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1. 
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MOJlH51 6O3OpH HHcTpyMeHTJl Ma3MyH MOx,H51 yJl 6O3OpH 6HJl H x,aMOx, Hr 6HpJlHK)l,a KypH6 YHl\HJl JlO3HM 6yJl HHcTpyMeHTapHi1 (TepMHHOJlOrH51) Ba MeTO)l,OJlOrH51 6HJlaH aHHl\JlaHa)l, .
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IT-CmpYMeT-mGpUU – 6y MOJlH51 Hi1 HHcTpyMeHTJl pHHHr Ma3MyHHHH TyJlHl\ HcpO)l,aJl BYH Max,cyc TH3HMJl wTHpHJlraH TepMHHOJlOrH51 6yJl , 6a3aBHi1 (Ta51HY) 6yJl KOHu, aJl (Ha3apHi1) TywyHYaJl Ma MyacH cHcp )l, HaMOeH 6yJla)l, .
VI TpyMeHTapHi1 3aMOHaBHi1JlHrH wyH)l, H6OpaTKH, yHHHr ep)l,aMH)l,a MOJlH51BHi1 HHcTpyMeHTJl pHHHr ai1HaH x,O3HprH Bal\T)l,arH Ma3MyH MOx,H51 HcpO)l,aJl Ha)l,H. Arap, x,ap l\ H)l,ai1
MOJlH51 i1 HHcTpyMeHTHH Bal\T yTHwH 6HJl H MOJlH51 6O3OpHHHHr 3aMOH TaJla6Hra MOc paBHw)l, y3JlyKcH3 TaKOMHJlJl 6OpHwH eKH l\aH)l,ai1)l, l\ HMYa x,Occara Ba cpyHKu,H51 a 3ra 6yJl H eKH Ma3MyHaH Ba waKJlaH y3rapHwH Ba x,.K. O6beKTHB Ta6HHi1 apaeH 6yJl , yH)l, aBBaJl H )l,aBp)l, Ta51 Y 6yJl aH TepMHHOJlOrH51 x,aM x,O3HprH 3aMOHra KeJl 3cKHpHwH Ta6HHi1 x,OJlaT)l, . X, cycaH, XVI acp)l,a 6a3aBHi1 x,HcO6Jl HraH TepMHHOJlOrH51 XXI acpra KeJl 6Hp MyHYa TaKOMHJlJl wH6 pHBO Jl raH Jl rHra Hl\
6yJl MyMKHH. AMMO, 3cKH )l, Bp)l,arH TywyHYaJl HHHr ax,aMH51 acJlO nacai1 Hw MyMKHH 3Mac, YyHKH yJl KeJl K)l, x,ap l\ H)l, i1 TepMHHJl HH TaKOMHJlJl wH Ba pHBO Jl HwHra 6a3Hc 6yJl x,HcO6Jl Ha)l,H. Owl\ Ya l\HJlH6 yMyMJl ai1 H)l, , x,ap l\ H)l, i1 51HrHJl y3Hra MOc eKH 6Hp Bal\TJl p yHyTHJl 3cKHJl )l, H KeJl YHl\ )l, .
WyH)l, i1 l\HJlH6, MOJlH51BHi1 HHcTpyMeHTHHHr 3aMOHaBHi1 TywyHYacHHH aBBaJl)l, rHJl
acOcJl , Jl HH x,O3HprH 3aMOH ax,OH MOJlH51 6O3OpHHHHr Ma3MyH MOx,H51TH)l,aH KeJl YHl\H6 (1-YH 6O6ra l\ paJlcHH), l\ i1H)l, rHYa TabpHcpJlaw MyMKHH: MO!l UT- MeT- – 6y, yMyMaH OJlraH)l,a, MOHeTH3a u,H51JlawraH peaJl 6a3Hcra 3KBHBaJl T (“3rH3 aHaJl r”) l\Hi1 a Ba x,OccaJl a 3ra 6yJl aH, Max,cyc Hl\ O)l,Hi1 l\ l\Hi1 MeXaHH3M 6HJlaH TabMHHJlaHraH, MOJlH51 6O3OpH)l, MyHOca6aTJl pHH 6eJlrHJl , waKJlJl HpyBYH Ba pHBO Jl H pyBYH, MOJlH51BHi1 pecypcJlapHH caMapaJl Tal\ HMJl
Ba l\ai1 Tal\ Jl HHwHHH TabMHHJlOBYH, Myai151 x,OJlJlap)l, MabJlyM waKJlJlap)l, )l, Ma)l, KeJl pyBYH BOcHTa cHcp )l, x,ap x,HJl TypJlap)l, , waKJl Ba Ma3MyHJl )l, HaMOeH 6yJla)l, aH x,aM HHBecTHu, H KanHTaJl (aKTHB, aMFapMa), x,aM TyJl B BOcHTacH, x,aM aJl x,H)l, MOJlH51BHi1 TOBap)l, .
MOJlH51 i1 HHcTpyMeHTHHHr 3KBHBaJl HTJl x,OccacH 6eBOcHTa Ba 6HJlBOcHTa, peaJl Ba HHc6Hi1 6yJl wH MyMKHH.
MOJlH51 i1 HHcTpyMeHTHHHr MOJlH51BHi1 TOBapJlHJl x,OccacH yHH 6Owl\ Typ)l,arH TOBapJlap)l,aH (KyYMac Ba HHTeJlJleKTyaJl MyJlK, x,OM awe Ba wy Ka6HJl ) cpapl\Jl KHMHHHr)l, (Hl\ )l, cy6beKTJl pH) TOMOHH)l, YHl\apHJlHwH, y3Hra x,Oc MOJlH51 6O3OpH)l, MyOMaJl )l, 6yJl , yH)l, Max,cyc cp HKu,H51JlapHH Ba pOJl 6a apHwH 6HJl H 6eJlrHJl Ha)l,H.
X, p l\ H)l, i1 MOJlH51BHi1 HHcTpyMeHTHH y eKH 6y 6eJl acOcH)l, TacHHcpJlaHHwHHHHr Ma3MyHH yHHHr x,Occa Ba x, cycH51TJl pH 6HJlaH 6OFJlHl\ x,OJl)l,a aMaJlHi1 ax,aMH51 6HJlaH 6eJlrHJl HHH x,HcO6ra OJl x,aM)l,a, arap KypHJl Jl TraH HHcTpyMeHT TypHHH KeJl YHl\ , Mal\ca)l, Ba cp HKu,H51cHHH, yHHHr 6O3Op MyOMaJlacHHH 6Hp 6HpH 6HJl Tal\l\ cJlai1)l, 6yJl , aJl ce3HJlapJl cpapl\ HaMOeH 6yJla)l, . MacaJl , nyJl Ba yHH TOBap TOHcp a ai1Jl pyBYH HHcTpyMeHTJl (Kpe)l, , YeK, KapTOYKaJlap Ba x,.K.) MyOMaJlacH yYyH yJlapra x,Oc 6yJl aH MOJlH51 6O3OpH cerMeHTJl – MOc paBHw)l, nyJl 6O3OpH Ba Kpe)l,HTJlap 6O3OpH Ba x,.K. 3apyp, BaJloTa yYyH BaJloTa 6O3OpH, cyFypTa pHcKJlapHHH 6Owl\ x,H3MaTJlapH yYyH cyFypTa nOJl Jl pH 6O3OpH, l\HMMaTJlH l\OFO3Jl p yYyH 3ca cpal\aT cpOH)l, 6O3OpH KepaK.
MOJlH51 i1 HHcTpyMeHTJl pHHHr TOBap cHcpaTH)l,arH acOcHi1 Mal\ca)l,JlapH)l,aH 6HpH cpOi1)l, OJl 6yJlraHJl yYyH yH)l, rH x,ap l\ H)l, i1 cp OJlH51 KanHTaJlHH ( aMFapMaHH) OpTTHpHw cOx, cH 3KaHJl MyHOca6aTH 6HJlaH yJl HHHr 6O3OpH – 6Hp Bal\THHHr y3H)l,a KanHTaJlJl ra l\ i1HJlMaJl p yYyH MyJl JlJlaHraH 6O3Op x,aM)l,Hp.
nyJl Ma6JlaFJl pH MOJlH51 i1 HHcTpyMeHTJl pHHHr x,ap l\aH)l,ai1 TypHra l\ i1HJl wH (i1yHaJlTHpHJlHwH) MyMKHH. yHHHr 6apYa x,OJlaTJl H)l, i1 JlTHpHJl raH nyJl Ma6JlaFJl pH Bal\T MO6ai1 )l, y3 OpTTHpMacHra (eKH 3apapHra) 3ra 6yJl wH, 51bHH cpOi1)l, eKH 3apap KeJlTHpHwH MyMKHH.
eMaK, MOJlH51 i1 HHcTpyMeHTJl y3 6O3OpH)l, MOJl 51BHi1 pecypcJl apFapMaYHJlap)l, (HHBecTOpJlap)l,aH) HcTebMOJlYHJl ra TOMOH Ba aKcHHYa i1yHaJlHw)l, x,apaKaT l\HJlHwHHH TabMHHJl BOcHTa.
MOJlH51BHi1 HHcTpyMeHTJl ep)l, )l, pecypcJlap x,apaKaTH l\yi1 )l, OMHJlJl a 6OFJlHl\:

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  MOJlH51BHi1 HHcTpyMeHTJl pHHHr )l, pOMa)l,JlHJl Ba pHcK )l,apa acH;
  
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  MOJl 51BHi1 HHcTpyMeHTJl pHH cOJlHl\l\a TOpTHw wapT wapOHTJlapH;
  
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  MOJlH51BHi1 HHcTpyMeHTJl pHHHr peaJl 6a3Hc 6HJlaH TabMHHJl HJlHrH Ba wy acOc)l, Hl\ O)l, Ba MOJlH51 6O3OpHHH 3KBHBaJleHTJlHrH;
  
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  aMH51 Hr MeHTaJlHTeTH Ba TaHJla6 OJl pHBO Jl MO)l, Jl ;
  
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  MaKpO- Ba MHKpOHl\ O)l,Hi1 6apl\apOpJlHK;
  
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  Tawl\H KyYJlap Ba x,O)l, aJlapHHHr MOJlH51BHi1 HHcTpyMeHTJlap 6O3OpHra TabcHpH Ba 6Owl\aJlap. MOJlH51 i1 HHcTpyMeHTJl p (l\ TJl l\OFO3Jl p, 6aHK KanHTaJlJl H, 6Owl\ Typ)l, MOJlH51
  

BOcHTaJl Ba Max, Jl TJl H) MOHeTH3au, 51Jl aH peaJl 6a3Hc Ba wy acOc)l, Hl\ cO)l, Ba MOJlH51 6O3OpHHH 3KBHBaJl HTJl rH Max,cyc caMapaJl Hl\ O)l,Hi1 Xyl\ l\Hi1 MeXaHH3M 6HJlaH TabMHHJl H 6yJla)l,H.
MOJlH51 i1 HHcTpyMeHTra x,Oc l\ i1H)l,arH aTpH6yTJl pHH KeJlTHpHw MyMKHH:

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  x,ap 6Hp TypHra MOc peKBH3HTH, waKJl , My)l,)l, TH, cOHH Ba Hapx,H;
  
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Yw6y aTpH6yTJl Ox, rH yYTacH MOJlH51BHi1 HHcTpyMeHTHHHr y3 6O3OpH)l, rH l\ BBaT nOTeHu,HaJl H 6eJlrHJlai1)l,H.
MOJlH51 i1 HHcTpyMeHTHHHr Ma3MyHH yHHHr 6O3Op)l,arH cp HKu,H51cH Ba pOJl , y 6HJlaH 6OFJlHl\ Hl\ O)l,Hi1 Xyl\ l\Hi1 MyHOca6aTJl p acOcH)l, 6eJlrHJl )l, . IOl\OpH)l, ai1 yTHJl HJl )l, H KeJl YHl\l\ H x,OJl)l, MOJlH51 i1 HHcTpyMeHT HHHr l\ i1 )l,arH cp HKu,H51Jl pHHH TabKH)l,Jl w MyMKHH:

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  y3Hra x,Oc 6O3Op Opl\aJl MOJlH51 i1 pecypcJl (KanHTaJlHH) Hl\ O)l,HeT)l,a (Hl\ O)l, cy6beKTJl H ypTacH)l, ) caMapaJlH Tal\ Jl Ba l\ai1 Tal\ Jl ;
  
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  nyJl)l, 6yJl MabJlyM wapOHTJlap)l, KBa3HnyJl cHcp )l, TyJl B BOcHTacH 6yJl OJlHw (m₂ Ba yH)l, H i1 nyJl arperaTJl pH TapKH6Hra KHpHTHJlraHJl H MyHOca6aTH 6HJlaH);
  
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  6Hp Bal\T)l,a Hl\ O)l,Hi1 Ba opH)l, Ma3MyHHH y3H)l,a My accaMJl wTHpraH x,OJl)l, yHHHr 3racH, YHl\apyBYHcH Ba )l, BJl ypTacH)l, rH Hl\THcO)l,Hi1 yl\ l\Hi1 MyHOca6aTJl pHH 6eJlrHJl ;
  
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  y3 3raJlapHra KanHTaJlra 3raJlHK Xyl\yl\H 6HJlaH 6Hpra 6Owl\a MabJlyM l\ywHMYa Xyl\yl\JlapHH (MacaJl , OBO3 6epHw, 6Owl\ yB)l, HwTHpOK 3THw, MabJl MOTra 3ra 6yJl , Kpe)l, pJl K MaBl\ Ba x,.K.) 6epHw;
  
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x, cycH51TJl pHHH HcpO)l, Jlai1)l,H.

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MOJlH51BHi1 HHcTpyMeHTJl TacHHcp yJl a OH)l, TywyHYaJl , MyHOca6aT Jlap, x,OccaJl Ba x, cycH51TJl pHHHr y3apO 6OFJlHl\Jl HHH OYH6 6epHwra x,aM)l,a 6y 6OFJlHl\Jl HH MaHTHl\aH l\ pHJl TH3HM KypHHHwH)l, HcpO)l, 3Ta)l,H. Wy i1ycHH)l, TacHHcp MOJlH51 6O3OpH Ma3MyH MOx,H51 , yH)l, rH Hl\ cO)l,Hi1 Xyl\yl\Hi1 MyHOca6aTJl apaeHJl Hra x,Oc x,OccaJl Ba l\ HyHH51TJlapHH Yyl\yppOl\ Ba KeHrpOl\ TywyHHwra x,H3MaT l\ Jl )l,H.
3aMOHaBHi1 MOJlH51 6O3OpH MOJlH51BHi1 HHcTpyMeHTJl HHHr TypJl x,HJlJl 6HJl H
My accaMJl raH 6yJlH6, yJl H 6Hp HeYa 6eJlrHJl acOcH)l, TacHHcp Jl wHH Tal\ O 3Ta)l, .

MyOMaJl ra YHl\apHJlHwH Mal\ca)l, – TyJlOB Ba nyJl ai1Jl HMacH (O6OpOTH) y3JlyKcH3Jl TabMHHJl , HHBecTHu,H51JlapHH aJl6 l\HJl Ba yJl 6yi1 Ya )l, Ma)l, OJl 6yi1 , MOc paBHw)l, : Kpe)l,HT nyJl cHecaTHHH aMaJl OwHpHwHHHr l\ p3 MyHOca6aTJl pHHH My accaMJl wTHpyBYH MOJlH51BHi1 HHcTpyMeHTJl ()l,aBJl Ba 6aHK HHcTpyMeHTJl pH), l\ ()l,aBJl Ba KOpnOpaTHB Mal\ca)l,)l, ) Ba yJlyw (KOpnOpaTHB Mal\ a)l,)l, ) MyHOca6aTJl pHHH HcpO)l, Jl HHBecTHu, OH MOJlH51BHi1 HHcTpyMeHTJl p.
MOJlH51 6O3OpHHHHr y eKH 6y cerMeHTH 6yi1 a: nyJl, Kpe)l,HT, BaJloTa, cyFypTa, Jl e51 yi1HHJlapH, l\ TJl l\OFO3Jl (cpOH)l,, KanHTaJl) 6O3OpJl HHcTpyMeHTJl pH.
a3HcHra Kypa: nyJl, BaJloTa, cyFypTa, TOBap ( yMJla)l, x,OM awe), KyYMac MyJl , HH)l, , cp cTaBKa (KeJl aK)l, )l, Ma)l,), l\ Jl l\OFO3 6a3HcJl MOJlH51 i1 HHcTpyMeHTJl .
VIl\ cO)l, HHr y eKH 6y cy6beKTHra Kypa: )l,aBJl 6Owl\ yBH Ba x,OKHMH51 Jl , 6aHKJl - Kpe)l, MyaccacaJlapH, cyFypTa TawKHJl Jl , 6Hp aJl , HOMOJlH51 TawKHJl Jl (KOpnOpaTHB) HHcTpyMeHTJl pH.
4Hl\ pHJlHw My)l,)l, TH 6yi1 a: l\ cl\a, ypTa Ba y3Ol\ My)l,)l,aTJl MOJlH51BHi1 HHcTpyMeHTJl p. MHJlJlHi1Jl 6yi1 : MHJlJlHi1, x,OpH Hi1 Ba x,aJll\ MOJlH51 Hi1 HHcTpyMeHTJl .
VIl\THcO)l,Hi1 l\ l\Hi1 Ma3MyHH 6yi1 : l\ p3 Ba yJlyw MyHOca6aTJl pHHH x,aM)l, x,OcHJlaBHi1 6yJl aH (6a3Hc, My)l,)l, , Xyl\yl\ Ba Ma 6ypH51TJl HH My accaM JlawHpyBYH) MOJlH51 i1 HHcTpyMeHTJl .
VIl\THcO)l,Hi1 l\ l\Hi1 x,OccaJlapHra Kypa HKKH rypyx,ra a paTHw MyMKHH: 6a3aBHi1 Ba 6a3HcJl MOJlH51 i1 HHcTpyMeHTaJl . a3aBHi1 HHcTpyMeHTJl pra yJlyw Ba l\ p3 MyHOca6aTJl pHHH y3H)l,a My accaMJl THpyBYH 3MHccH51Jl yBYH ()l, aTHBJlap)l, Tawl\ ) Ba 3MHccH51Jl Mai1)l, aH l\ O3Jlap KHpa)l, . a3HcJl Jl 3ca )l, BaTHBJl (x,OcHJlaBHi1 l\ aTJl l\ FO3Jl ) KHpa)l, .
4Hl\apHJlHw Ba MyOMaJla YerapacH 6yi1 Ya: aJlOx,H)l, MaMJl , perHOH Ba x,aJll\ MHl\ec)l, YHl\apHJl BYH Ba MyOMaJl )l, 6yJl BYH MOJlH51BHi1 HHcTpyMeHTJl p.
WaXcJl a HHc6aTaH YeKJl wJlap 6yi1 Ya: 6apYara Ba YeKJl aH waXcJl a cOTHJla)l, aH MOJlH51BHi1 HHcTpyMeHTJl .
WaKJl 6yi1 Ya: Max, 6JlaHKJlap KypHHHwH)l, Ba 3Jl x,HcO6Jlap)l, (cYeTJl )l, )
opHTHJl BYH MOJlH51BHi1 HHcTpyMeHTJl .
Ba3Hcp Jl H 6yi1 : cy6beKTJl pHHHr HYKH Ba Tawl\H Hl\ O)l,Hi1 Mal\ca)l, Hcp aTJlapHHH l\OHHl\ BYH MOJlH51BHi1 HHcTpyMeHTJl .
HKu,H51cH 6yi1 : HHBecTHu, OH HHcTpyMeHTJlap (l\ MaTJl l\ FO3Jl ), 6aHKJlapHHHr MOJlH51JlawTHpHw HHcTpyMeHTJl H (Kpe)l, , )l, O3HT, ceJl , nJl HK KapTOYKaJl , YeKJl Ba x,.K.), pHcKHH MOJlH51Jl wTHpHw HHcTpyMeHT Jl pH (cyFypTa nOJlHcJlapH), TyJlOB HHcTpyMeHTJl pH (MHJlJlHi1 Ba x,OpH Hi1 BaJloTa, x,aJll\ BaJloTa, KBa3HBaJl (nceB)l,OBaJloTa), 6Hp a KOTpOBKacHra 3ra 6yJl aH BaJloTa cHcp )l, yTyBYH OJl , nJl a, KyMyw, KaMe6 3Jl TJl , l\ 6ax,O TOwJl Ba x,.K.), TOBap Tal\cHMJl BYH HHcTpyMeHTJl (TOBap BappaHTH, KOHOcaMeHT, OM6Op ryBOx,HOMacH Ba wy Ka6HJl ), rapOB l\OFO3Jl , JlOTepe51Jl .
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TyJlOB My)l,)l,aTH 6yi1 : cnOT Ba My)l,)l,aTJlH 6O3Op HHcTpyMeHTJl pH.
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MOJlH51BHi1 HHcTpyMeHTJl HHHr cpyH)l, eHTaJl x,OccaJl yJl HHr napaMeTpJlapH (cHcp KypcaTKHYJl ) Opl\aJl Hcp )l,aJlaHa)l, .
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   MOJlH51 Hi1 HHcTpyMeHTHHHr l\ H)l, i1 aTpH6yTJl 6Op?
   
4. 
   MOJlH51BHi1 HHcTpyMeHTHHHr l\ H)l, i1 cp HKu,H51Jl HHH 6HJl cH3?
   
5. 
   MOJlH51BHi1 HHcTpyMeHTHH l\ai1 H 6eJlrHJl 6yi1HYa TacHHcpJlaw MyMKHH?
   

Tonmupu !l

1. 
   MOJlH51BHi1 HHcTpyMeHTHHHr x,ap 6Hp TacHHcp 6eJl H 6yi1 a TaBcHcpJlaHr.
   
2. 
   TepMHHJl p Jl FaTHHH Ty3HHr.
   

2. l\HMMaTrH Kono rap TacHHH Ba TaBcHH

/(uMMam!lu ozo1!lap11u11z Ma1My11u, Ma caOu aa py11«u.uR!lapu

K, TJl l\ FO3Jl MOJlH51 i1 HHcTpyMeHTJl pHHHr 6Owl\ TypJl pH)l, H cp pl\Jl 3Hr KaTTa Ba aJlOx,H)l, 6O3OpHra 3ra 6yJl H rypyx,HHH TawKHJl 3TraHJl rH MyHOca6aTH 6HJlaH yJl HHHr Ma3MyH-
MOx,H51 H Max,cyc paBHw)l,a KypH6 YHl\Hw Mal\ca)l, MyBOcpHl\. TabKH)l,Jlaw OH3KH, l\ MaTJl l\ Jl MOJlH51 i1 HHcTpyMeHTJl pHHHr 6Hp TypH 6yJlraHJl yYyH yMyMaH OJl aH)l,a Ma3MyHaH cHHOHHM)l,Hp (2.1 naparpacpra l\ paJlcHH), JleKHH yJl MOJlH51BHi1 HHcTpyMeHT Jl pHHHr 6Owl\ TypJl pH)l,aH MabJl M Hx, TJl pH 6HJlaH cpapl\ l\HJl )l, .
K, TJl l\OFO3Jl p Hl\ O)l,HeT)l,a y3 ax,aMH51 , ypHH Ba cp HKu,H51Jl HHH aJlJlal\aYOH Hc6OTJl aHJl Hra l\apaMac)l, yJl HHr Ma3MyHH TyFpHcH)l, x,aHy3raYa l\ FHH 6ax,cJl )l, 3TH6 KeJl l\)l, . MacaJl , .P.XHKcHHHr cp Ya¹², 3aMOHaBHi1 nyJlJl p y3Ol\ My)l,)l, TJl HcTebMOJl TOBapH 3Mac, 6aJl H l\HMMaTJlH l\ O3Jl Hr TypH cHcpaTH)l, HcpO)l,aJl Ha)l,H. POccH51Jl OJlHMJl pHHHr cp pHYa¹³, l\ MaTJl l\OFO3 cp KanHTaJl cHcp )l, HaMOeH 6yJl BYH BOcHTa Ba x,.K. yH)l,ai1 6ax,cJlap l\ MaTJl
l\ Jl HH waKJlaH TypJl , Ma3MyHaH yx,waw, Jl HH, TyJlHl\Jl H 6HJlaH a paJla)l,HraH x,a M)l, rH MabHO)l, TaJll\ l\HJlHHHwHra OJl KeJl Ol\)l, . Yw6y TeH)l,eHu,H51 l\ TJl l\OFO3Jl 3BOJlou, 51cH)l,a Ta6HHi1 x,OJlaT)l, , YyHKH 6apYa Ha3apHi1 TaJll\HHJlap Bal\T yTHwH 6HJlaH l\ MaTJl l\OFO3Jl pHHHr Ma3MyH MOx,H51 TaKOMHJlJl wH6 6OpraHH yYyH y3rapHwH O6beKTHB apaeH)l,Hp. WyHHHr yYyH l\ TJl l\OFO3Jl p Ba yJl HHHr 6O3OpHHH x,O3HprH 3aMOH)l, rH Ma3MyH MOx,H51 , Hl\ O)l, eT)l,arH ax,aMH51 , pOJl Ba cp HKu,H51Jl H)l, H KeJl YHl\l\ H x,OJl)l, (I-YH 6O6ra Ba ai1HHl\ a 1.1.1-1.1.3 MO)l,eJlJl a l\apaJl H) MOJlH51 i1 HHcTpyMeHT cHHrapH (2.1 nparpacp l\apaJl H) l\ i1 )l, Ya TaJll\ H l\ Jl MyMKHH.
K, TJl l\OFO3 – 6y, yMyMaH OJl aH)l,a, MOHeTH3au,H51JlawraH (nyJl 6HJlaH TabMHHJlaHraH) peaJl 6a3Hcra 3KBHBaJl (“3rH3 aHaJl r”) l\Hi1 a (6ax, ra) Ba x,OccaJl a 3ra 6yJl aH, Max, Hl\ cO)l,Hi1- Xyl\ l\Hi1 MeXaHH3M 6HJlaH TabMHHJl raH, y3Hra x,Oc 6O3Op)l, MOJlH51 i1 MyHOca6aTJl pHH 6eJlrHJl ,

¹² .P.XHKc. CTOHMOcTb H KanHTaJl.-M.: npOrpecc, 1988.-365 c.

¹³ PIHOK u,eHHIX 6yMar H erO cpHHaHcOBIe HHcTpyMeHTI: YYe6HOe nOcO6He/nO)l, pe)l,.B.C.TOpKaHOBcKOrO.-Cn6.:A0
«KOMnJleKT», 1994.-421 c.;
UeHHIe 6yMarH: YYe6HHK/nO)l, pe)l, B.VI KOJl HHKOBa, B.C.TOpKaHOBcKOrO.-2-e H3)l,., nepepa6. H )l, .-M.: HcI H cTaTHcTHKa, 2000.-448 c.; MHpKHH 51 . UeHHIe 6yMarH H cpOH)l,OBIi1 pIHOK.-M.: nepcneKTHBa, 1995.
waKJlJl HpyBYH Ba pHBO Jl HTHpyBYH, MOJlH51BHi1 pecypcJl caMapaJl Tal\cHMJl HHwH Ba l\ i1 Tal\ Jl wHHH TabMHHJlOBYH, Myai151 x,OJlJlap)l, MabJlyM waKJlJlap)l, )l, Ma)l, KeJl pyBYH BOcHTa cHcp )l, x,ap x,HJl TypJl )l, , waKJl Ba Ma3MyHJlap)l, HaMOeH 6yJla)l, aH x,aM HHBecTHu, KanHTaJl (aKTHB, Max, c cp H)l, aMFapMacH 6Oi1Jl H, l\ MaTJl l\OFO3Jl nOpTcpeJl ), x,aM TyJl B BOcHTacH, x,aM aJlOx,H)l,a cpOH)l, 6O3OpH TOBapH)l, .
K, TJl l\ FO3 6Hp Bal\THHHr y3Hra Hl\ O)l,Hi1 KaTerOpH51 Ba opH)l, KOHcTpyKu,H51 cHcpaTH)l,a Ma3MyHra 3ra.
K, TJl l\OFO3HHHr 3KBHBaJl HTJl x,OccacH MOJlH51 i1 HHcTpyMeHTJl p HHHr 6Owl\ TypJl cHHrapH 6eBOcHTa Ba 6HJl cHTa, peaJl Ba HHc6Hi1 6yJl MyMKHH. Yw6y x,Occa 3Ba3Hra l\ Jl
l\ Jl yJl HH YHl\apyBYHcHHHHr (3MHTeHTHHHHr) “3rH3 aHaJlOrH” (51 3KBHBaJl HTH) cHcp TH)l,a HaMOeH 6yJla)l,H. OH)l, KypHHHwH)l, rH (cpOH)l, 6O3OpH) TOBapJlHJl rH x,OccacH 3ca yHH 6Owl\ Typ)l, TOBapJlap)l, (KyYMac Ba HHTeJlJleKTyaJl MyJl , x,OM awe Ba wy Ka6HJl ) cpapl\Jl KHMHHHr)l, (3MHTeHT,
51 MyOMaJl ra YHl\apyBYH, 6yJl Hl\ O)l, cy6beKTJl pH) TOMOHH)l,aH YHl\apHJlHwH, y3Hra x,Oc l\ TJl l\OFO3Jl 6O3OpH)l, MyOMaJl )l, 6yJl , yH)l, Max,cyc cp HKu,H51Jl HH Ba pOJl 6a apHwH 6HJlaH 6eJlrHJl )l, . yH)l, l\ TJl l\ FO3Jl HHHr pOJl Ba cp HKu,H51Jl H MOJlH51 i1 HHcTpyMeHTJl p cHHrapH aHHl\JlaHa)l, (2.1 nparpacp l\apaJl H). O3Op x,OccacH l\ MaTJl l\OFO3HH nyJl a 51l\HHJl )l, , YyHKH y MabJl M wapOHTJl p)l,a nyJl cp HKu,H51cHHH 6a apa OJla)l, , TyJlOB BOcHTacH cHcpaTH)l,a l\ JlJl HHJl MyMKHH. K, MMaTJl l\ HHHr cp H)l, MeHTaJl x,OccaJlapH ai1Jl HyBYaHJl , Jl BH)l,JlHJl H, aJl )l,OpJlHJlHrH, pHcKJlHJlHJl Ba wy Ka6H 6Owl\ KypcaTKHYJl 6HJlaH 6eJlrHJlaHa)l, . YMyMaH OJlraH)l, , l\ MaTJlH l\OFO3Jl x,OccaJl HH ol\OpH cHcp )l, cpOH)l, 6O3OpHHHHr caMapaJlH x,OJl HH 6eJl HJlai1)l, .
PeaJl 6a3Hcra 3KBHBaJl 6yJl aH l\ Jl l\OFO3Jl ep)l, )l, cpOH)l, 6O3OpH Opl\aJl caMapaJlH HHBecTHu,HOH Ba TpaHccp (TyJl ) apaeHJl , Hl\ cO)l, cy6beKTJl HHHHr Mal\ca)l,Jl Ba TapTH6JlawTHpHJlraH Hl\ HcO)l,Hi1 Xyl\ l\Hi1 6O3Op MyHOca6aTJl pH aMaJl OwHpHJla)l,H. yH)l, l\ TJl
l\ FO3 aJlOx,H)l, TOBap Ba MOJlH51BHi1 HHcTpyMeHT cHcp )l, y3H)l, My accaMJlawTHpraH peaJl KanHTaJlHHHr (eKH 3raJl Xyl\ l\ ) x,aM 3KBHBaJl HTH, x,aM TypJl waKJl Ba Ma3MyH)l, rH “cHMBOJl ” 6yJl HaMOeH 6yJla)l, . MOc paBHw)l, y y3HHHHr aJl x,H)l, l\ MaTJl l\OFO3Jl 6O3OpH)l, Max, c TOBap cHcp )l, 3pKHH MyOMaJla)l, 6yJl , 6Hp Bal\ HHHr y3H)l, napaJlJleJl Tap3)l, peaJl 6a3HcHHH y3Hra x,Oc 6O3OpH)l, )l,OJl3ap6JlHJl Ba 6O3OprHpJlHJlHrHHH 6eJlrHJlai1)l,H. Y3 HaB6aTH)l,a aKcHHYa peaJl 6a3Hc x,aM y3H My accaMJl raH l\ MaTJl l\OFO3HHHr TOBap cHcp )l, cp H)l, 6O3OpH)l, H (3pKHH MyOMaJl
apaeHH)l, ) x,OccaJl (MabJl M KypcaTKHYJl 6HJl Hcp )l,aJl aH) cHcp )l, HH 6eJl HJlai1)l, .
WyHHHr yYyH l\ TJl l\OFO3 “cpOH)l, HHcTpyMeHTH” cHcpaTH)l,a “cpOH)l, 6Oi1Jl rH” )l, 6 HcpO)l, Jl )l, , yHHHr ep)l,aMH)l,a peaJl 6Oi1Jl Jl ra (6a3Hcra) 3ra 6yJl HMKOHH51 nai1)l,O 6yJl )l, . y 3ca cpOH)l, 6O3OpH KOHboHKTypacHra 6OFJlHl\ x,OJl)l,a 6Oi1JlHKJlapHH 6Hp cy6beKT)l, H 6Owl\ Hra yTHwHwH (x,apaKaTHHH) TabMHHJlai1)l,H, HaTH a)l,a l\ MaTJl l\OFO3Jl p 6O3OpH Opl\aJl MOJlH51BHi1 pecypcJl HH Hl\ O)l,HeT)l,a caMapaJl Tal\cHMJl HHwH Ba l\ i1Ta Tal\cHMJl HHwHHHHr l\ HyHH51TJl apaeHH By y)l, KeJla)l,H.
IOl\OpH)l, ai1THJlraHJl p)l,aH KeJl YHl\l\ H x,OJl)l, , 3KBHBaJl HTJlHJl TaMOi1HJlH acOcH)l, l\ MaTJl
l\ FO3 Ba yHHHr peaJl 6a3HcHHH y3apO “3rH3 aHaJl r” cHcp )l, 2.2.1-YH pacM)l, KeJl pHJl cXeMa 6HJlaH HcpO)l, Jl MyMKHH. CXeMa)l, : – 6a3Hc (51 l\ MaTJl l\OFO3HHHr 6a3HcH); K,K, – 6a3Hcra 3ra 6yJl aH l\ Jl l\OFO3; HKKH TapacpJl a i1 aJl pHJlraH cTpeJlKa Ba K,K, ypTacH)l, 3KBHBaJl T 6OFJlHl\Jl HH 6HJl)l,Hpa)l,H.



PacM.2.2.1. K, MMaTJlH l\OFO3 Ba yHHHr 6a3HcH 3KBHBaJleHTJlHJlHrH cXeMacH
2.2.1-YH pacM)l, 6a3HcHH ( ) peaJl MO)l,eJlJl THpHJl raH (Ta)l,l\Hl\ 3THJlaeTraH) O6beKT cHcp )l, , l\ TJl l\OFO3HH (K,K,) 3ca O6beKT MO)l,eJl )l, 6 l\ 6yJl l\HJlHw MyMKHH. y 3ca O6beKTHHHr MaTeMaTHK MO)l, Jl H yHHHr 3KBHBaJl HTH 6yJl w l\ MaTJl l\OFO3 x,OccaJlapH (KypcaTKHYJl pH) ep)l,aMH)l,a Hcp )l,aJl Opl\aJl MaTeMaTHK MO)l,eJlJl THpHw HMKOHHHH 6epa)l, . 51 MO)l,eJl ep)l, )l, K,K, x,OccaJl HH MaTeMaTHK Tap3)l, MO)l,eJlJl THpHw acOcH)l, peaJl O6beKT (6a3Hc) x,OccaJl HH Ta)l,l\Hl\ 3THw MyMKHH. Yw6y MaTeMaTHK eH)l, yB MeH yYyH x,aMHwa ap)l, l\Jl Ba x, pMaTJl 6yJl Ba KeJl aK)l, x,aM 6yJl 6 KeJl )l, aH 6yoK ycTO3Jl HM AKa)l, HK reOprHi1 EBreHbeBHY nyXOB Ba BHKTOp
e)l,OpOBHY EB)l, OBJl p TOMOHH)l,aH 6yTyH )l,yHe)l,a yTraH acpHHHr 60-70-YH i1HJlJl H)l, TaH OJl "KBa3HaHaJl rJl Ha3apH51 H” HOMH 6HJlaH TeXHHK O6beKTJl pHH MO)l,eJlJlawTHpHw yYyH HJl 6Op HwJl YHl\HJl Ba Ta)l,6Hl\ 3THJl ¹⁴. WyH)l, i1 6yoK ycTO3Jl HMHHHr HOe6 HJl i1 HHOBau, OH TacpaKKypJl HJl 6yHe)l, 3THJlraH MaKTa6Jl a x,aMHwa cO)l,Hl\ 6yJl aH x,OJl)l, KBa3HaHaJl Jl Ha3apH51
)l, BOMHi1Jl acOcH)l, Hl\ O)l, , MOJlH51 TH3HMH Ba 6O3OpJl cOx, Jl H yYyH HJl 6Op 90-YH
i1HJlJl p)l,aH 6OwJl pHBO Jl HTHpH6 l\ JlJl wra a3M l\HJl)l, M. yHHHr HaTH acH)l,a MyaJlJlHcp TOMOHH)l,aH OJl aH Ba yw6y KHTO6)l, 6aTacpcHJl KeJl pHJlraH HJlMHi1 Ba aMaJlHi1 HwJlaHMaJl KBa3HaHaJl Jl Ha3apH51 HHH Hl\ O)l, Ba MOJlH51 cOx, Jl H yYyH x, M ai1 MOcJl Hc6OTJl MOl\)l, .
Ai1 HJl aHJl ra Ba 2.2.1-YH pacM)l, H cXeMara acOcaH, MaKpOHl\ )l,Hi1 )l,apa a)l, peaJl ceKTOp Ba l\ TJl l\OFO3Jl 6O3OpH ypTacH)l, rH 3KBHBaJl HTJlHJl 6OFJl HHwHH 2.2.2-YH pacM)l, KeJlTHpHJlraH MO)l, Jl KypHHHwH)l, HcpO)l,aJl w MyMKHH. Yw6y Ty3HJlMaBHi1 MO)l,eJl)l,a: M – MaKpO6a3Hc; K,K, – l\HMMaTJlH l\OFO3Jlap (MOJlH51) 6O3OpH.


PacM.2.2.2. K,K, Ba MaKpO6a3HcHHHr y3apO 3KBHBaJleHTJlHJl rH MO)l, Jl
y MO)l,eJl)l, (2.2.2-pacM), 2.2.1-YH cXeMa)l, Hra yx, , MaKpO6a3HcHH (M ) peaJl MO)l,eJlJl THpHJl raH (Ta)l,l\Hl\ 3THJlaeTraH) O6beKT cHcp )l, , l\ MaTJl l\ 3Jl 6O3OpHHH (K,K, ) 3ca O6beKT (M HH 3KBHBaJleHT aKc 3TTHpyBYH) MO)l,eJlH )l,e6 l\a6yJl l\HJlHw MyMKHH. 2.2.1 Ba 2.2.2 pacMJlap)l,arH HKKH TapacpJlaMa i1yHaJlTHpHJlraH cTpeJlKaJlap Ba K,K,; M Ba K,K, ; Ba M ; K,K, Ba K,K, ypTaJlapH)l,arH 3KBHBaJl HT 6OFJlHl\Jl HH 6HJl)l,Hpa)l,H.
KBa3HaHaJl MO)l,eJlJlap O6beKTJl pHH ( yMJla)l,aH l\ MaTJl l\ FO3Jl Ba MOJlH51 6O3OpHHH) aJl e6paHK Ba )l,HcpcpepeHu,HaJl TeHrJlaMaJlap ep)l, )l, MO)l,eJlJl THpHw)l, l\yJlJl Jla)l, .
KBa3HaHaJl Jl Ha3apH51cHra acOcJl 6, 2.2.1 Ba 2.2.2-YH pacMJlap)l, KeJl pHJlraH MO)l,eJlJl H l\ i1H)l, rHYa, 51 MyBO3aHaTJl wyBYH (TapTH6Jlaw THpHJl BYH) KBa3HaHaJl MO)l,eJl cHcpaTH)l,a HcpO)l, Jl MyMKHH. y MO)l, Jl cp OJlH51 H MaTeMaTHK KypHHHw)l, cpOpMaJlJl HpHJl wH MyMKHH,
51 y Ma3MyHaH l\ i1H)l, rH yMyMHi1 KypHHHw)l,arH MaTeMaTHK TeHrJl Jl eYHMHra KeJl HJl MyMKHH:
AX – F = s (2.2.1)
KypHHHwH)l, H aJl e6paHK TeHrJlaMaJlap cHcTeMacHra (TeHrJl a)l, s MHHHMyM l\Hi1MaTra HHTHJlTHpHJla)l, )
eKH
n(dx/dru)+A(x)X=F(ru), x(0)=x₀ (2.2.2)

¹⁴ nyXOB r.E. VI36paHHIe BOnpOcI TeOpHH MaTeMaTHYecKHX MawHH.-K.: VI3)l,. AH YCCP, 1964.; nyXOB r.E., EB)l,OKHMOB B.., CHHbKOB M.B. Pa3p51)l,HO aHaJl rOBIe BIYHcJl TeJl HIe cHcTeMI.-M.: COB.pa)l,HO, 1978.-256 c.

KypHHHwH)l, H O)l,)l,Hi1 )l,HcpcpepeHu,HaJl TeHrJlaMaJl cHcTeMacHra (KOwH MacaJlacH).
TeHrJlaMa (2.2.1) acOcH)l, l\ Jl l\ 3HHHr 3KBHBaJl TJl Jl (MyBO3aHaT x,OJl ) 3pHwHw MO)l,eJl 2.1.3-YH pacM)l, KypcaTHJl )l, TawKHJlJlawTHpHJla)l, . yH)l, TeHrJlaMaHHHr MaTeMaTHK eYHMH (HJl)l,H3H) MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl aHrJl Ta)l,H, 51 H HJl)l,H3HH TOnHw
yYyH TaHJla6 OJl MaTeMaTHK MeTO)l, MO)l,eJl)l,a MOJlH51 6O3OpHHH MyBO3aHaTJl wTHpHw MeXaHH3MH cp JlH51THHH 6eJl Jlai1)l, . MO)l,eJl)l, : K,K, – l\ MaTJl l\ 3 (eKH K,K, ), MM – MyBO3aHaTJl THpyBYH MeXaHH3M, F – TabcHp 3TyBYH OMHJlJlap, X – 3KBHBaJl HTJlawTHpHw (TapTH6Jl wTHpHw) napaMeTpJlapH.
TeHrJl (2.2.2) acOcH)l, l\ TJlH l\OFO3HHHr 3KBHBaJl HTJlHJlHrH (MyBO3aHaT) x,OJl Hra 3pHwHw MO)l,eJl 2.2.4-YH pacM)l, KypcaTHJl )l, TawKHJlJlawTHpHJla)l, . yH)l, TeHrJlaMaHHHr MaTeMaTHK eYHMH MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl aHrJl Ta)l,H, 51 H eYHMHH TOnHw yYyH
TaHJla6 OJl MaTeMaTHK MeTO)l, MO)l,eJl)l,a MOJlH51 6O3OpHHH MyBO3aHaTJl wTHpHw MeXaHH3MH cp JlH51THHH 6eJl Jlai1)l, . MO)l,eJl)l, : X₀ – 6OwJlaHFHY TapTH6Jl THpyBYH )l,HcKpeT)l, H napaMeTp, X_K – HaB6aT)l, 3KBHBaJl Jl THpyBYH (TapTH6Jl THpyBYH) )l,HcKpeT)l, H napaMeTp.

F(ro)