º¼×Šƒw’“†²Ù¢ ‡†‡§h€2”Œ›| K{#{Ž{J{Ž{J{J{Ž{J{a{Ž{J{Ž{J{J{. ”Œ”. œ œ. . z. ç Ú zqÞ z|z zqœ zߤ zCÄ zCÄ zqÅ zCÊ zCÊ zqç.

(11) ö η¡oqpC³´uwo ©ª‡–[‚“™´ƒw§h–[›w¨ó´ ´ƒE ‡§n”ƒw‹”Œ ‡ ‡›qäEƒE€2”Œ›| ‰§h›| ¼€2”Œ Q–n‚š‡ ‡ƒwŸ´ƒE€•–n†K{šÙ¢ .™‡ƒw’“€•”§n‹¹ƒw’h÷A ð‡È–n’“›|‡‚ïäEƒw’“”}  ƒE€•”›| ‡‚Ö›| ø‚“€»ƒE ‡†´ƒw’“†Ã›|™>€2”›w j™´ƒßù|›wú͂ª´ƒßä|–ØŸÍ–h–n ™‡’•›w™Í›|‚“–n†ƒw ‡†€•’2ƒw†‡–h†Ã”Œ j€2ª‡–N›qäw–n’W Y€2ª‡–V  §n›w‡ ¼€2–n’3È"ƒw’“ºw–h€n{û‘Šƒw’•’“”–h’[›|™€•”›| ‡‚Ž’•–h™‡’•–h‚•–n ¼€Â›| ‡–N›E¨€2ª‡–NÈ›|’•–"™Í›w™‡‡‹¹ƒE’ލy›|’“È"‚[›E¨€2ª‡›|‚“– ‚•›L ¢§ßƒE‹‹–h† ü“ý>þLÿ ֛w™€2”Œ›| ‡‚n{.ñ†›|‡Ÿ‡‹Œ–HŸ´ƒw’“’•”–h’Ö›|™>€2”›w j”‚3ƒE ›|™€2”Œ›| °×˜ª‡”Œ§»ªø”‚ֺ𠇛Q§»ºw–h†F”Œ ›|’J›|€Ž€2ª‡–Â󴒕‚W€Ö€2”ŒÈ"–3€•ª´ƒE€J€2ª‡–"‡ ‡†‡–h’•‹ŒùQ”Œ ‡À²ƒw‚“‚•–¡€[€2›|§»ª‡–n‚[›w ‡–"›E¨Š€¢×`›.Ÿ‡ƒw’•’“”–n’“‚Ž™’•”›w’a€•› – >™‡”Œ’2ƒE€•”›| 6{ ©ª‡–ŠÈ"ƒw” J™‡‡’“™Í›w‚•–Š›w¨€2ª‡”Œ‚€2ª–n‚•”Œ‚”Œ‚€2›¾‡‚•–Ó€2ª‡–Чh›|È[Ÿ‡”Œ ´ƒE€•›|’•”ƒw‹|È–h€2ª›>†J€2›ïäEƒw‹Œ‡–Ó†›|‡Ÿ‡‹Œ– Ÿ´ƒw’“’•”Œ–n’Š›|™>€2”›w ‡‚Ÿ¼ùH€2ª‡–£‚•–a›w¨’•–h܇–n§h€•”›| ؙ‡’“” ‡§h”™‡‹Œ–w{ÆÇ”}€2ªH€•ª‡”‚È–h€•ª‡›>†6÷€2ª‡–£§h›| ¼ä|–h’•À|–h ‡§n– ‚•™A–n–h†<”Œ N€2ª‡–£†‡›w‡Ÿ‡‹–V ¢Ÿ´ƒE’•’•”Œ–n’Чnƒw‚•–a”Œ‚Ѝcƒw‚“€•–n’Š€2ª‡ƒw ¿€•ª‡–£‚•”Œ ‡À|‹Œ–¡ ¢Ÿ‡ƒw’•’“”–n’ӧ߃w‚“–w{Æ –J”ŒÈ"™‹–nÈ–n ¼€ ƒw‹ŒÀ|›|’•”}€2ª‡È‚֔Œ €2ª‡–<ˆÉ‹ƒw ‡À|‡ƒwÀ|–Nƒw †Ã§h›|È"™”‹–"€2ª‡–hÈݟ¼ù€2ª‡–<¦>‡ Fˆˆ#§h›|È"™”‹–h’Ö’“‡ ‡ ‡”Œ ‡À ‡ ‡†–n’ަ>›|‹ƒw’•”Œ‚aÄ>{Å{[©ª‡–à†´ƒE€2ƒØƒw’•–àÀ|–h ‡–n’•ƒE€2–h† ›| .€•ª‡– Ñ oqpC³Í­6ⳁpEu lql ×ӛ|’•ºð‚W€»ƒE€•”›| .ט”Œ€•ª œ|Þ|މÁ NˆŠ~ ƒw ‡†ø|ÄEŲÁ‰‘iž£Û˜ñ£Áû{©ª‡–õ’•–n‚“‡‹Œ€•” ‡À‰ƒw‹Àw›|’•”}€2ª‡È ”Œ‚Žª”À|ª‡‹}ù – §n”Œ–n ¼€Ö¨y›w’ ™‡’“”§n”Œ ‡À.€2ª‡”Œ‚€¢ùQ™A–<›E¨£Ÿ´ƒw’“’•”–h’à›|™€2”Œ›| K÷5טª‡”§»ªÃ”‚"ƒE€Â‹–nƒw‚“€"ƒw Û|’•†‡–h’"›E¨šÈ"ƒwÀ| ‡”}€2‡†‡–N¨cƒw‚W€2–h’ €2ª‡ƒw ¿€•ª‡–aŸ‡” ›|È"”ƒw‹Í€•’•–h–JÈ–h€•ª‡›Q†Ø×˜”}€2ª¿Ÿ´ƒw§»º¼×`ƒw’•†<” ‡†‡§h€2”Œ›| K{5©ª‡–JŸ‡” ›|È"”ƒw‹Ð€2’•–h–ŽÈ–h€•ª‡›Q† ט”Œ€•ª²Ÿ´ƒw§»º¼×`ƒw’•† ”Œ ‡†‡‡§¡€2”›w ‰€»ƒwºE–n‚aƒwŸA›|€ÖzqÞ"€•”È–n‚¾€•ª´ƒw ‰€•ª‡–[§h›|È[Ÿ‡”Œ ´ƒE€2›w’•”¹ƒE‹GÈ"–¡€2ª‡›Q†‰×˜”Œ€•ª ”†–n ¼€2”Œ§ßƒw‹K™‡ƒw’2ƒwÈ–h€•–n’“‚n{©ª‡–J§n›|È֟‡” ´ƒL€2›|’“”¹ƒw‹AÈ"–¡€2ª‡›Q†Ø”‚§h‹–߃E’•‹Œùõ‚•‡™A–n’“”›|’h{ . . . .

(12). .

(13)   & $

(14) . .  °

(15) j  (  .  !. "#%$&$'. (. *. Payoff($). +. 0. ). X. Terminal Stock ( Price($). Œ” À|‡’•–Öz|{Œz ~€Žƒw ‡† §ßƒw‹Œ‹ƒw’“–[€¢×`›¿Ÿ´ƒw‚“”§[€¢ùQ™Í–h‚a›w¨Óó‡ ´ƒw ‡§h”¹ƒw‹)›w™€2”Œ›| ‡‚n{Ö©ª‡–hù²×Ӗn’“–Â󇒕‚“€a€•’2ƒw†‡–h† ›| ƒw ›|’“À¼ƒw ‡” n–n† – §»ª‡ƒw ‡À|–"” øzqÚ¼Êwœ>{[ñ §ßƒw‹Œ‹)›|™€•”›| .À|”}ä|–h‚a€•ª‡–ઇ›|‹Œ†‡–n’š€•ª‡–à’•”Àwªð€£€•›ØŸ‡ù.€2ª– ‡ ‡†–n’•‹}ùQ” ‡Àaƒw‚“‚•–¡€5Ÿðù[ƒš§n–h’“€»ƒE” 3†´ƒE€•–Š§ßƒE‹‹–h†Ö€2ª–– >™‡”’•ƒE€2”Œ›| ֆ‡ƒE€2–Ѝy›|’)ƒï§n–h’“€»ƒE” 3™‡’“”§n–E{ñX™‡>€ ›|™€•”›| ‰À|”Œäw–n‚ª‡–[ª‡›|‹Œ†‡–n’„€2ª‡–Ö’•”Àwªð€¾€2›N‚“–n‹‹Ï€2ª–3‡ ‡†‡–h’•‹ŒùQ”Œ ‡ÀNƒw‚“‚•–h€aŸ¼ù‰ƒH§n–h’“€»ƒE” ²†´ƒL€2–Ö¨y›|’ïƒ §n–h’“€2ƒw” ™‡’•”Œ§n–E{)©ª‡”‚?§n–h’“€2ƒw” "™‡’•”Œ§n–˜”‚?§ßƒw‹Œ‹–h†à€•ª‡–„‚“€2’“”ºE–’“”§n–E{5—𙁀2”Œ›| ‡‚5§ßƒE õŸA–¾§h‹¹ƒw‚“‚•”Œó‡–n†HƒE‚ ñïÈ–n’“”§nƒw ‰›|’ ‡’•›w™Í–nƒw K{ïñ¾‹‹G€2ª–Ö›|™€•”›| ‚¾†‡”Œ‚•§h‡‚•‚“–n†.” ¿€2ª‡–Ž€2ª‡–h‚•”‚ïƒw’•– ‡’•›|™A–߃E K÷Aטª”§»ª §ßƒE <ŸA–£– >–n’“§n”Œ‚•–n†<›| ‡‹}ùH›| N€2ª–J– >–n’•§h”‚“–ކ´ƒL€2–£Ÿ‡€„ ‡›E€˜ŸÍ–¡¨y›|’•–E÷´ ´ƒwÈ–n‹Œù" ‡›w€„–nƒw’•‹}ùõ– –h’•§h”‚•–E{ –h€ æŸA–`€2ª–Š‚“€•’•”ºE–Š™‡’“”§n–Šƒw ‡† €2ª–`ó´ ´ƒw‹>™‡’•”Œ§n–Š›E¨´€2ª‡–Ё ‡†‡–n’“‹ŒùQ” À£ƒw‚•‚“–h€n{©ª‡–Š™´ƒßù|›Eú ¨y’•›wÈ ª‡›|‹Œ†‡” Ààƒ ‡’“›|™A–߃w ¿§ßƒw‹Œ‹K›|™€•”›| ؔŒ‚ Èõƒ Gò »Þ¼ô ©ª‡”Œ‚”‚ŸA–n§ßƒE‡‚•–E÷>”}¨ ÷¼€•ª‡–ª‡›|‹Œ†‡–n’)ט”Œ‹‹– >–n’•§h”‚“–ïƒw †Â’“–n§h–n”Œäw– ”Œ –¡ú6–h§h€n÷ðטª”‹– ”Œ¨ ÷‡€2ª‡–aª‡›w‹†‡–h’Š×˜”‹‹Í ‡›w€˜– –h’•§h”‚•–Žƒw ‡†Ø€2ª–J§nƒw‹‹6”‚Š×ӛ|’“€•ª‡‹–h‚•‚Öò ”ŒÀ|‡’•–Öz|{Œzqô¡{ z ,. C. .-0/214353768:9<;>=@?BA. D. . E. E. . F. D. G. D. HJI. E. K LHJINMOG P. RHJITSUG. @HJITWXG. D. D. DQ. VHJI MG ,.

(16) . Y[ZJ\L]D^`_Ja5bK\Lcd^KZ. e. Payoff($). g. 0. f. X. Terminal Stock e Price($). Œ” À|‡’“–[z|{ ¦>”È”‹ƒw’•‹}ù|÷¼€2ª– ‡’“›|™A–߃w ¿™‡€„›|™€•”›| Nª‡ƒw‚„ƒ3€•–n’“È"”Œ ´ƒw‹6äEƒw‹Œ‡–£›w¨ È"ƒ 6ò »Þ|ô ©ª‡”Œ‚‚„ŸA–n§ßƒE‡‚•–E÷K”Œ¨ v÷̀•ª‡–Öª›|‹†‡–h’„ט”Œ‹‹Ï– >–h’•§n”Œ‚•–Ö€•ª‡–Ö’“”À|ª¼€ïƒw ‡†²’“–n§h–n”Œäw– û”Œ –hú͖n§¡€ß÷Gטª‡”Œ‹–[”}¨ v÷K€•ª‡–3ª‡›|‹Œ†‡–n’ïט”Œ‹‹ ‡›w€a– >–h’•§n”Œ‚•–3€2ª–3’•”Àwªð€£ƒw ‡†.€2ª‡–à™‡>€a›|™€2”Œ›| ²”Œ‚ ×ӛ|’“€•ª‡‹–h‚•‚Öò ”ŒÀ|‡’•–Öz|{ wô¡{ ,. `- hVi<9j68k9R;>=@?BA. lE. m dGMnHJI4P. G. G. SoHJI. Q. . WqHJI. GpMUHJI. . ,. Dr. stuBu vw2uyxz {v'|!. Š‘ ƒw’“’•”Œ–n’ï›w™€2”Œ›| ‰”Œ‚šƒõºð” †.›w¨5– >›w€•”§Ö™‡ƒE€2ª>  †‡–n™A–n †‡–n ¼€J›|™€•”›| K{¾Ù €š†‡”}ú6–h’•‚ï¨y’“›|È ƒH‚“€2ƒw ‡†´ƒw’“† ›|™€•”›| J” a€2ª‡ƒE€v”Œ€vÈõƒßù£– >™‡”’“–ÓŸA–h¨y›|’“–Ó– >™‡”’•ƒE€2”Œ›| a›|’§h›|È–?”Œ ¼€2›„– >”‚W€2–n §n–`ŸA–h¨y›w’•–?– >™‡”’•ƒE€2”Œ›| K÷ †‡–h™Í–h ‡†‡” À¿›w ²€2ª‡–3‚“™Í–h§n”Œó‡§ßƒE€•”›| K÷Íטª‡–n §n–h’“€2ƒw” .Ÿ´ƒE’•’•”Œ–n’“‚£ƒw’•–3ª”Œ€ß{aÙ¢ .€2ª”‚ª‡–n‚“”‚n÷GŸ‡ƒw’•’“”–n’ ™‡’“”§n–£”Œ‚˜§n›| ‡‚W€»ƒw ¼€n÷´”Œ€˜ ‡–¡ä|–n’„È›Cäw–a†‡‡’•”Œ ‡À3€2ª‡–a›|™>€2”›w ‚‹Œ”Œ¨y–E{ ©ª‡–n’“–ïƒE’•–€¢×`›J€¢ùQ™Í–h‚Ó›w¨ÍŸ´ƒw’“’•”Œ–n’›|™€•”›| ‚ ºð ‡›Q§»º| ¢›|>€`ƒE ‡†"ºð ‡›Q§»º| ¢”Œ "›|™>€2”›w ‡‚n{ñ ºð ‡›Q§»º|  ›|€J›|™>€2”›w .”‚a‚•”ŒÈ"”Œ‹¹ƒw’˜€2›¿ƒØ‚“€»ƒE ‡†´ƒw’“† ›|™>€2”›w û– >§n–n™>€Ž€•ª´ƒE€ß÷Gטª‡–h €•ª‡–à‡ ‡†‡–h’•‹ŒùQ”Œ ‡À¿ƒw‚•‚“–h€ ¥‚ ™‡’“”§n–õ’•–߃E§»ª‡–n‚"ƒ²§n–h’“€»ƒE” Ÿ´ƒw’“’•”Œ–n’ °÷€•ª‡–N›|™€•”›| j§h–߃w‚“–n‚3€2› – ”Œ‚“€n{°Ù¢ €2ª‡–N§nƒw‚•–N›E¨ïƒ.§nƒw‹‹ ºð ‡›Q§»º¼  ›|€n÷€2ª‡–"Ÿ´ƒw’“’•”–h’a”‚JÀ|–n ‡–h’2ƒw‹Œ‹Œù ŸA–n‹Œ›C× €2ª‡–"‚“€2’“”ºE–õ™‡’“”§n–‰ò ûô¡{N©ª‡”Œ‚Ö›|™>€2”›w ”Œ‚ ‚•›wÈ"–¡€2”È–n‚?’•–¡¨y–n’“’•–n†N€•›3ƒw‚ƒÖ†›Cט Q ½ƒw ‡†Q ¢›|€`›|™€•”›| K{Ù¢ H€2ª‡–š§nƒw‚•–ï›w¨vƒÖ™‡€ŠºQ ›>§»º| ¢›w€Š×˜”Œ€•ª ÷Ѐ2ª–[›|™€•”›| <”‚ï‚“›|È–h€2”ŒÈ"–h‚¾’“–h¨y–h’•’•–h†²€2›NƒE‚šƒw ²™> ½ƒw †> ¢›|>€š›|™€•”›| 6{¾©ª‡–ÖºQ ›>§»º| ¢”Œ ›|™€•”›| ”Œ‚£‚•”È”‹ƒw’n{JÆÇ”Œ€•ªû’“–h¨y–h’•–n §n–"€•› ”À|’•–Nz|{œ÷vƒN†‡›qט > ½ƒw †> ¢”Œ û›w™€2”Œ›| ”‚JƒN§ßƒw‹Œ‹€2ª´ƒL€ §n›wÈ"–h‚” ¼€2›3– ”Œ‚“€•–n ‡§h–J›w ‡‹ŒùÂטª‡–n ؀2ª–£Ÿ´ƒw’•’“”–h’ ò ôӔ‚’“–߃w§»ª‡–h†K÷Ѓw ‡†¿ƒw N™> ½ƒw †> ¢”Œ ›|™€•”›| Ž”‚ƒï™‡€€2ª´ƒL€§h›|È"–h‚”Œ ð€•›š– >”Œ‚“€2–h ‡§n–`›| ‡‹Œù£×˜ª–n [€2ª–ŠŸ´ƒw’“’•”–h’ ò ûôG”‚v’•–nƒw§»ª‡–h†K{ –h ‡–n’•ƒw‹‹}ù£‚•™A–߃EºQ”Œ ‡À‡÷L€2ª‡–?™‡’•”Œ§n–?›w¨Ðƒ„Ÿ´ƒw’•’“”–h’v›w™€2”Œ›| Ž”Œ‚ϧ»ª‡–߃w™A–n’€2ª´ƒw փ„‚W€»ƒw †´ƒw’•†Ö›|™€2”Œ›| K{ ©ª‡”Œ‚Ž”Œ‚JŸA–n§nƒw‡‚“–Nƒw†‡†‡”}€2”Œ›| ´ƒw‹)§h›| ‡†‡”}€2”Œ›| ‡‚aƒw’“–"”ŒÈ"™A›|‚•–h† ›w €2ª–"Ÿ´ƒE’•’•”Œ–n’a›|™€•”›| Fòc”R{–E{Œ÷v‚“€•›>§»º ™‡’“”§n–ÖÈ[‡‚“€š–n”Œ€•ª‡–n’¾€2›|‡§»ª.›w’𠇛w€š€•›|‡§»ª.€2ª–[Ÿ´ƒw’“’•”–h’’•” ÀH€2ª‡–[›w™€2”Œ›| ¥‚”}¨y–ލy›|’¾”Œ€¾€2›NŸA– –n‹Œ”À|”ŒŸ‡‹–J¨y›|’£– >–h’•§n”Œ‚•–"ƒE€a– >™‡”Œ’2ƒE€•”›| ´ô¡{[ñ¾ ”ŒÈ"™A›|’“€2ƒw ¼€š”Œ‚•‚•–”Œ‚£€2ª‡–3¨y’•– ð‡–n ‡§¡ù.ט”Œ€•ª טª”§»ª €2ª–Öƒw‚“‚•–¡€ï™‡’“”§h– ø”‚˜›|Ÿ‡‚“–n’Wä|–n†<¨y›|’€2ª‡–a™‡‡’“™Í›w‚•–J›w¨€•–n‚“€•” ‡À3טª‡–¡€2ª‡–h’¾€•ª‡–aŸ´ƒw’•’“”–h’„ª‡ƒw‚˜ŸÍ–h–n ’•–nƒw§»ª‡–h†K{Š—ï¨ €•–n ؀2ª‡–£€2–h’•È‚›w¨ƒà§h›| ¼€2’•ƒw§h€¾‚“€2ƒE€2–£€2ª‡ƒE€ ”Œ‚›|Ÿ‡‚•–h’“äw–n†²›| §n–Jƒ3†´ƒßù|{ . D. D. . . R}. '-. D. &}. ~. D. L~. €qG. ~S‚G. ,. D. 0~. L~ƒ€UG. . @~. L~ƒS„G. . R}. . . †. H. H.

(17) œ. Y[ZJ\L]D^`_Ja5bK\Lcd^KZ. X ‡. S ˆ. H. Œ” À|‡’“–3z|{œ Ù¢ ‰€2ª”‚€2ª‡–h‚•”Œ‚n÷Ð×`–Ž™‡’•›|™A›|‚“–փ§n›|È[Ÿ” ´ƒE€•›|’•”ƒw‹6È–h€•ª‡›Q†¿€•›õ™‡’“”§n–JŸ´ƒw’“’•”Œ–n’˜›|™€•”›| ‡‚˜”Œ‚„†‡– €2› ùQ‡ Ú R{Æ –˜€•ª‡–n "§n›|È™´ƒw’“–”Œ€•‚™Í–h’“¨y›|’“Èõƒw §n–„ƒwÀ¼ƒw”Œ ‡‚“€€•ª´ƒE€5›w¨Í€2ª‡–˜‚W€»ƒw ‡†‡ƒw’•†ÂŸ´ƒw§»º¼×`ƒw’•† ”È™‡‹Œ–nÈ–n ¼€»ƒE€•”›| 6{ „‡È"–h’•”Œ§ßƒw‹Í– >™Í–h’•”ŒÈ"–h ð€•‚‚•ª‡›q× €2ª´ƒE€ ùQ‡ ¥‚„ƒw‹Àw›|’•”}€2ª‡È ”‚`‚•‡Ÿ‡‚W€»ƒw ¼€•”¹ƒw‹Œ‹Œù ŸA–h€•€•–n’h{ ,. F. `- ‰Š=R‹Œ?Ž14?‘RD’?“/V1”353 14?‘–•—;>?4=”˜V;™143!š›<œkœ‘A. ! Ÿž. @ . ¡. F. . R}. ¢£|¤!¥!$w ¦Žst%uBuBv'w2u§x¨z v'|!. >¦ ›|È–õŸ‡ƒw’•’“”–n’Ž›|™€•”›| ‡‚ާn›| ¼€2ƒw” °€¢×ӛ Ÿ´ƒw’“’•”–h’•‚ ƒw ‡† Uט”Œ€•ª òY¦Q–n– ”ŒÀ|‡’•–¿z|{¥¤ðô¡{ žš–n™A–n †‡” ‡Àû›| ª‡›q× €2ª–<Ÿ´ƒE’•’•”Œ–n’“‚àƒEú6–h§h€Â€2ª‡–¿– >”Œ‚“€2–h ‡§n–¿›w¨¾€2ª‡–¿›|™€•”›| ‡‚h÷?äEƒw’“”›|‚Ÿ‡ƒw’•’“”–n’ ›|™€•”›| ‚?§nƒw Ÿ͖„†‡–hó‡ ‡–n†K{ ›|’5”Œ ‡‚“€2ƒw ‡§n–E÷Q€•ª‡–˜›|™€•”›| ÂÈõƒßù3§h›|È–„”Œ ¼€2›a– >”‚W€2–h ‡§n–¾›| ‡‹Œù[”Œ¨ÍŸÍ›w€•ª Ÿ´ƒw’“’•”Œ–n’•‚˜ƒE’•–aª‡”Œ€n{ ~. ª©. ,. «©t€t~. . ,. . H X ¬. S ­. L. ” À|’•–[z|{¥¤ ư–Âט”‹Œ‹’•–n‚W€2’“”§h€[ƒE€•€•–n ¼€2”Œ›| ûª‡–n’“–õ€2›¿€2ª‡–§߃w‚“–õ€2ª‡ƒE€Ž€•ª‡–õ›w™€2”Œ›| §h›|È–n‚Ö”Œ ¼€2›¿– >”‚W€2–n §n– ›| ‡‹}ù ”Œ¨Ó€2ª‡–‡ ‡†‡–h’•‹}ù>”Œ ‡À²ƒE‚•‚•–¡€Ö€•›|‡§»ª‡–h‚[–n”}€2ª‡–h’ŽŸ´ƒE’•’•”Œ–n’h÷ƒw †j§ßƒw‹Œ‹”Œ€J†‡›|Ÿ‡‹–Ÿ´ƒw’“’•”–h’ާnƒw‹‹”}¨ €2ª–›w™€2”Œ›| .”‚aƒH§nƒw‹‹R{3—ï€2ª‡–h’£äwƒE’•”¹ƒL€2”›w ‡‚ ‡§n‹Œ‡†‡–3›|™€•”›| ‚ï€2ª´ƒL€a§n›|È–3” ¼€2›Ø– ”Œ‚“€•–n ‡§h–›w ‡‹Œù ”Œ¨„ŸA›w€2ªøŸ´ƒE’•’•”Œ–n’“‚"ƒE’•–Nª‡”}€Âƒw ‡†ø›|™€•”›| ‡‚[€•ª´ƒE€àºð ‡›Q§»º| ¢›|€àטª‡–h F›| –¿›w’3ŸÍ›w€•ªøŸ´ƒw’•’“”–h’•‚àƒw’“– ,. ®-¯‰Š=”i‘°Ž35œ±D•²1”›<›<;>œk›„68:9<;>=”?„14?4–•—;>?‘=@˜V;™143Tšl›<œkœ4A. . D.

(18) ¤. Y[ZJ\L]D^`_Ja5bK\Lcd^KZ. ‡ª ”}€ß{)©ª‡–h‚•–ïäEƒw’“”¹ƒE€•”›| ‚?§nƒw Nƒw‹Œ‹´ŸÍ–¾‚•›|‹}ä|–h†HŸ¼ù"€•ª‡–ï‚•ƒwÈ"–¾È"–¡€2ª‡›Q†K{Æ –ï‚“ª´ƒw‹Œ‹A†–nÈ›| ‡‚“€•’2ƒE€•– €2ª”‚`€•ª‡–n‚“”‚Š€2ª‡ƒE€€2ª‡–£’“–hÜ´–h§h€•”›| ؙ‡’“” ‡§h”™‡‹Œ–ï§n›w‡™‡‹–h†Nט”Œ€2ªH€•ª‡–£” §n‹‚•”›w > ¢– §h‹‡‚“”›| "™‡’•”Œ ‡§n”Œ™‡‹– §ßƒE ŸÍ–؃w™™‡‹”Œ–n†°€•›.†‡–n’“”Œä|–õ§n›|È[Ÿ” ´ƒE€•›|’•”ƒw‹¨y›|’•ÈÖ‡‹¹ƒw–¨y›|’Ö†›|‡Ÿ‡‹Œ–HŸ´ƒw’“’•”–h’[›|™€•”›| ‚n{.©ª‡–h‚•– ¨y›|’“È[‡‹¹ƒE–š‹›¼ƒE†H€2›Â– §n”Œ–n ¼€¾ƒw‹À|›w’•”Œ€•ª‡È‚n{ D. . ´³. µNuB!¶·!uBw|¸º¹¼»!v&p¹¼»TwVv&. ©ª‡–h’•–Žƒw’•–a‚•›wÈ"–£§»ª´ƒE™€2–h’•‚ N€2ª‡”Œ‚Š€2ª‡–h‚•”‚h{?Æ –a” ¼€2’“›>†‡§n–£€2ª–JŸ‡ƒw‚•”Œ§J§h›| ‡§h–n™€•‚ïƒw †<– ™‹¹ƒw”Œ €2ª–š”†‡–nƒw‚Š”Œ H†‡–h€2ƒw”‹Œ‚Ó”Œ õ€2ª”‚˜ˆ`ª´ƒE™€2–h’n{5Ù¢ N›|’•†–n’`€•›[‡ ‡†‡–h’•‚W€»ƒw ‡†N€•ª‡–𙇒“”§n”Œ ‡À[È–h€•ª‡›>†›|‹›|ÀEù|÷ ×Ӗõƒw‹Œ‚•›¿ƒw†‡†ûŸ´ƒw§»ºðÀ|’“›|‡ ‡†û” >¨y›|’•È"ƒE€2”Œ›| .ƒwŸA›|€£ó‡ ´ƒw ‡§h–õƒw † È"ƒE€2ª–nÈ"ƒE€2”Œ§n‚£ƒw † §h›|È"™€2–h’ ‚•§h”–h ‡§n–N”Œ ˆ`ª´ƒw™€•–n’>{ ©ª‡–غw–h’• ‡–h‹Š›w¨˜€2ª–H€2ª‡–h‚•”‚h÷€2ª‡–N§h›|È[Ÿ‡”Œ ´ƒE€2›w’•”¹ƒE‹È"–¡€2ª‡›Q†øƒw ‡†€2ª– Ÿ‡”Œ ‡›|È”¹ƒw‹|€•’•–n–`È"–¡€2ª‡›Q†[ט”Œ€•ª[Ÿ´ƒw§»º¼×`ƒw’•†à” †‡‡§h€•”›| Ö‡‚•–h†Â”Œ [™‡’“”§n”Œ ‡À›|‡Ÿ‡‹Œ–ŠŸ´ƒw’“’•”–h’›w™€2”Œ›| ‡‚n÷ ƒw™‡™A–߃E’•‚ .ˆ`ª´ƒE™€2–h’šœ{˜Æ°–J€2ª‡–h ²ª´ƒßä|–Ö§n›|È™‡€2ƒE€2”Œ›| ´ƒw‹G’“–n‚•‹Œ€2‚ïƒwŸA›|€„€2ª‡–ާn›|È[Ÿ” ´ƒE€•›|’•”ƒw‹ È–h€2ª›>†NƒE ‡†N§n›|È™´ƒw’“–¾€•ª‡–£ƒw§h§n‡’•ƒw§hùHƒw ‡†N– §h”–n §hùH›E¨v€•ª‡–n‚“–š€¢×`›3È–h€•ª‡›Q†‡‚Š” Nˆ`ª´ƒw™€•–n’Ф‡{ ”Œ ´ƒw‹‹}ù|÷ð×`–JÀ|”}ä|–£§n›w ‡§n‹Œ‡‚•”Œ›| ‡‚„ƒw ‡†N¨y€•‡’•–£×ӛ|’•ºN”Œ ¿ˆ`ª´ƒw™€•–n’ïÄ>{ D. ,. .

(19)   & $

(20) ¾. ½.   !  ( +

(21) j    ª¿. rŒ. ¹q»Tw. sÀ$'%¶¯Á¤¦‘µÂ¶Ã»T|$'w2ƒxz {v|¤. u v'¶ v&TÄ. Å. |ÂTw2$. © ª‡–`ùw–߃w’`zqÚ¼Êwœ˜×Šƒw‚)ƒïÈ"”Œ‹–h‚“€2›w ‡–Ó”Œ Žó´ ‡ƒw ‡§n–E{)Ù¢ ր•ª‡–`ù|–nƒw’n÷E€2ª‡–˜ˆ`ª”§ßƒEÀ|›š‘`›|ƒw’•†à—𙁀•”›| ‚ ð  §»ª´ƒw À|–¾×`ƒw‚`¨y›| ‡†‡–n†Hƒw ‡†õŸA–n§nƒwÈ–¾€2ª–„ó´’“‚“€`›|’•À¼ƒE ‡” h–n†"¨cƒE§n”‹Œ”Œ€¢ùލy›|’Ó›w™€2”Œ›| ‡‚5€2’2ƒE†‡” ‡À{ñ‚•›‡÷ €¢×ӛN™‡’•›w¨y–h‚•‚“›|’•‚£ƒL€ï€2ª–àÁ‰ƒw‚“‚2ƒw§»ªð‡‚“–h€•€•‚aÙ¢ ‡‚“€•”Œ€2>€2–[›w¨)©–h§»ª‡ ‡›|‹Œ›|Àwù|÷ ”‚“§»ª‡–n’ï‘`‹¹ƒw§»º¿ƒw †ûÁ¿ù¼  ’•›w ²¦>§»ª›|‹–h‚n÷Й‡‡Ÿ‡‹Œ”‚“ª‡–n†‰ƒw ‰ƒE’“€2”Œ§n‹Œ–£” N€2ª‡– ´þ )þ ˜þ ÿ »þ 6þ š€•ª´ƒE€„§n›| ¼€2ƒw” ‡–h† ¨y›|’¾›|™€2”Œ›| ‰™’•”§h” ‡À¨y›|’•ÈÖ‡‹¹ƒw–E{頻‡–Ö§n–n‹Œ–nŸ‡’•ƒE€2–h† ‘`‹¹ƒE§»º¼ ½¦>§»ª‡›|‹Œ–n‚š›w™€2”Œ›| ‰™‡’“”§h” ‡À"È"›Q†‡–n‹Ï×`ƒw‚ ›| ‡–£›E¨G€2ª‡–£È›|‚“€Š‚•”Àw ‡”Œó´§nƒw ¼€Š†‡–¡ä|–h‹›|™‡È–n ¼€•‚„”Œ õ€2ª–£™‡’•”Œ§n” À[›w¨Ïó´ ´ƒw §n”¹ƒE‹6” ‚“€2’“‡È–n ¼€2‚h{©ª‡– È"ƒE€2ª‡–hÈõƒL€2”§h‚š›w¨?€2ª‡”Œ‚š¨y›|’•ÈÖ‡‹¹ƒ ¥‚š†‡–h’•”}äwƒL€2”›w .”‚ ð‡”Œ€•–à§n›|È™‡‹– Í÷G‚•›Ø×`–‚•ª´ƒE‹‹)›|È”Œ€š”Œ€£ª‡–h’•–E{ ¦>–h– ¥Ä G¨y›|’È›|’“–£†‡–h€2ƒw”‹Œ–n†N” >¨y›|’•È"ƒE€2”Œ›| K{vư–a’•–¡äQ”–h× €2ª‡–aÈ›>†–n‹ ¥‚ƒw‚“‚•‡È™€•”›| ‡‚˜ŸA–n‹Œ›C×a{ z|{˜©ª‡–à‚W€2›Q§»º²™‡’•”Œ§n–[¨y›|‹Œ‹›qט‚ª‡–à‹›|ÀE  ‡›|’“Èõƒw‹v†‡”Œ‚“€2’“”Ÿ‡>€2”›w K{Ž©ª”‚aÈ"–nƒw ‡‚š€•ª´ƒE€£€2ª–‹Œ›|ÀE  ƒw’“”Œ€•ª‡È›w¨€2ª–[‚“€•›>§»º<™‡’•”Œ§n–ލy›w‹‹›qט‚˜€2ª‡–Ö ‡›|’•È"ƒw‹v†‡”‚W€2’“”Ÿ‡€•”›| 6{¾©ª‡–Ö‹›|ÀE  ‡›|’“Èõƒw‹G†”‚W  €•’•”Ÿ€2”Œ›| H”‚Šƒ[§n›| ¼ä|–h ‡”–h ¼€ïƒE ‡†Ø’•–߃E‹”‚W€2”Œ§ï§»ª´ƒw’•ƒw§h€•–n’“” ߃L€2”›w H›w¨v‚“€•›>§»ºH™’•”§h–šŸA–n§ßƒE‡‚•–a”Œ€ ’“–hÜ´–h§h€2‚„‚“€•›>§»ºðª‡›w‹†‡–h’•‚ ЋŒ”È”Œ€2–h†õ‹Œ”¹ƒwŸ‡”Œ‹”}€¢ù|{ >{˜©ª‡–h’•–Žƒw’•–£ ›Â€2ƒ >–n‚˜›|’€2’•ƒw ‡‚2ƒE§h€2”Œ›| N§n›w‚“€2‚h{ œ{˜©ª‡–h’•–Žƒw’•–£ ›"†‡”}äQ”†‡–h ‡†‡‚˜†‡‡’“” ‡À[€•ª‡–a‹”Œ¨y–ï›w¨€•ª‡–a›|™€•”›| K{ ¤‡{˜©ª‡–h’•–Žƒw’•–£ ›"’“”‚•º|  ‹–n‚“‚˜ƒw’•Ÿ”Œ€2’•ƒwÀ|–š›w™‡™Í›w’“€2 ‡”Œ€•”–n‚h{ Ä>{˜©ª‡–a’“”‚•º| Y¨y’•–n–a’•ƒE€2–£›w¨” ¼€•–n’•–h‚“€n÷A’h÷‡”‚§h›| ‡‚W€»ƒw ¼€ß{ Ł{˜©ª‡–a›|™>€2”›w ‡‚˜ƒw’•– ‡’“›|™Í–nƒw K{ ‘`‹¹ƒE§»ºNƒw ‡†‰¦>§»ª‡›|‹Œ–n‚˜†‡–h’•”Œäw–n†Ø€2ª‡–£¨y›|‹Œ‹›qט” ÀÖ¨y›|’•ÈÖ‡‹¹ƒÖ¨y›|’Š€•ª‡–a§ßƒw‹Œ‹K›|™€•”›| jò •ô jò ¡ô ƒw ‡†Ø€2ª–a¨y›w‹‹›qט”Œ ‡ÀÖ¨y›|’“È[‡‹¹ƒJ¨y›|’Š€2ª‡–a™‡>€¾›w™€2”Œ›| jò ¡ô jò •ô Ä E@. Æ. ,. Ç mÈ`ÉDÊJË.Ì. ±}. ÎÍVÏ. mÌÐ LÑË.̎ҷ mÊ mÓÔ. 2†. D. Š mž. }. Æ. '}. m. —E. Ž-. Õ×Ö. H{Ø. Ù±Ú @MÛGÝܟÞ5ßàLá&Ø. LÙãâ DP. ä. R-. Ö. GÝܟÞ5ßàLá&Ø. ÎMåÙãâ @MnH{Ø. ÎMåÙ±Ú.

(22) Å. æ ^KçŒè éëê5b´ìãíã]D^îa.Zï_ãð. טª‡–h’•–. ‹ Kò ûô ò H<ñmG. Ö. Ù±Ú. Ö. â. ó&ôŽònõ. õ4÷. Ùãâ. ö. ٮڔM«õ ÷. ||ô ñ. [ö. ö. jò Íô n§ ‡ÈÖ‡‹¹ƒE€•”Œäw–£ ‡›|’•È"ƒw‹Í™‡’•›|Ÿ‡ƒwŸ‡”‹Œ”Œ€¢ù ƒw  Q‡ƒw‹” n–n†NäEƒw’“”¹ƒw ‡§h–£›w¨€•ª‡–a§n›| ¼€•” ð‡›|‡‚“‹Œùõ§n›|È™͛w‡ ‡†‡–h†<’“–h€2’• ¿›| ¿€•ª‡–a‚“€•›>§»º §n›w ð€•” ð‡›|‚•‹Œùõ§n›|È™A›|‡ ‡†‡–h†<’“”‚“º¼ Y¨y’•–h–J’•ƒE€2– §n‡’“’•–n ¼€„‚“€•›>§»ºN™’•”§h– ‚“€•’•”Œºw–a™‡’•”Œ§n– €•”È–š€2›à– >™‡”Œ’2ƒE€•”›| N›w¨ƒw ¿›|™€•”›| Ø. õ. <ò. Ö. >ø. â. Ö. C. Ö. ó&ô. Ö. H. Ö. ö. G. Ö. . rŒDr. ¹q»Tw. Å. w2u|. st%uBuBv'w2uyxz {v'|. u v'¶ v&TÄ. Å. |ÂTw2$. ©ª‡–aäEƒw‹‡–£›E¨)ƒ ‡’•›w™Í–nƒw <†›Cט Q ½ƒw ‡†Q ¢” اnƒw‹‹K”Œ‚ ò 5ô °ò Íô ò ?ô jò Ðô טª‡–h’•– ‹ ‡ò ûô ò ||ô w טª‡–h’•–  H”Œ‚Š€2ª‡–a‚W€2›Q§»º ¥‚„†‡”ŒäQ”†–n ‡†NùQ”–h‹† ´ƒE ‡† ¿”Œ‚Š€2ª‡–£€2”ŒÈ"–¾€2›àÈõƒL€2‡’“”Œ€¢ù|{ Q‡ƒE€2”Œ›| ²ƒwŸA›qä|–3ƒE‚•‚•È"–h‚¾€2ª‡ƒE€¾€•ª‡–ց ‡†‡–n’“‹ŒùQ” Àõƒw‚“‚•–¡€£™‡’•”Œ§n–a¨y›|‹‹Œ›qט‚„Àw–n›|È–h€•’•”§J‘`’“›q׊  ‡”ƒw HÈ›w€2”Œ›| Hƒw †H”‚І‡–ï€2›ÂÁ¿–n’“€•›| zqÞ R{)ñ ‡’•›w™Í–nƒw N†‡›qט > ½ƒE ‡†> ¢›w€§ßƒE‹‹A§ßƒw NŸA–𙇒“”§n–h† äQ”¹ƒ[€2ª–J”Œ > ¢›w€™´ƒw’“”Œ€¢ùõ’•–n‹ƒE€2”Œ›| K{)©ª–aäEƒw‹Œ‡–£›w¨)ƒ ‡’“›|™A–߃w ¿‡™> ¢ƒw ‡†>  ” N™‡€„”Œ‚ Aô ðò 5ô jò Íô ¼ò 5ô jò ñï‹}€2ª‡›|À|ªj§n‹Œ›|‚•–h†>  ¨y›w’•È«‚•›w‹€•”›| ‡‚J– >”Œ‚“€ß÷€2ª‡–H‚W€2‡†>ù°›w¨˜ ð‡È–n’“”§nƒw‹5È"–¡€2ª‡›Q†‡‚ÖŸ‡ƒw‚•–h†›| Ÿ‡”Œ ‡›|È”¹ƒw‹ÍÈ"›Q†‡–n‹Œ‚”‚˜‚“€•”‹Œ‹G‡‚•–¡¨y‡‹G¨y›|’€2ª‡–J ‡–h× ”Œ ‡‚•”ŒÀ|ª¼€2‚˜”Œ€˜Ÿ’•” À|‚n{ÓÙ €šƒw‹Œ‚•›àª´ƒw‚¾ƒw™‡™‹”§nƒE€2”Œ›| ‡‚ €2›a– ›E€2”§˜›|™>€2”›w ‡‚)טª‡–n’“–„€•ª‡–€2–h’•È” ´ƒw‹™´ƒßù|›wúN¨y‡ §h€2”Œ›| à”‚5 ‡›| Q ¢‚“€2ƒw ‡†´ƒE’•†K÷Qƒw ‡†à§h‹›|‚“–n†> Y¨y›|’•È ‚•›w‹€•”›| ‡‚˜ƒE’•–£ª´ƒw’“†¿€•›à§n›|È–£Ÿ¼ù|{ E. â[û. HBÜ ÞîùLá L~ŠñúH. ø. â. Rü~. Ö. ñ H@G. :†. [ž5ò. â. >øNM«õ ÷. â. Ø. ñ. ö. Îö. ö. ó&ô”M«ýëònõ â õ. Ö. Þ. dó&ô4M«ý·ònõ. õ”÷. þ. Hnÿj~. â[û. dø MOGÝÜ Þ5ßàá L~Nñ.H. Ø. J}. â. ñ. ö. E{†. . Ÿž. ºE. E. GÝܟÞ5ß à á L~ŠñúH. â[û. Þ. â. Ø. øònõ ÷. ÎM. ö @MªH{ܟÞîùá ~NñúH. â[û. Ø. ´M·ø. . D. rŒ¡. ¹q»Tw. . v'wVTw2u£u{|¶. wV. <Á ›Q†‡–n‹Œ‚5›w¨6‚W€2›Q§»º3™‡’•”Œ§n–„ƒw’“–„‚•´ƒw‹Œ‹Œù֔ 3€2–h’•È‚?›E¨Í€•ª‡–„ÆÇ”Œ–n ‡–h’5™‡’•›Q§n–h‚•‚n{©ª–„ÆÇ”Œ–n ‡–h’?™’•›Q§n–n‚“‚ ”‚ƒï™´ƒw’W€2”Œ§n‡‹ƒw’G€¢ù>™A–Š›w¨ÍÁ<ƒw’•ºE›C䎂“€•›>§»ª‡ƒw‚“€•”§Š™‡’“›>§h–n‚“‚n{)Ù €ª´ƒw‚)ŸA–n–h 3‡‚•–h†3ŸÍ–¡¨y›|’•–Ó” [™‡ª¼ùQ‚•”Œ§n‚€•› †‡–h‚•§n’“”ŸA–¾€•ª‡–šÈ›w€2”Œ›| "›E¨ÏƒŽ™´ƒE’“€2”Œ§n‹Œ–„€•ª´ƒE€Š”Œ‚Ó‚“‡Ÿ“–h§h€Š€•›3ƒŽ‹ƒw’•À|–„ ð‡È[ŸA–n’Ó›w¨Ï‚•È"ƒw‹‹´È›|‹Œ–n§n‹¹ƒw’ ‚•ª›>§»ºð‚¾ƒw ‡†¿”‚‚•›wÈ"–¡€2”È–n‚’“–h¨y–h’•’•–h†¿€•›Âƒw‚˜ ‡›|’•È"ƒw‹Œ” n–h†Ø‘`’•›qט ‡”ƒw ØÈ"›E€2”›w K{ Æ.

(23) Ê. æ ^KçŒè éëê5b´ìãíã]D^îa.Zï_ãð. Uñ ™‡’•›Q§n–h‚•‚h÷>÷×˜ª‡”§»ªØ¨y›|‹Œ‹›qט‚Ó€•ª‡–šÆÇ”–h ‡–n’™‡’“›>§h–n‚“‚„§nƒw ¿ŸÍ–£‡ †‡–n’“‚“€2›Q›Q†¿Ÿ¼ùN§h›| ‡‚“”†‡–h’•” À €2ª–§»ª‡ƒw ‡À|–h‚Ž”Œ .”Œ€2‚šäEƒw‹Œ‡–3” ‚“Èõƒw‹Œ‹”Œ ð€•–n’WäwƒE‹‚£›w¨?€2”ŒÈ"–E{ –h€  ïŸÍ–[€•ª‡–à‹–n Àw€2ª ›w¨`ƒN‚•È"ƒw‹‹ ” ¼€•–n’“äEƒw‹A›w¨G€•”È–ïƒw †

(24)  [ŸA–¾€2ª–š§»ª´ƒw ‡Àw–š” [†‡’•”Œ ‡À V{©v›Ö¨y›|‹Œ‹›q× €•ª‡–¾ÆÇ”Œ–n ‡–h’Š™‡’•›Q§n–h‚•‚h÷ €2ª–n’•–Jƒw’“–£€¢×`›ÂŸ´ƒw‚“”§a™‡’•›w™Í–h’“€2”Œ–n‚  àÈ[‡‚W€„‚2ƒE€•”‚“¨ ù ~’•›|™A–n’W€¢ù z|{ Ù ¨ a”Œ‚)ƒ¾äEƒw’“”¹ƒwŸ‹–5טª‡”§»ª3¨y›|‹Œ‹›qט‚v€•ª‡–`ÆÇ”Œ–n ‡–h’)™‡’•›Q§n–h‚•‚h÷ð€•ª‡–n ÷|€2ª‡–`§»ª´ƒw ‡À|–`›w¨ÐäwƒE’•”¹ƒEŸ‡‹– à†‡‡’•”Œ ‡Àƒ3‚•È"ƒw‹‹K”Œ ¼€2–n’WäEƒw‹K›w¨v€2”ŒÈ"–  V÷´‚2ƒE€•”‚“ó‡–n‚ F.    . Ö. טª‡–h’•–  ”Œ‚˜ƒà’•ƒw ‡†‡›wÈ †‡’2ƒßט”Œ ‡À3¨y’•›|Èɀ2ª‡–a‚“€2ƒw ‡†´ƒE’•†‡” n–n†¿ ‡›|’“ÈõƒE‹K†‡”‚W€2’“”Ÿ‡€•”›| 6{ ~’•›|™A–n’W€¢ù<>{ ©ª‡–šäEƒw‹–š›w¨ Ö¨y›|’Šƒw ¼ù"€¢×Ó›à†‡”Œú͖n’“–n ¼€‚•ª›|’“€”Œ ¼€2–n’WäEƒw‹‚Ó›w¨Ï€2”È– Ӄw’•–š”Œ ‡†‡–h™Í–h ‡†‡–n ¼€n{ ‘Óù‰™‡’•›|™A–n’W€¢ù°zw÷  H”Œ€•‚•–h‹Œ¨5ª´ƒw‚šƒH ‡›|’•È"ƒw‹v†‡”‚W€2’“”Ÿ‡€•”›| 6÷Aטª‡”Œ‹–Ö~5’“›|™A–n’“€¢ù.õ”È™‡‹”Œ–n‚€2ª‡ƒE€  ¨y›|‹Œ‹›qט‚ƒaÁ<ƒw’•ºE›Cä֙‡’•›Q§n–h‚•‚h{)©ª‡–‚“€•›>§»ºJ™‡’“”§n–`‡ ‡†‡–h’€2ª‡–Š‘`‹¹ƒw§»º| ½¦>§»ª‡›|‹Œ–n‚)È›>†–n‹ð€2ª‡–h [¨y›|‹‹Œ›Cט‚ C.  . Ö. ÙîH. H. . RÙ Rò„Hõ<Ù ±Q. ©ª‡”Œ‚J™’•›Q§n–n‚“‚Ö”Œ‚J§nƒw‹‹Œ–n†.€2ª–"À|–h›|È–h€2’“”§à‘`’“›qט ‡”¹ƒw ûÈ›w€2”Œ›| ¥ç Y{"Ù €J×`ƒw‚J‡‚•–h†°€2›¿‚“€•’•‡§¡€2‡’“– €2ª–JŸ” ‡›|È”¹ƒE‹ÍÈ›>†–n‹K”Œ ¿ – Q€„‚•–n§¡€2”Œ›| K{ n mž. . rŒ´³. ¹q»Tw. . sÀv&T|. v'%$jÅ. |ÂTw2$. ”Œ’•‚“€n÷>×Ӗ£’•–¡ä>”Œ–h× €2ª‡–£†‡”Œ‚•§h’•–h€•–¡ Y€2”È–šƒE™‡™‡’•› >”È"ƒE€•”›| €2›[€2ª–£À|–n›|È–h€•’•”Œ§£‘`’•›qט ‡”ƒw NÈ›w€2”Œ›| K÷  !. { ›|’Ÿ‡’“–häQ”Œ€¢ùw÷‡×`–J‡‚“– ø” ؙ‡‹ƒw§n–a›w¨ ˜òRÞ¼ôV÷€2ª‡–a§h‡’•’“–n ¼€„‚“€2›Q§»ºN™‡’“”§n–E{ ˆ`›| ‡‚“”†‡–h’5€•ª‡–˜‚“€•›>§»º[™’•”§h–" €•”È–`¨y’•›wÈ ‡›q× ò €2”ŒÈ"– h–n’“›ðô „ò# “ô¡{ ¾ ‡†–n’€2ª‡–˜À|–h›|È–h€“  ’•”Œ§[Ÿ‡”Œ ‡›|È”¹ƒw‹G’•ƒw ‡†‡›|Èæ×`ƒw‹º<È"›Q†‡–n‹R÷͔Œ ƒõ™A–n’•”Œ›>†.›E$¨  V÷6€2ª–3‚“€2›Q§»º‰™’•”§h–[–n”}€2ª‡–h’š” §n’•–nƒw‚•–h‚ €2› %<ט”}€2ªØ™‡’“›|Ÿ´ƒwŸ‡”Œ‹”}€¢ù &¿›|’˜†‡–h§n’•–nƒw‚•–h‚„€•› àט”Œ€2ªØ™‡’“›|Ÿ´ƒwŸ”‹”}€¢ù¿z '&°òR¦>–n– ”Àw‡’•–aQ{ŒzCôV{ ”’“‚“€n÷×`–J”È™A›|‚•–ª´ƒE€ ( ˜)ò  “ô *,+.-ƒw ‡0† /21 ˜)ò  “ô ò 3+4-657 XzCô +.-8*:9 ;. ©ª‡–J– >™A–n§h€•–n†<‚“€2›Q§»ºN™‡’“”§n–aƒL€€2”È–  `”‚À|”}ä|–h <Ÿ¼ù & % òWz 0&Aô ¾–h ‡§n–E÷Л|‡’Šó´’“‚“€„’•– Q”’•–hÈ"–h ¼€¾”Œ‚€2ª‡–a– ð´ƒE‹”Œ€¢ùõ›w¨– >™Í–h§h€•–n†‰™’•”§h–w÷ & % òWz '&Aô *<+4,. &. ÙîH. Ö. H. ,. <Ù Žò„Hõ<Ù. H. H. 0. ¤H. BH. NH{Ù. @

(25). ,. M. ,. üH. [ž Ö. H{Ü. [ž Ö. ãó®üH. â. H. LÜ. M. . . JH. †. ò. ·M. '†. H{ÙkQ. JH. %ò. . ·M. ÑH{Ù. Ö. H{Ü. [Q. ´Ü. â. H. â. õ. â. DQ.

(26) ç. æ ^KçŒè éëê5b´ìãíã]D^îa.Zï_ãð. =p. Su. S 1-p. Sd. ”TGOŒQ<À|bd‡c,’•b–HU6e6>U8Dg{}fiz hQ<GjXMk:_aU6DON ?T> GOQ<bc,bUle6U8DmAfo@CnBEp D)FHhrG:q I2JLKMDONF P)D)Q!ROS TGVU6RWF XYFZU8DONFHG[Q]\<FZP"D)Q X^`_aU8DON ,. ú-¤•l;>?‘=@˜å;™1”3. X=@4œk3kA. ©ª‡–aäEƒw’•”ƒw ‡§n–£›E¨€•ª‡–aŸ‡” ‡›wÈ"”ƒw‹Í‚W€2›Q§»ºH™‡’“”§n–JƒE€" `”Œ‚À|”Œäw–n ¿Ÿðù &vò %6ô ò½z '&Ðônò Qô Çò *<+.-yô ¦>›à›|‡’˜‚“–n§n›w ‡†‰’“– ð‡”’“–nÈ–n ¼€„”‚Š€•ª‡–a– ð´ƒw‹Œ”Œ€¢ùH›E¨äEƒw’“”¹ƒw ‡§h–w÷ &vò %Íô ò½z 0&Aônò >ô ò *<+4-yô s. ›|’ &t% ò½z '&Aô *<+4u. ٢ș͛|‚“” ‡vÀ % z|÷×Ӗާnƒw ¿À|–h€€•ª‡–a‚•›|‹Œ€2”Œ›| % ,5 +.5 +.-ƒw w† & *,% +.Ù¢ <ƒà’“”‚“º¼  ‡–n>€2’2ƒE‹G–n§n›w ‡›|ÈÖùwt÷  3ƒw ‡† |  . &9 òWz w|ô ò½z ||ô Ù ¨6×Ӗƒw’“€•”Œ€2”Œ›| [€2ª–˜€•”È–Š€2›J– >™‡”Œ’2ƒE€•”›|v xX”Œ ð€•›Ž ™A–n’•”Œ›>†‚n÷¼€2ª‡–h  y 5{ ¦>–h– ç ´¨y›|’5È›|’•– †‡–¡€»ƒw”Œ‹–n†¿ƒw ‡ƒw‹ŒùQ‚•”Œ‚n{ â. LH. ò. '†. â. H{Ù. M. â. LH{Ü. Q. '†. â. H. ò. ·M. â. JÙ. M. â. LH{Ù. ò. ·M. Ù. M. â. MªÜ. â. H{Ü. â. Ö. õ. Ö. â. H. â. õ. â. DQ. DQ. Ö. Ö. ÷. Ü. Ö. PÙ. ܟÞ. ÷. Ö. Ü. MªÙ. ¤MªÙ. Q. ó. Kñ. . Ö. Rò. Kñ. óåM«õ õ. â. ñ. DQ. Ö. I. % Ÿž.

(27)   & $

(28) z.     

(29)   . ¡Â. ¹q»Tw¨sÀv&T|.    . v'$T¹Uu{wVw. Å. {. wå»T|Â. v». {. st¶ÃÁ. |. À%uB. ‘. ¦. !!¶ë{v|¤. © ª‡–¾Ÿ‡” ‡›wÈ"”ƒw‹È–h€•ª‡›>†"”‚ט”†–n‹Œùà‚•–n†õ” ™‡’•”Œ§n” ÀŽ›|™>€2”›w ‡‚n{)ñ ‚“€2ƒw ‡†´ƒE’•†HƒE‹À|›|’“”Œ€•ª‡Èê¨y›|’5€2ª– Ÿ‡”Œ ‡›|È”¹ƒw‹ÍÈ"›Q†‡–n‹Ï”Œ‚˜€•ª‡–JŸ‡” ‡›wÈ"”ƒw‹6€2’“–n–JÈ"–¡€2ª‡›Q†Ø×˜”Œ€2ª<Ÿ´ƒw§»º¼×`ƒw’•†²”Œ ‡†‡‡§¡€2”Œ›| K{Š©ª‡”Œ‚¾È–h€•ª‡›Q† äEƒw‹–n‚€2ª‡–a›|™>€2”›w NŸðùؒ“‡ ‡ ‡”Œ ‡À3¨y’•›|Èɀ2ª‡–£€•–n’•È” ‡ƒw‹6 ‡›Q†‡–h‚¾Ÿ´ƒE§»ºð×`ƒw’“†‰” N€•”È–ï€2ª‡’“›|‡À|ªØ€2ª– €2’“–n–E{©ª‡–¾äEƒw‹Œ‡–˜›w¨K†‡›w‡Ÿ‡‹–„Ÿ´ƒw’“’•”Œ–n’5›|™€•”›| ‡‚5§nƒw õŸA–¾§h›|È™‡€2–h†HŸ¼ù3€2ª‡”Œ‚ÓÈ–h€•ª‡›Q†õƒw‚5¨y›|‹Œ‹›qט‚n{ Æ –aט”Œ‹‹Í‡‚•–a€2ª‡–a†‡›w‡Ÿ‡‹–£Ÿ‡ƒw’•’“”–n’§nƒw‹‹Kƒw‚˜ƒw ¿– ƒwÈ™‡‹–E{ . }C(i+1,j+1) p. }C(i,j). }C(i+1,j). 1-p. ”FHD)ŒFHÀ|GC‡Ul’•‰–ïPOU6œŠ{}Fjz DONF‹MTd~c,GO FZ‰ŒDONFZP)FZP ŠFZ‰4Q<D)~ FZPaDOU6[F<€ K_aNU6e8MF$‚ DONF‹P)FZRWQ3‰ŠoŠFZ

(30) ‰Q<> D)FZPCP)DOc,D)F<„q ƒ NFj†G‡P)DTdc,GVc<["ˆ –h€ Žò  )QôІ‡–n ›w€2–J€2ª‡–J§ßƒw‹Œ‹KäEƒw‹‡–JƒE€˜€•”È– `ƒw †‰‚“€2ƒE€2– ´{ ”Œäw–n òm z ) zqô˜ƒE ‡† mò  °z )Qô¡÷🴃w§»º¼×`ƒw’•†N”Œ ‡†‡‡§¡€2”Œ›| ¨y›w’5€•ª‡–„Ÿ‡” ‡›wÈ"”ƒw‹È›>†–n‹vòc‚“–n– ”À|’•–„œ{}zCô)‚2ƒßùQ‚ mò  #>ô)”Œ‚ O+.- 8ò & Žò  z # zqô ò½z '&Ðô mò  z )Qô•ô ”Œ¨ŠŸ´ƒw’•’“”–h’•‚Žƒw’•–" ‡›w€Ž” ¼ä|›|‹}ä|–h†K{‰Ù ¨˜›|>€Ö‚W€»ƒE€•v– ²§n›|’“’•–h‚•™A›| ‡†‡‚Ö€•›.ƒ<‚W€2›Q§»º ™’•”§h–õ›w¨ ›|’ ˜÷ €2ª–n mò  #>ô‚•ª›|‡‹†‰ŸÍ– h–n’“›H” ‡‚W€2–nƒw†K{頻”‚ ‡§n”Œ†‡–n ¼€2ƒw‹‹}ùN‚•ª‡›qט‚š€•ª‡–ÖäEƒw‹–Ž›w¨€•ª‡–Ö†›|‡Ÿ‡‹Œ– Ú ,. ú-B•²1. Õ. Õ. F. .ò. 4‹V1”›<„’?44i Ž9<;>=”?. 5=@›ª9 ‘œÝ•l;>?‘=@˜å;™1”3. X=@4œk3kA. . ÑP. Õ. ,. úP. Ü Þ5ß. Õ. Jò. úP Vò. Rò. M. Õ. Jò. ïò. .P Vò. Õ. .P. ë~. Õ. ÑP. %. ÑP. ©.

(31) qz Þ Ÿ´ƒw’“’•”Œ–n’[§nƒw‹‹ÓƒE€<òm )QôŽ”‚Ö– ð´ƒw‹`€•›²€2ª´ƒL€3›w¨˜€2ª‡–N‚W€»ƒw †´ƒw’•†ø§nƒw‹‹ÓÈ"”Œ Q‚Ö€2ª´ƒL€3›w¨˜€2ª‡–N†›|‡Ÿ‡‹Œ– Ÿ´ƒw’“’•”Œ–n’ºð ‡›Q§»º¼  ›|€Ó§ßƒw‹Œ‹äQ”¹ƒ£€2ª‡–˜”Œ > ¢›|>€5™´ƒw’•”}€¢ù|{‘`ƒw§»º¼×Šƒw’“†H” †‡‡§h€•”›| 3ט”Œ‹‹–¡ä|–h ð€•´ƒw‹Œ‹Œùà’•–nƒw§»ª €2ª–J”Œ ‡”Œ€•”¹ƒw‹A ‡›Q†‡–JƒE€ŽòRÞ »Þ¼ô¡÷‡ƒw ‡†Ø›|‡’˜†‡›|Ÿ‡‹–£Ÿ´ƒE’•’•”Œ–n’§nƒw‹‹K”Œ‚™‡’•”Œ§n–h†K{ ‘.’ v“ ” ïè. ^Kç. –•— g’. ŸcCZkê±\[^K]Ñc™ê. !èK\ J^`_. P. '†. `P. ¡ÂDr. ˜ ™. ¹q»Tw. ¨w. Ýw2¶ë{v'|. uBv&!¶. v&z!$'w. ñ€•›>›|‹„×`–.‚“ª‡›|‡‹Œ†ÇºQ ›C× €2› ‡†‡–n’“‚“€2ƒw ‡†Ç€2ª‡–.§h›|È[Ÿ‡”Œ ´ƒE€2›w’•”¹ƒE‹È"–¡€2ª‡›Q†X”‚õ€•ª‡–.’•–¡Ü´–n§¡€2”Œ›| ™‡’“” ‡§h”™‡‹Œ– ¥Ú Y{ Ù¢ÈõƒEÀ|” ‡–šƒà™‡ƒw’“€•”§n‹Œ–ï‚W€»ƒw’W€2‚„ƒE€™A›|‚•”}€2”Œ›| òRÞ 1QôV÷‡›| N€2ª‡–a”Œ ð€•–nÀ|’•ƒw‹6‹ƒE€•€•”§h–šƒw ‡†Nט”Œ‚•ª‡–h‚˜€•› ’•–nƒw§»ª‰mò š ›¡ô¡{)ÆÇ”}€2ª‡›w€5‹›|‚“‚›w¨ÍÀ|–n ‡–h’2ƒw‹Œ”Œ€¢ùw÷ðƒw‚•‚“‡È"œ– 1 H› ÇÞ>{)©ª‡–˜™´ƒw’W€2”§h‹–”Œ‚§n›| ‡‚W€2’•ƒw” ‡–h† €2›3È›qä|–š€•›¿mò  Fz ) zCôӛ|’aŽò  Fz # ÃzCôÓ¨y’“›|Èmò  #>ôV÷>€•ª‡–šä|–h’“ùH×`ƒßùõ€2ª–£™‡’•”Œ§n–š‡ †‡–n’€2ª– Ÿ‡”Œ ‡›|È”¹ƒw‹AÈ"›Q†‡–h‹K”‚‚“‡™‡™A›|‚•–h†<€2›à–¡ä|›|‹}ä|– mò  )Qaô 9 mò  Çz ) zCôŠƒw‚“‚•›Q§n”ƒE€2–h†¿×˜”}€2ªN€2ª‡–a‡™¿È›Cäw–w÷ A9 % mò  )Qaô 9 mò  Çz ) XzCôŠƒw‚•‚“›>§h”¹ƒE€•–n†Nט”Œ€•ª¿€•ª‡–a†‡›qט <È›qä|–E÷ 9 ¾›q× È"ƒw ¼ù<‚“‡§»ª.™´ƒE€•ª‡‚ï§nƒw <€•ª‡–Ö™‡ƒw’“€•”§n‹Œ–£€»ƒwºE–Ž€2ª‡ƒE€ï€•›|‡§»ª²›|’„§n’“›|‚•‚„€2ª‡– ‡ ½ƒ >”ŒH‚ ž°©ª‡”Œ‚ ð‡–n‚W€2”Œ›| H§ßƒE HŸÍ–ï’•–n™ª‡’2ƒw‚“–n†Øƒw‚`ƒJäEƒw’“”¹ƒw ¼€Ó›w¨G€2ª‡–¾Ÿ´ƒw‹Œ‹›w€?™‡’“›|Ÿ‡‹–hÈ<{ ”}ä|–h õ€2ª´ƒL€ƒŽ§nƒw ‡†‡”Œ†´ƒE€•– ‚“€2ƒw’“€•‚ט”Œ€•ªàƒï¨y–h×Ӗn’)äw›w€2–h‚)€2ª´ƒw [€•ª‡–›|™‡™A›| ‡–h ¼€„òyטª‡”Œ§»ªà”‚ ›w€‡ ‡§h›|ÈÂÈ"›| ֔ [È"ƒw ¼ù֙‡ƒw’“€•‚)›w¨ €2ª–ï×`›w’•‹†´ôӃw ‡†õ–n ‡†‡‚™õט”Œ€•ªHŸH¨y–h×Ӗn’`äw›w€2–h‚n÷‡ª›C× È"ƒw ¼ùà׊ƒßùQ‚§ßƒw H€•ª‡–ïäw›w€2–h‚ŠŸÍ–ï§n›|‡ ¼€•–n† ” Nטª‡”Œ§»ª¿€•ª‡–£×˜” ‡ –n’ ¥‚ä|›w€•–ާh›|‡ ¼€„– ð´ƒw‹Œ‚€2ª‡–a›|™‡™A›| ‡–h ¼€ ¥‚¾ƒL€¾‹Œ–߃w‚W€˜›| ‡§h<– ž  mž. `P&M. @P'M. :P åÿ. :ò. .P ·ò. :ò. úP VM. ÑP. .-. P. Jò. úP åò. P. Jò. úP —M. JH. H. JH. H{Ù. . —ø. m. . †. '}. '†. &}. (0 , a). ŸJ  . (n , -b) (0 , -a). ” À|‡’“–aœ{ 2‚ ¡ ¢€ ¢~ 4~ € `¡ ¤£ ¦¥ ˆ`›| ‡‚“”†‡–h’5ƒw ¼ù[‹–hÀ|”Œ€•”È"ƒE€2–5™´ƒL€2ª3¨y’•›|È òRÞ 1Qôv€•›Âòmš ›¡ô€•ª´ƒE€–h”Œ€2ª–n’€•›|‡§»ª‡–h‚?›w’)§n’“›|‚•‚“–n‚ €2ª– ‡ ¢ƒ >”‚h{ –hw€ §†‡–h ‡›w€2–à€2ª–à󇒕‚“€Ž™A›|‚•”}€2”›w .”Œ€aª´ƒw™™Í–h ‡‚n{õ‘Óù.’•–¡Ü´–n§¡€2”Œ ‡À¿€•ª‡–™͛|’W€2”Œ›| .›w¨ €2ª–™‡ƒE€2ª.¨y’•›wÈ òRÞ 1Qôï€2`› §÷σ¿™´ƒL€2ª.¨y’•›|ÈÝòRÞ W1>ô¾€•› òmš ›¡ôš”‚š€•ªQ‚J§h›| ‡‚W€2’•§h€2–h†K{ ¾›w€•– €2ª‡ƒE€a€2ª‡”Œ‚J™‡ƒE€2ªû§n’“›|‚•‚“–n‚Ž€•ª‡– ‡ ½ƒ >”‚JƒEw€ §{N¦>–h– ”ŒÀ|‡’“–àœ{ H¨y›|’a”‹Œ‹‡‚W€2’•ƒE€2”Œ›| K{[ñ È›|È"–h ¼€ ¥‚ ’•–¡Ü´–n§¡€2”Œ›| °‹Œ–߃w†‡‚a€2›¿€2ª‡–"§n›| §n‹‚•”›w €2ª‡ƒE€Ž€•ª‡– QÈ[ŸÍ–h’Ö›w¨Š™´ƒE€2ª‚J¨y’“›|È òRÞ 1Qôš€2›Žò 𠐛¡ô €2ª‡ƒE€£€2›|§»ª €•ª‡– ‡ ½ƒ >”Œ‚š”‚£– ‡ƒE§h€2‹}ù‰€•ª‡–à QÈ[ŸÍ–h’£›w¨Ó™´ƒE€2ª‚š¨y’•›|ÈÝòRÞ H1Qô„€•› mò š ›¡ô¡{Ö©ª‡”‚£”Œ‚ ,. `- š. ‘œ. œ ±35œ Ž9<;>=”?„hV›<;>? R;>8k35œ `P&M. 5=”›„•—;>?4=”˜V;™143. ø. m. %14?44=@˜. X143. 5A. ”P&M. F. `P&M. ±P. ø. m. @P'M. ¤ . ,. &}. ±P'M. ø. m. D. ±P. @P'M. @P&M.

(32) |z z €2ª–Ö§n–h‹–hŸ‡’2ƒE€•–n†<’•–h܇–n§h€•”›| ‰™‡’•”Œ ‡§n”Œ™‡‹–a›w¨ñï ‡†‡’–N¨ ò½zqçw¤¼ÞL 2zqځzCÊwô`™‡‡Ÿ‡‹Œ”‚•ª–n†‰”Œ °zqçwç¼Ê<ò ” ¼€šƒE ‡† ÆÇ”‹Œ‚•›| Ê ¹ô Ú R{ ¦>” §n–<ƒw ¼ùø‚•‡§»ª ™‡ƒE€2ªÃ§n›| ‡‚“”‚W€2” Àû›E¨š FÈ›qä|–h‚"È[‚“€"ª´ƒßä|–'› ©1jÈ›|’•–؆‡›qט ÃÈ"›qä|–h‚ òª¢ »z,«|‚2ôa€•ª´ƒw ‡™øÈ›Cäw–n‚¿ò]ª [z,«|‚»ôV÷€2ª–N†‡–n‚“”’•–h† ð‡È[ŸA–n’3– ð´ƒE‹‚Ö€•ª‡–N ð‡È[ŸA–n’[›w¨˜×`ƒßù>‚[€•› ™A–n’•Èց€2–"òmš Y1 Y›¡ô |¬ª [z,«|‚˜ƒE ‡†jòŽš ?1 ­›¡ô |¬ª½ 2z,«|‚n÷>טª‡”§»ª¿”‚– Q‡ƒw‹G€2› ® y<¯±š °‡¯±² ¨y›|’–¡ä|–n 6÷A ›| > ¢ –nÀ¼ƒE€•”Œäw:– š ­1 ?› ³ ƒw ‡† h–n’“›¿›E€2ª‡–h’“ט”‚“–w{J©ª‡–3 ‡–hÀ¼ƒE€2”}ä|–vš ´1 µ›J§ßƒw‚“–3§ßƒw ŸA–[†‡”Œ‚•’•–hÀ¼ƒw’“†‡–n†.‡ †‡–n’š€•ª‡–3§n›| Q  ä|–h ¼€2”›w K÷ ® š¶ Þ[¨y›|’ ¶ FÞ›w’ ¶ ?š ³ ‘.’ v“ ” ïè. ^Kç. –•— g’. ŸcCZkê±\[^K]Ñc™ê. !èK\ J^`_. F. < mž V Ÿž. ò. ò. ŒM. —M. Ññ. '†. ò. ò. 2ò. Ññ. †. ò. 2ò. â. !. Šò. lò. Ö. ¡Â¡. ¹q»Tw. |. ‘TwV. . |¸. "t|. €. S. ¥!v&T—|uBv'%$jÅ. wå{»T|Â!. ñï ƒw‹Œ€•–n’• ‡ƒE€2”}ä|–¿™‡’•”Œ§n” À È–h€•ª‡›>†Ã‡‚•–h‚H§n›wÈ[Ÿ‡” ‡ƒE€2›|’“”§h‚n{Lj`›| ð€•” ‡À €2ª‡–< QÈ[ŸÍ–h’õ›w¨ïäwƒE‹”† ™´ƒE€•ª‡‚š€2ª‡ƒE€£‹–nƒw†²€2›HƒH™´ƒw’“€•”§h‡‹¹ƒw’„€2–h’•È” ´ƒw‹v™‡’“”§n–Ö”‚ª‡–3”†‡–nƒõŸA–nª‡”Œ ‡†²€2ª‡–3ª”À|ª‡‹}ù¿– §n”Œ–n ¼€ §n›wÈ[Ÿ‡” ‡ƒE€2›|’“”¹ƒw‹QÈ–h€2ª›>†à€2›a™‡’“”§n– ‡’“›|™Í–nƒw †‡›|‡Ÿ‡‹Œ–˜Ÿ´ƒw’•’“”–h’›|™€2”Œ›| ‡‚h{Ù €2‚5™A–n’W¨y›|’•È"ƒw ‡§h–¾ƒE ‡† ƒw§h§n‡’•ƒw§hùNט”Œ‹‹KŸA–a†‡›>§h‡È–n ¼€2–h†<”Œ ²ˆ`ª´ƒE™€2–h’„¤{5Æ –J†‡–n’“”Œä|–aŸA–n‹Œ›C×§n›|È֟‡” ´ƒL€2›|’“”¹ƒw‹Ð¨y›|’•ÈÖ‡‹¹ƒw– ¨y›|’›|™>€2”›w ‡‚Š€2ª´ƒL€˜§n›|È–a” ¼€2›3– ”Œ‚“€•–n ‡§h–Ö›| ‡‹}ùH”}¨–h”Œ€•ª‡–n’Ÿ´ƒE’•’•”Œ–n’”Œ‚ª‡”Œ€n{ . E. D. ·¸. (0 , a). ¹J. ·¸. ºK. s. (0 , -a). ¼ ½¸. H. (n , -b). »L. ·. ”GVc<Œ‰À|ЇQ3’•[À–¿œ_{c<œ e8'S¡BEGVQ3[ÂÁÄÃ!ÅHpaƤÇ.D)¾ Q ÁÉÈMÅHpj¿~ ÊWÇ4[ËP)4D¥ NU6¦D4FZ€ U8DONMFH‚ G¦sbc,¡ GOGV¢U6FH€ GZK–¢c<‰~ Š:DONFHGOF$[ËP)4D.~ FWÌU6P)DOP¦c<‰Í4ƒ ˆmNNU8FD (0 , -( a+2s )). ,. ±-. œJ8kœ:1®9<œk. 8k8J35; Ž1±9<;>=@? ª=. “9 ‘œ. œ `3îœ Ž9R;>=@?¼hV›<;>? R;>8k35œ4A. TGOFZRWFZŠFZŠb–fÎwˆmNU6DHqÏ#‰RWQ3ˉŒDOUl‰ÐvDONF‰–Ë[œb±FHG$Q<B¦PVËRVN_c<e8S!PHKtGOFWÑFZRWDiDONFTdc,DON†GVP)Dic,D"Ò¬c<‰Š DONFZ‰wc,DCÓ

(33) q. ”ºw–€•ª‡–¾’“–hÜ´–h§h€•”›| à™‡’“” ‡§h”™‡‹Œ–†‡–n‚“§n’•”ŒŸÍ–h†"–nƒw’•‹Œ”–h’n÷¼§n›w ‡‚•”Œ†‡–n’?ƒ£™´ƒw’W€2”§h‹–‚W€»ƒw’W€2‚?ƒE€?™Í›w‚•”Œ€•”›| Rò Þ 1Qô›| <€•ª‡–J” ¼€2–hÀ|’2ƒw‹G‹ƒE€•€•”§h–ŽƒE ‡†‰”Œ‚„†–n‚“€•” ‡–h†‰¨y›|’Žòm𠐛hôטª‡”§»ª<‹”Œ–n‚˜ŸÍ–¡€¢×`–h–n ²€•ª‡–J€¢×ӛ Ÿ´ƒw’“’•”Œ–n’•‚h{êÆÇ”}€2ª‡›|>€N‹›|‚“‚N›w¨JÀ|–n –n’2ƒE‹”Œ€¢ùw÷ïƒE‚•‚•È"–¬1 H› Ýށ{ ñ¾‚¿ŸA–h¨y›w’•–w÷„€2ª‡–.™‡ƒw’“€•”§n‹Œ–‰”Œ‚ §n›w ‡‚“€•’2ƒw”Œ ‡–n†²€•›HÈ"›qäw–Ö€2› òŽ z ) zCô˜›|’3òŽ z ) zCô¨y’•›|È òŽ )Qô¡{¾Æ°–ާn‹¹ƒE”È €2ª‡ƒE€š€2ª– F. `P&M. ”P&M. :P „ÿ. Rò. .P 2ò. <ò. úP lM. ÑP.

參考文獻

相關文件

• Use the Black-Scholes formula with the stock price reduced by the PV of the dividends.. • This essentially decomposes the stock price into a riskless one paying known dividends and

The bivariate binomial values with 270 time steps are compared with the values generated by Hilliard and Schwartz [1996], the Hull-White stochastic volatility model [1987], and

Biases in Pricing Continuously Monitored Options with Monte Carlo (continued).. • If all of the sampled prices are below the barrier, this sample path pays max(S(t n ) −

Biases in Pricing Continuously Monitored Options with Monte Carlo (continued).. • If all of the sampled prices are below the barrier, this sample path pays max(S(t n ) −

1、曾擔任以國家、重要城市為名,至少以二個版面以上刊登國際 新聞,且發行對象以全國或全球讀者為目標之平面媒體或通訊 社(例如:《美國新聞與世界報導》(U.S. News

Simonato, 1999, “An Analytical Approximation for the GARCH Option Pricing Model,” Journal of Computational Finance 2, 75- 116.

Keywords: Parisian options, barrier options, option pricing, algorithm, binomial tree model, combinatorial method, Monte Carol simulation, inverse Gaussian distribution,

• A knock-in option comes into existence if a certain barrier is reached.. • A down-and-in option is a call knock-in option that comes into existence only when the barrier is