Y3I>EK11ctoh pecnYI>U11kac11 ou11 ba ypta

MorHH 6o opHHHHr HKTHcoAHM MoAerH

Yw6y 6O6HHHr 1.1 naparpacpH)l, ai1THJlraHJl p)l,aH KeJl YHl\H6, MOJlH51 6O3OpHHHHr Hl\ O)l,Hi1 MO)l,eJl Hcp )l,aJl MyMKHH. Yw6y MO)l,eJl MaTeMaTHK waKJl)l, 3K3OreH (KHpyBYH) Ba 3H)l, reH (YHl\ BYH) y3rapyBYHJl p (napaMeTpJlap) 6OFJlHl\Jl H, 51 H 3K3OreH napaMeTpJlapHHHr (A) 3H)l, napaMeTpJlapra (B) TabcHpHHH, HcpO)l,aJlai1)l,
MOJlH51 6O3OpH KOHboHKTypacH MOJlH51 HHcTpyMeHTJl 6yi1 TaJl 6 Ba TaKJlHcp)l, H waKJlJlaHa)l, .
MOJlH51 HHcTpyMeHTHra (MVI) TaJl Q^d yHHHr 6O3Op Hapx,H (KypcH) P_a Ba aMFapMaJlap x,a MHra S
x,aM)l,a HHcpJl51u,H51 x,HcO6ra OJl BYH )l,apOMa)l, cTaBKacHra r 6OFJlHl\, 51
Q^d =D(P_a, S, r) (1.6.1)
TaKJlHcp 3ca Q^s MOJlH51 HHcTpyMeHTHHHHr 6O3Op Hapx,H P_a Ba )l,apOMa)l, cTaBKacHra r x,aM)l, TaJl l\ Jl )l,HraH HHBecTHu,H51 x,a MHra I 6OFJlHl\, 51 H
Q^s =S(P_a, I, r) (1.6.2)
yH)l,a P_a HKKH OMHJl 6HJlaH 6eJl HJl )l, : TaJla6 Ba TaKJlHcp HHc6aTH; MVI 6yi1 KanHTaJl 3au,H51JlaHraH )l,apOMa)l, x,a MH. Y3 HaB6aTH)l, , )l, Ma)l, cTaBKacH r l\ i1H)l, rHJl 6OFJlHl\:
)l, Ma)l, HHr peaJl cTaBKacH R Ba HHcpJl51u, 51 )l, acH; )l, Ma)l, x,HcO6JlaHa)l, aH My)l,)l, Jl cOHH n.
O3Op Hapx,H (KypcH) P_a TaJl 6 Ba TaKJlHcp MyBO3aHaTH capH y3rapa)l, , 51 :
Q^s = Q^d (1.6.3)
WyH)l, i1 l\HJlH6, (1), (2), (3) TeHrJl Jl MOJlH51 6O3OpHHHHr Hl\ O)l,Hi1 MO)l,eJl TawKHJl
l\HJla)l, . YJlap)l, r Ba S - 3K3OreH napaMeTpJlap (A), P_a, I (MVI cOTHw 3Ba3Hra aJl l\HJlHHraH HHBecTHu,H51Jl p Q) - 3H)l,OreH napaMeTpJlap (B). Yw6y napaMeTpJlapHHHr y3apO 6OFJlHl\JlHrHHH (yJl HHr l\Hi1 HH aBBaJl)l, MabJl M )l, OJl ) 1.6.1-YH pacM)l, KypcaTHJl aHH)l, TaJl Ba TaKJl cp r MyBO3aHaT MO)l,eJl ep)l, )l, HcpO)l,aJl MyMKHH. y MO)l,eJl ep)l, )l, S,I eKH r Jl pHHHr y3rapHwH MOJlH51 6O3OpHra l\ H)l, i1 TabcHp KypMaTHwHHH KypHw MyMKHH. MacaJl , S OwHwH 6HJl Q^d yca)l, , r OwHwH 6HJlaH 3ca Q^s KaMa51)l,H, 6y x,OJl)l, Hapx,HHHr MyBO3aHaT l\Hi1MaTH P_a^* OpTa)l, , MVI
MHl\)l,OpHHHHr MyBO3aHaT l\ i1 3ca Q^* KaMa51)l,H.
rpacp )l, TaJla6HH HcpO)l, Jlai1)l,HraH 3HHacHMOH YH3Hl\ MOJlH51 HHcTpyMeHTHra 6yJl TaJla6 Ba yHHHr Hapx,H P_a ypTacH)l,arH HHc6aTHH aKc 3Ta)l,H. TaKJlHcpHH HcpO)l,aJl i1)l, H 3HHacHMOH YH3Hl\ TaKJlHcp l\HJlHHa)l,HraH MOJlH51 HHcTpyMeHTH Ba yHHHr Hapx,H P_a ypTacH)l, HHc6aTHH aKc 3Ta)l, .
rpacp )l, x,ap HKKaJla YH3Hl\HHHr KecHwyB Hyl\ cH 6O3Op)l, Hapx,HHHr MyBO3aHaT x,OJl H KypcaTa)l, , 51 H TaKJl cp l\ JlHHraH MOJlH51 HHcTpyMeHTJl TaJl MOc KeJla)l, .
Ai1 OH3KH, wyHra yx,waw MO)l, Jl Y.Wapn⁹ TOMOHH)l,aH x,aM HcpO)l,aJl HraH.





P
_P*
Q^* Q
PacM.1.6.1. TaJla6 Ba TaKJlHcpHHHr MyBO3aHaT MO)l, Jl
Owl\ TH3HMJl H Ha3apH51cHra acOcaH ¹⁰ B H A HHc6aTHHH MOJlH51 6O3OpHHHHr yTKa3Hw cp HKu,H51 H cHcpaTH)l,a HcpO)l,aJlaw MyMKHH, 51 :
W(Q^d, Q^s ) = {B(P_a, Q)}/{A(r, S)} (1.6.4)
Yw6y HcpO)l, (5) HHBecTHu,H51Jl Ba MOJlH51 6O3OpH)l,arH Te6paHHwJl p ypTacH)l,arH 6OFJlHl\JlHKHH TywyHTHpa)l, , MOJlH51BHi1 HHcTpyMeHTJl pra HHBecTHu,H51Jl pHH i1yHaJlTHpHw TyFpHcH)l,a l\ pOp l\ 6yJl l\HJlHw HMKOHHHH 6epa)l,H. W(Q^d, Q^s) KypcaTKHYH l\Hi1MaTH MOJlH51 6O3OpHHHHr aJl )l,OpJlHJlHrHHH x,aM Hcp )l,aJlai1)l, . MacaJl , W(Q^d, Q^s)HHHr KaMai1HwH HHBecTHu,H51Jl pHHHr l\ l\ pHwHra x,aM)l,a Q^dHH nacai1 OJl KeJla)l,H.
yH)l, H Tawl\apH, W(Q^d, Q^s) Ha3apH51cH MOJlH51 6O3OpH)l, H Te6paHHwJl Max, Jl T HwJl
YHl\ w Ba 6aH)l,Jl HHr Te6paHHwJl 6HJl y3apO 51l\ 6OFJlaHraH )l, l\a6yJl l\HJl wra acOc 6yJl OJl )l, .
Arap W(Q^d, Q^s ) Ba A(r, S) y3rapyBYHJlapHHHr l\Hi1 Jl pH MabJlyM 6yJl , B(P_a, Q) y3rapyBYHHH
MOJlH51 6O3OpHHHHr Hl\ O)l,Hi1 MO)l,eJl 6yi1 HaTH aBHi1 cp HKu,H51 )l, 6 l\ 6yJl l\HJlHw MyMKHH. y

⁹ Wapn Y., AJl KcaH)l,ep r., 3i1Jl . VIHBecTHu,HH: nep.c aHrJl.-M.: VIHPA M, 1999.-cc.95-114.

¹⁰ epTaJl Hcp Jl. 06W,a51 TeOpH51 cHcTeM O63Op npO6Jl H pe3yJl TaTOB.-«CHcTeMHIe HccJl )l, HH51».E erO)l,HHK. M.: HayKa, 1969; COBpeMeHHa51 TeOpH51 cHcTeM ynpaBJleHH51/nO)l, pe)l,. K.T.JleOH)l, ca.-M.: HayKa, 1970.-512 c.; AJl KcaH)l,pOB A.r.
0nTHMaJlbHIe H a)l,anTHBHIe cHcTeMI.-M.: BIcwa51 wKOJl , 1989.-263 c.;
WOXab3aMHi1 W.W. KaYecTBO HH)l,ycTpHH pIHKOB: cp HcOBOrO H u, HIX 6yMar.-T.: TVI, 2004.-138 c.;
WOXab3aMHi1 W.W. KOHu, TyaJl HIi1 nO)l, O)l, K cHcTeMHOMy HccJle)l,OBaHHo H pa3BHTHo pIHKOB: cp HcOB H u, X 6yMar.//06W, eHHIe HayKH B Y36eKHcTaHe, 2005, 21-2.
cp HKu,H51 MOJlH51 6O3OpHHHHr Hl\ HcO)l, T)l,arH pOJl Ha cp l\ T “6apOMeTp” cHcpaTH)l,a, 6aJl H MOJlH51BHi1 pecypcJl H pal\ 6aT Ba KOHboHKTypa (TaJl Ba TaKJl cp) TabcHpH acOcH)l, Tal\ Jl wH Ba l\ai1 Tal\ Jl wH apaeHJl HHHHr peryJl51 OpH cHcp TH)l, x, Hcp )l,aJlai1)l, .
Ai1 OH3KH, KeJlTHpHJlraH Ha3apHi1 x, JlOcaJl Ba l\ HH51TJl .TO6HH¹¹ Ha3apH51 6HJl



x,aMOx,aHr)l,Hp.

Caao!l!lap

1. 
   K, Jl l\OFO3Jl 6yi1HYa TaJla6 Ba TaKJlHcp HHMa?
   
2. 
   TaJl 6 Ba TaKJlHcpHH MyBO3aHaTH HHMa?
   
3. 
   YTKa3Hw cp HKu,H51 H HHMa?
   

Tonmupu !l

1. 
   K, MMaTJl l\OFO3Jl TaKJlHcpHHH Tax,JlHJl l\HJlHHr.
   
2. 
   TaJla6HH Tax,JlHJl l\HJlHHr.
   
3. 
   TepMHHJl p Jl FaTHHH Ty3HHr.
   

4. MorHH 6o opHHHHr M Bo aHaT x, aTHHH HoAaroB'l T HrMaBHM- HKu, Har MoAerrapH

MabJlyMKH, 6apYa MaMJlaKaTJl )l, MOJlH51 6O3OpHHHHr cpaOJlH51TH TapTH6Jl THpHJla)l, (MyBOcpHl\JlawTHpHJla)l,H Ba Ha3OpaT l\HJlHHa)l,H).
Wy MyHOca6aT 6HJlaH, yHH TapTH6Jl r KOHu, yaJl 3HJlMaBHi1 MO)l,eJl H MaTeMaTHK Hyl\ H Ha3ap)l,aH cpOpMaJlJl HpHJlraH Tap3)l, KypH6 YHl\aMH3. yH)l, H Mal\ca)l, – MOJlH51 6O3OpHHHHr TapTH6Jl wTHpH JlHwH l\ HyHH51 Jl pHHH TyFpH TywyHHw)l,Hp.
Yw6y 6O6HHHr OJl)l, rH naparpacpJl H)l, KeJlTHpHJlraH MOJlH51 6O3OpHra OH)l, TywyHYa, x,OccaJlap, l\ HyHH51TJlap Ba x, Jl caJl acOcH)l, , yHH MyBO3aHaT Jl yBYH (TapTH6Jl THpHJl BYH) KBa3HaHaJl r MO)l, Jl cHcpaTH)l,a HcpO)l, Jl MyMKHH. y MO)l,eJl cp OJlH51 MaTeMaTHK KypHHHw)l, cpOpMaJlJlawTHpHJl wH MyMKHH, 51 y Ma3MyHaH l\ i1H)l, yMyMHi1 KypHHHw)l, rH MaTeMaTHK TeHrJl MaJl p eYHMHra KeJl HJl H MyMKHH:
AX – F = s (1.7.1)
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 (1.7.2)
KypHHHwH)l, H O)l,)l,Hi1 )l,HcpcpepeHu,HaJl TeHrJlaMaJl cHcTeMacHra (KOwH MacaJlacH).
TeHrJl (1.7.1) acOcH)l, MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl THra 3pHwHw MO)l,eJl 1.7.1-YH
pacM)l, KypcaTHJl aHH)l, TawKHJlJlawTHpHJla)l, . yH)l, TeHrJlaMaHHHr MaTeMaTHK eYHMH (HJl)l, ) MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl H aHrJlaTa)l, , 51 HJl)l,H3HH TOnHw yYyH TaHJla6 OJl aH MaTeMaTHK MeTO)l, MO)l,eJl)l,a MOJlH51 6O3OpHHH MyBO3aHaTJl wTHpHw MeXaHH3MH cp OJlH51 HHH 6eJl Jlai1)l,H. MO)l,eJl)l,a: M – MOJlH51 6O3OpH, MM – MyBO3aHaTJlawTHpyBYH MeXaHH3M, F – TabcHp 3TyBYH OMHJlJlap, X
– TapTH6Jl pHw napaMeTpJl .
TeHrJl (1.7.2) acOcH)l, MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl THra 3pHwHw MO)l,eJl 1.7.2-YH
pacM)l, KypcaTHJl aHH)l, TawKHJlJlawTHpHJla)l,H. yH)l, TeHrJlaMaHHHr MaTeMaTHK eYHMH MOJlH51 6O3OpHHHHr MyBO3aHaT x,OJl H aHrJl )l, , 51bHH eYHMHH TOnHw yYyH TaHJla6 OJl MaTeMaTHK MeTO)l, MO)l,eJl)l,a MOJlH51 6O3OpHHH MyBO3aHaTJl wTHpHw MeXaHH3MH cp OJlH51 HHH 6eJl HJlai1)l,H. MO)l,eJl)l,a: X₀ – 6OwJlaHFHY TapTH6Jl THpyBYH )l,HcKpeT)l,arH napaMeTp, X_K – HaB6aT)l, TapTH6Jl THpyBYH
)l,HcKpeT)l, H napaMeTp.

¹¹ Tobin J. The Theory of Portfolio Selection in F.H/Hahn and F.R.P. Brechling (eds), The Theory of Interest Rate, London, Macmillan, 1965, pp.3-51.

F(ro)