Lq hdfk vlpxodwlrq uxq/wkh sruwirolr lv uroohg ryhu 63 |hduv lq txduwhuo|
vwhsv/l1h1 453 wlphv1 Hdfk uroo0ryhu frqvlvwv ri d qxpehu ri vwhsv1 Wkhvh duh ghvfulehg lq ghwdlo ehorz1
61614 Fdofxodwlqj frxsrq sd|phqwv
Lq hdfk vlpxodwlrq vwhs/wkh uvw qxpehu fdofxodwhg lv wkh vxp ri doo frxsrq sd|phqwv gxh lq wkdw shulrg1 Wklv qxpehu lv fdofxodwhg vlpso| dv wkh frxsrq sd|phqw lq hdfk fxuuhqf|/wlphv wkh vlpxodwhg I[ udwhv iru wkdw sduwlfxodu shulrg1 Wkh frxsrqv duh irxqg lq froxpqv 5/7/9 dqg ; ri wkh sruwirolr pdwul{ lq Iljxuh 51
Iljxuh 5= Fdofxodwlqj wkh frxsrq sd|phqwv
… … … … … …
FRXSRQV
^FRXSRQV`i^I[` !FRXSRQFRVW
61615 Fdofxodwlqj jurvv eruurzlqj uhtxluhphqwv
Wkh eruurzlqj uhtxluhphqw iru wkh vshflf shulrg lv fdofxodwhg lq d vlplodu zd|= wkh dprxqwv pdwxulqj duh irxqg lq froxpqv 4/6/8 dqg : ri wkh sruwirolr pdwul{ lq Iljxuh 6/dqg wkh| duh frqyhuwhg wr qrplqdo Vzhglvk nurqd dw wkh vlpxodwhg I[ udwhv1 Wklv jlyhv wkh eruurzlqj uhtxluhphqw vwhpplqj iurp wkh ghew lwvhoi1 Wkhuh lv dovr d qhw eruurzlqj uhtxluhphqw dulvlqj iurp wkh jryhuqphqw*v exgjhw lq wkh vlpxodwhg hfrqrp|1 Wklv exgjhw ghflw2vxusoxv lv dgghg wr wkh eruurzlqj uhtxluhphqw iurp pdwxulqj erqgv/jlylqj wkh wrwdo
qdqflqj qhhg1 Ilqdoo|/wkh wrwdo qdqflqj qhhg lv glvwulexwhg ryhu wkh irxu fxuuhqflhv dffruglqj wr wkh doorfdwlrq wdujhw ri wkh vwudwhj|1
Iljxuh 6= Fdofxodwlqj jurvv eruurzlqj uhtxluphqwv
^SULQFLSDOV`i^I[` !ERUURZLQJUHTXLUHPHQW IURPPDWXULQJGHEW SULQFLSDOV
… … … … … …
61616 Ilqdqflqj jurvv eruurzlqj uhtxluhphqwv
Wkh qh{w vwhs lq wkh vwudwhj| vlpxodwlrq lv wr ohw wkh vkruwhvw erqgv pdwxuh1 Wklv lv grqh vlpso| e| prylqj wkh frqwhqwv ri doo urzv lq wkh sruwirolr pdwul{
xs rqh urz/dqg vhwwlqj wkh dprxqwv lq wkh odvw urz wr }hur1 Wkh sruwirolr pdwul{ zloo qrz frqwdlq wkh sruwirolr dv lw zrxog orrn diwhu wkh pdwxulwlhv ri wkh fxuuhqw shulrg kdyh rffxuuhg/exw ehiruh dq| qhz erqgv kdyh ehhq lvvxhg1
Wkh eruurzlqj qhhg pxvw eh qdqfhg lq d zd| wkdw pdnhv wkh sruwir0 olr phhw wkh gxudwlrq wdujhw/li srvvleoh1 Wr eh deoh wr ghwhuplqh dw zklfk gxudwlrq srlqw zh vkrxog eruurz/zh qhhg wr nqrz wkh pdunhw ydoxh dqg gxudwlrq ri wkh ghew rxwvwdqglqj lq hdfk ri wkh irxu fxuuhqflhv1 Wr fdofxodwh wkhvh zh qhhg irxu vhwv ri glvfrxqw idfwruv/rqh iru hdfk fxuuhqf|1 Lq wkh hfr0 qrplf2qdqfldo vlpxodwlrq/zh vlpxodwh rqo| wzr srlqwv rq wkh |lhog fxuyh/
wkh wkuhh0prqwkv prqwkv udwh dqg wkh whq0|hdu udwh1; Wr jhw wkh glvfrxqw idfwruv zh wkhuhiruh olqhduo| lqwhusrodwh |lhogv iru hdfk pdwxulw| exfnhw/dqg wkhq frqyhuw wkhp wr glvfrxqw idfwruv lq wkh vwdqgdug zd|=
_s| '
E n o|| +4<,
Vlqfh zh kdyh wkh fdvk rzv ri wkh sruwirolrv rujdql}hg lq pdwxulw| exfn0 hwv/dqg nqrz wkh wlph wr pdwxulw| ri hdfk exfnhw/lw lv qrz vwudljkwiruzdug wr fdofxodwh wkh pdunhw ydoxh/ 6|/ri hdfk sduw ri wkh ghew +Vzhglvk nurqd/
;Iru lq dwlrq0olqnhg erqgv/zh vlpxodwh wkh yh dqg wkluw| |hdu srlqwv rq wkh |lhog fxuyh1
hxur/grooduv dqg lq dwlrq0olqnhg, dv
6|'[
Ss| _s|c +53,
zkhuh | ghqrwhv wkh wlph +lq txduwhuv, wr pdwxulw| ri hdfk pdwxulw| exfnhw dqg uxqv iurp wr 2f> Ss| ghqrwhv wkh fdvk rz lq exfnhw | dqg _s| lv wkh glvfrxqw idfwru dvvrfldwhg zlwk pdwxulw| |1 Zlwk wkh vdph qrwdwlrq/wkh gxudwlrq ri hdfk sduw ri wkh ghew fdq eh fdofxodwhg dv<
_o@|J? '
SSs| _s| |
6| +54,
Qrwh wkdw wkh gxudwlrq ri wkh glhuhqw sduwv ri wkh ghew duh qrw djjuhjdwhg/
vlqfh wkh gxudwlrq wdujhwv duh vshflhg shu fxuuhqf|/dqg qrw iru wkh sruwirolr dv d zkroh1
Jlyhq wkh pdunhw ydoxh dqg gxudwlrq ri wkh ghew rxwvwdqglqj ehiruh qhz ixqglqj/lw qrz srvvleoh wr ghwhuplqh dw zklfk gxudwlrq srlqw zh vkrxog
qdqfh wkh suhvhqw eruurzlqj qhhg1 Ghqrwh wkh gxudwlrq ri wkh ghew ehiruh qhz ixqglqj _f/wkh pdunhw ydoxh ri wkh ghew ehiruh qhz ixqglqj 6f dqg wkh eruurzlqj uhtxluhphqw Ko1 Lq rughu wr phhw wkh gxudwlrq wdujhw _W/wkh eruurzlqj uhtxluhphqw kdv wr eh ixqghg dw d fhuwdlq dyhudjh gxudwlrq _@/ zklfk fdq eh fdofxodwhg dv=
_W ' _f6fn _@Ko
6fn Ko ', _@' _WE6fn Ko _f6f
Ko +55,
Wkh hqwluh eruurzlqj uhtxluhphqw lv dvvxphg wr eh fryhuhg e| lvvxhv ri sdu erqgv/l1h1/erqgv zlwk dq lqwhjhu qxpehu ri |hduv wr pdwxulw| dqg d frxsrq pdnlqj wkh suhvhqw ydoxh htxdo wkh qrplqdo dprxqw1 Lq qrplqdo Vzhglvk nurqd/hxurv dqg grooduv sdu erqgv zlwk rqh ru whq |hdu pdwxulwlhv
<Whfkqlfdoo|/wklv htxdwlrq jlyhv wkh Ilvkhu0Zhloo gxudwlrq/vlqfh zh xvh wkh glvfrxqw idfwruv fruuhvsrqglqj wr }hur frxsrq udwhv wr glvfrxqw wkh fdvk rzv1 Wkh pruh iuhtxhqwo|
xvhg Pdfdxoh| gxudwlrq xvhv glvfrxqw idfwruv surgxfhg e| wkh |lhog0wr0pdwxulw| ri wkh vshflf erqg1 Wkh glhuhqfh ehwzhhq wkhvh wr phdvxuhv lv vpdoo= zlwk dq xszdug vorslqj
|lhog fxuyh/Ilvkhu0Zhloo phwkrg zloo jlyh d voljkwo| orzhu gxudwlrq wkdq wkh Pdfdxoh|
phwkrg1
duh xvhg1 Iru lq dwlrq0olqnhg ghew/yh dqg wkluw| |hduv pdwxulwlhv duh xvhg1 Jlyhq wkh glvfrxqw idfwruv fdofxodwhg iurp wkh vlpxodwhg lqwhuhvw udwhv/wkh frxsrq S ri d sdu erqg pdwxulqj lq |hduv fdq eh fdofxodwhg xvlqj wkh iroorzlqj htxdwlrq=
Wkh gxudwlrq ri wkh sdu erqgv lv fdofxodwhg xvlqj htxdwlrq +54,1
Iru hdfk fxuuhqf| zh qrz kdyh wkh gxudwlrq dqg frxsrqv ri sdu erqgv pdwxulqj rqh dqg whq |hduv iurp qrz1 Zh dovr nqrz dw zklfk gxudwlrq srlqw zh qhhg wr eruurz lq hdfk fxuuhqf| wr phhw wkh gxudwlrq wdujhw1 Vlqfh wkdw gxudwlrq srlqw lv xqolnho| wr frlqflgh zlwk wkh gxudwlrq ri d vlqjoh sdu erqg/
qhz ixqglqj lv xvxdoo| grqh xvlqj erwk sdu erqgv lq hdfk fxuuhqf|1 Wkh dprxqwv wr eh eruurzhg lq hdfk ri wkh wzr erqgv duh fdofxodwhg lq wkh vdph zd| dv vwdqgdug eduehoo fdofxodwlrqv1 Ohw _ ghqrwh gxudwlrq dqg qrplqdo dprxqwv +htxdoolqj fohdq dqg gluw| sulfhv dv zh duh zrunlqj zlwk sdu erqgv,1 _Wlv wkh gxudwlrq qhhghg wr phhw wkh wdujhw dqg vxshulqglfhv 7 dqg u ghqrwh wkh vkruw0whup dqg orqj0whup sdu erqg/uhvshfwlyho|1 Wkh vxp ri qrplqdo dprxqwv lq wkh wzr erqgv pxvw htxdo wkh eruurzlqj uhtxluhphqw Ko1 Wkh dprxqwv wkdw vkrxog eh doorfdwhg wr vkruw0whup dqg orqj0whup erqgv/ 7 dqg u' Lq vrph fdvhv/wkh gxudwlrq qhhghg wr phhw wkh gxudwlrq wdujhw lv rxwvlgh wkh udqjh ri sdu erqg gxudwlrqv1 Doo ixqglqj lv wkhq grqh lq wkh vkruwhvw ru wkh orqjhvw sdu erqg/dv dssursuldwh1 Qdwxudoo|/wkh gxudwlrq wdujhw fdqqrw eh h{dfwo| phw lq wkrvh fdvhv1
61617 Erqg uhsxufkdvhv
Lq prvw fdvhv wkh jurvv eruurzlqj uhtxluhphqw lv odujhu wkdq }hur zh qhhg wr eruurz lq rughu wr uhqdqfh pdwxulqj erqgv dqg2ru d exgjhw ghflw1 Krzhyhu/vrphwlphv lw pd| kdsshq wkdw wkh jurvv eruurzlqj uhtxluhphqw lv ohvv wkdq }hur1 Wklv kdsshqv zkhq wkh vlpxodwhg hfrqrp| vkrzv d exgjhw vxusoxv wkdw lv odujhu wkdq wkh vxp ri pdwxulqj erqgv lq wkh sruwirolr1 Lq wkrvh vlwxdwlrqv/wkh uroo0ryhu surfhgxuh ehfrphv pruh frpsolfdwhg1 Lqvwhdg ri lvvxlqj qhz erqgv/zh qrz kdyh wr ex| edfn erqgv1 Ex|edfnv pxvw eh grqh lq d zd| wkdw pdnhv wkh sruwirolr gxudwlrq phhw wkh vwudwhj| wdujhw dqg fdq rqo| eh pdgh dprqj wkrvh erqgv wkdw duh fxuuhqwo| lq wkh sruwirolr1 Ixuwkhupruh/lqglylgxdo fdvk rzv ri d erqg fdqqrw eh erxjkw edfn vhsd0 udwho|/exw pxvw eh kdqgohg dv d zkroh1 Lq h{wuhph fdvhv/lw pd| kdsshq wkdw doo ri wkh rxwvwdqglqj ghew lv erxjkw edfn1 Zkhq qr erqgv duh ohiw wr ex| edfn/dq| uhpdlqlqj vxusoxvhv duh ghsrvlwhg lq wkh fdvk pdunhw iru rqh txduwhu dw wkh wlph1 Iru d pruh ghwdlohg ghvfulswlrq ri krz erqg uhsxufkdvhv duh kdqgohg lq wkh prgho/vhh Ehujvwuùp ) Kropoxqg +5333,1