Медведев Г.А. Математические основы финансовой экономики. Часть2
Подождите немного. Документ загружается.
?
»
»
¼
º
«
«
¬
ª
c
c
¸
¸
¹
·
¨
¨
©
§
³
);77$77%UGXU @`>H[S^H[S
qlhfh`gh\uqbkeblv\y\ghcnhjf_:gZeh]bqghklhbfhklv\fhf_gl
\j_f_gbWnvxq_jkgh]hdhgljZdlZk^Zlhc^hklZ\dbLgZ^bkdhglgmx
h[eb]Zpbxk^Zlhcih]Zr_gbyL
?
!
L\ujZ`Z_lky\nhjf_dhlhjZy
lZd`_^himkdZ_l\uqbke_gb_\y\ghf\b^_
?>JLL
?
_)
@ ?>_oj
^
U <LL
?
:LL
?
`
_) @
Y\ey_lkyebwlZfh^_evohjhrhhij_^_e_gghc"OZeebMZcl^hdZ
au\Zxl qlh _keb \ g_dhlhjuc fhf_gl \j_f_gbkdZ`_f ba\_klgZ
\heZlbevghklvklZ\dbUb\heZlbevghklvh[eb]Zpbc\k_okjhdh\ih]Z
r_gbylh]^ZlZddZd
GJWL
JWLGU
<WL:WLJWL< WLG:
\heZlbevghklv^bkdhglghch[eb]Zpbbkhkjhdhfih]Zr_gbyLjZ\gZ
V
<LJLblZddZdwlhba\_klghfh`gh\u\_klb <L^ey
\k_oLIhkdhevdm<LklZeZba\_klghcfh`ghi_j_ibkZlv:L
kihfhsvxnhjfmeuGhl_i_jvagZy<Lfufh`_fgZclb
.Zihlhfb
E
bajZ\_gkl\ZLh]^Zi_j\h_^bnn_j_gpbjh\Zgb_
:L^Z_l
§·
c
D V
¨¸
©¹
³³
H$ 7 H H G\GV
Z\lhjh_±
> @
ccc
E DV
³
H$7$7 H HG\
lj_lv_^bnn_j_gpbjh\Zgb_ijb\h^bld\ujZ`_gbx
> @
c cc c c ccc
EEE
H$7$7$7$7
c
DED V
H
WlhmjZ\g_gb_fh`_lg_bf_lv_^bgkl\_ggh]hj_r_gbyhlghkbl_evgh
D
b
V
ghhgh^Z_lgZfjZ\_gkl\h
D
c
E
D
V
M
L
^ey g_dhlhjhc ba\_klghc nmgdpbb dhlhjh_ m^h\e_l\hjy_lky _keb
\aylvgZijbf_j
V
H
M
L
D
c
E
D
H
M
L
^eyg_dhlhjh]hnbdkbjh\Zggh]h
H
!
Hq_\b^ghqlhwlZfh^_evbk
dexqbl_evgh]b[dZyb^eyex[hcbkoh^ghcdjb\hc^hoh^ghklbfh`_l
[ulvkh]eZkh\ZgZkex[hc bkoh^ghc\j_f_gghckljmdlmju\heZlbev
ghklbH^gZdhhp_gdZfh^_ebgZhkgh\_j_Zevguo^Zgguog_y\ey_lky
ijZdlbq_kdhc <hi_j\uo djb\Zy ^hoh^ghklb g_ [m^_l dZdhceb[h
]eZ^dhc djb\hc aZ^Zgghc ^ey \k_o iheh`bl_evguo j_Zevguo agZq_
gbc gZ ijZdlbd_ hgZ ba\_klgZ lhevdh gZ h]jZgbq_gghf fgh`_kl\_
kjhdh\ih]Zr_gbyh[uqgh
kkhfgbl_evghclhqghklvxbaf_j_
gbyHl\kydhcijhp_^mjudhlhjZylj_[m_l^bnn_j_gpbjh\Zgbywlhc
©djb\hcªg_ke_^m_lh`b^Zlv^hklZlhqghclhqghklb<h\lhjuo^Z`_
_keb fh`gh [ueh [u ihemqblvhp_gdb nmgdpbc
D
E
b
V
gZhkgh\_
^Zgguog_lijbqbguihdhlhjhcfu^he`guihemqblvkh\iZ^Zxsmx
hp_gdm_keb \uihegbf lZdhc `_ZgZeba\j_f_gghc kljmdlmju g_^_
e_ciha`_
Emqr__gZqlhfh`ghgZ^_ylvky
wlhh]jZgbqblv
D
E
V
lZd
qlh[uhgbe_`Zeb\g_dhlhjhffZehfiZjZf_ljbq_kdhfk_f_ckl\_Z
aZl_fhp_gblviZjZf_lju<dZq_kl\_gZbf_gvr_]hij_^klZ\eyxs_]h
bgl_j_kk_f_ckl\Zfh`ghjZkkfZljb\Zlvfh^_ev<Zkbq_dZ\dhlhjhc
nmgdpbb \ujh`^Zxlky \ dhgklZglu b p_gu h[eb]Zpbc aZ^Z\Z_fu_
nhjfmehchij_^_eyxlkyijhklh
D D
§·
¨¸
EE E
©¹
H
PW U
HHWY
E
E
V
WlhlqZklguckemqZc^hklZlhqghdhgdj_lguc^eygZkqlh[ubk
ke_^h\Zlv _^bgkl\_ggmx g_`_eZl_evgmx hkh[_gghklv ]Zmkkh\hc fh
^_ebZbf_gghlhqlhijhp_glgu_klZ\dbfh]ml[ulvhljbpZl_evgu
fbBlZd\fh^_eb<Zkbq_dZij_^_evgufjZkij_^_e_gb_f
U
y\ey_lky
1
D
E
V
E
b_kebfu\u[_j_f
D
E
^hklZlhqgh[hevrbfihkjZ\
g_gbx kh klZg^Zjlguf hldehg_gb_f
V
E
lh fh`_f ij_^klZ\blv
qlh hljbpZl_evgu_ ijhp_glgu_ klZ\db [m^ml fZeh\_jhylgu H^gZdh
\u[jZ\qbke_ggu_agZq_gby
D
E
V
bf__f
D
E
V
E
D
E
OQ
W3W
o
Wlh
]h\hjbl h lhf qlh \hi_j\uo \ klZpbhgZjghf j_`bf_ \_jhylghklv
hljbpZl_evguo ijhp_glguo klZ\hd hq_gv fZeZhdhehî
\h
\lhjuokj_^g__agZq_gb_
U
jZ\ghbg_y\ey_lkyg_[eZ]hjZamfghc
]h^h\hcklZ\dhcZ\lj_lvbop_guh[eb]ZpbcjZklmlwdkihg_gpbZev
ghqlhy\ey_lkyZ[kmj^gufP_gZJLg_ih^gbfZ_lky^h_^bgbpu
\ l_q_gb_ hq_gv^ebl_evgh]h \j_f_gb b fh^_ev ^ey dhlhjhc fh`_l
lZdihemqZlvky^he`gZ[ulvbebhl\_j]gmlZbebbkihevah\Zlvkykhk
lhjh`ghklvx Wlh]h g_^hklZlhqgh qlh[u ijh[e_fhc fh`gh [ueh
ij_g_[j_qv
JZkkfhljbfijhp_kkkihlklZ\db
U
\f_klhijhp_kkZ
U
ghlh]^Z
ijhklh_ ]Zmkkh\h ih\_^_gb_ bkq_aZ_l H^gZdh fu fh`_f mklZgh\blv
ke_^mxsbcj_amevlZl
Ij_^iheh`bf qlh
U
±]Zmkkh\ ijhp_kk ?
U
P
khY
U
U
U
Lh]^Z
d
?_oj
¸
¸
¹
·
¨
¨
©
§
³
/:7
?_oj
¸
¸
¹
·
¨
¨
©
§
³
/:7
d
d
°
¿
°
¾
½
°
¯
°
®
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
³
0/:700
H[S
°
¿
°
¾
½
°
¯
°
®
¸
¸
¹
·
¨
¨
©
§
¸
¸
¹
·
¨
¨
©
§
U
¸
¸
¹
·
¨
¨
©
§
UPU
³³
GVGW*(H
H[S
]^_
5
{
³
GXU
DDHD:(D*
)S {
b
)
y\ey_lky^hiheg_gb_fnmgdpbbklZg^Zjlgh]hghjfZevgh]hjZk
ij_^_e_gby
LZdbfh[jZahf
d
»
»
¼
º
«
«
¬
ª
¸
¸
¹
·
¨
¨
©
§
»
»
¼
º
«
«
¬
ª
¸
¸
¹
·
¨
¨
©
§
³³
/:7/:7
H[SH[S
d
d
H[S
»
»
¼
º
«
«
¬
ª
¸
¸
¹
·
¨
¨
©
§
U
¸
¸
¹
·
¨
¨
©
§
UPU
³³
GVGW*
Ijbf_g_gb_g_jZ\_gkl\Z
S
d
D
D
H
D*
^Z_l ohjhr__ h[hkgh\Zgb_ ^ey \u[hjZ bkihevam_fuo \_ebqbg GZ
ijbf_j^eyfh^_eb<Zkbq_dZ
P
HHU
E
D
U
HH
E
V
ihwlhfm
@VK>
VHHGW
E
E
V
U
³
IjbgbfZy agZq_gby iZjZf_ljh\ ba \ur_ijb\_^_ggh]h ijbf_jZ
D
E
V
ihemq_gb_p_guh[eb]Zpbbkh
kjhdhfL
^Z_l^eyL
±b^eyL
±
Ij_^klZ\e_ggh_ml\_j`^_gb_^hdZau\Z_lkykbkihevah\Zgb_fg_
jZ\_gkl\ZB_gk_gZblh]hnZdlZqlh_kebO
b
=
y\eyxlkyghjfZevgu
fbkgme_\ufkj_^gbf?O
lh]^Z^eyex[uo
T
?_
O
T
_oj?
=
*
T
khYO
=
Hp_gdZ k\_jomfh`_l[ulvohjhr_cZiijhdkbfZpb_cjZa
ghklbf_`^mp_gZfbh[eb]Zpbcijbbkihevah\Zgbb]Zmkkh\Zijhp_kkZ
U
b iheh`bl_evghc qZklb
U
Wlh h[tykgy_lky l_f qlh _^bgkl\_gghc
bkihevam_fhc ZiijhdkbfZpb_c ^ey ihemq_gby g_jZ\_gkl\Z y\
ey_lky
_
d
O
>eyfZeuoO
!
jZaghklvO
_ bf__lihjy
^hdHO
b^ey[hevrboagZq_gbcOhgZjZ\gZHO ghijbmkj_^
g_gbb jZkij_^_e_gb_ \_ebqbgu
U
[m^_l bf_lv [ukljh mf_gvrZx
sbckyo\hkl_kebfu\u[_j_fiZjZf_ljudhlhju_h[_ki_qb\ZxlfZ
eu_ agZq_gby \_jhylghklb hljbpZl_evguo agZq_gbc kihlklZ\db LZ
dbfh[jZahfZiijhdkbfZpby^he`gZ[ulvlhqghc
Dhf[bgbjh\Zgb_g_aZ\bkbfuonZdlhjh\
Ijb h^ghf_jguo fh^_eyo g_y\gh ih^jZamf_\Z_lky qlh ehdZev
gu_ baf_g_gby p_gu h[eb]Zpbb \k_o kjhdh\ ih]Zr_gby iheghklvx
dhjj_ebjh\ZguHgblZd`_^hg_dhlhjhckl_i_gbh]jZgbq_gunhjfZ
fbdjb\uo^hoh^ghklbdhlhju_bfbfh]mlihjh`^Zlvky>eyihemq_
gbyf_g__h]jZgbqbl_evguofh^_e_cijboh^blkyi_j_oh^blvdfgh]h
f_jguffh^_eyfDh]^Zdhebq_kl\hnZdlhjh\m\_ebqb\Z_lkyqbke_g
gucZgZebafh^_e_cklZgh\blky\k_[he__b[he__ljm^gufihwlhfm
\hajZklZ_l \Z`ghklv ihemq_gby j_r_gbc \ aZfdgmlhc nhjf_ beb
[ebadbodaZfdgmlhcnhjf_<k\yabkwlbfkgZqZeZijhbeexkljbjm_f
ih^oh^&,5gZijbf_j_^\monZdlhjh\Ihke_wlh]hjZkkfhljbffgh
]hnZdlhjgu_fh^_eb^eydhlhjuofh`ghgZclbj_r_gby\aZfdgmlhc
nhjf_Ihwlhfm\fgh]hnZdlhjghfkemqZ_h]jZgbqbfky]Zmkkh\ufbb
K,5fh^_eyfb LZd dZd ]Zmkkh\u fh^_eb ij_^iheZ]Zxl [hevr_ \ha
fh`ghkl_c^eyihemq_gbyZgZeblbq_kdh]hj_r_gbyb^eylh]hqlh[u
k^_eZlv fh^_eb dhebq_kl\_ggh khihklZ\bfufb gZqg_f k fgh]hnZd
lhjghc\_jkbbfh^_ebK,5ZaZl_fihkljhbf]Zmkkh\mfh^_evdhlh
jmxijbkihkh[bfdlhc`_bkoh^ghc\j_f_gghckljmdlmj_bihemqbf
kh]eZkh\Zggu_oZjZdl_jbklbdbnZdlhjh\
>`Dhdk>`Bg]_jkheebKJhkkK,5ij_^eh`bebdhgkljmb
jh\Zlvfgh]hnZdlhjgmxfh^_eviml_f^h[Z\e_gbyg_aZ\bkbfuonZd
lhjh\<kemqZ_^\monZdlhjh\wlhhagZqZ_lhij_^_e_gb_djZldhkjhq
ghcklZ\dbdZd
U
W
5
O
W
O
W
O
W
O
W
]^_
G
O
W
P
O
W
GW
V
O
W
G
<
W
G
O
W
P
O
W
GW
V
O
W
G
<
W
^eyg_dhlhjuonmgdpbc
P
P
V
b
V
bg_aZ\bkbfuoijhp_kkh\[jh
mgh\kdbo^\b`_gbc<
b<
G_aZ\bkbfhklvnZdlhjh\O
bO ^Z_l\hafh`ghklvaZibkZlvp_gm
^bkdhglbjh\Zgghch[eb]Zpbb\\b^_
J
W
b ?
¸
¸
¹
·
¨
¨
©
§
¿
¾
½
¯
®
³
GVV;
H[S
?
H[S
; VGV
§·
½
°°
¨¸
®¾
¨¸
°°
¯¿
©¹
³
b^hoh^ghklvjZ\gZ
m
W
b m
W
bm
W
b
]^_m
W
b±^hoh^ghklvgZh[eb]Zpbxk^Zlhcih]Zr_gbyb\fhf_gl
\j_f_gb
W
_keb[uijhp_kkdjZldhkjhqghcklZ\dbijbgyeagZq_gb_O
LZdbfh[jZahf_kebbf__lkyj_r_gb_^eydjb\hc^hoh^ghklbdh]^Z
djZldhkjhqgZyklZ\dZke_^m_lijhp_kkmlh]^Zbf__lkyj_r_gb_
^eydjb\hc^hoh^ghklbb\fgh]hnZdlhjghcfh^_eb
NZdlhjgZy fh^_ev k ^\mfy g_aZ\bkbfufb ^bnnmabyfb k d\Z^
jZlguf dhjg_f dhlhjZy [ueZ \\_^_gZ&,5bamqZeZkv \ ^Zevg_cr_f
NEhg]klZnhf b ? R\Zjp_f /RQJVWDII 6FKZDUW] Z lZd`_
JQ_ghfbEKdhllhf&KHQ6FRWWIj_^iheZ]ZehkvqlhdZ`
^uc ba ijhp_kkh\ O
m^h\e_l\hjy_l mjZ\g_gbx \b^Z k jZaebq
gufb
N
T
b
V
bg_aZ\bkbfufb[jhmgh\kdbfb^\b`_gbyfbEhg]klZn
bR\Zjpihemqbebnhjfmeu^eyhipbhgh\gZ^bkdhglbjh\Zggmxh[
eb]ZpbxZQ_gbKdhll\u\_ebnhjfmeu^eyhipbhgh\gZ^jm]b_NI
ijhp_glguo klZ\hdEhg]klZn b R\ZjpaZf_lbeb qlh \heZlbevghklv
djZldhkjhqghc klZ\db y\ey_lky lZd`_ ebg_cghc dhf[bgZpb_c ^\mo
nZdlhjh\ ihwlhfm djZldhkjhqgmx klZ\dm b __ \heZlbevghklv fh`gh
ijbgylv \ dZq_kl\_ ^\mo nZdlhjh\ lZd `_ dZd \_dlhj ^hoh^ghkl_c
fh`ghijbgbfZlv\dZq_kl\_nZdlhjh\\ex[hcZnnbgghcnZdlhjghc
fh^_ebH^gZdhdZdmdZau\ZxlQ_gbKdhllklhqdbaj_gbyijh\_^_
gby \uqbke_gbc ijhs_ jZ[hlZlv k g_aZ\bkbfufb nZdlhjZfb q_f k
djZldhkjhqghc klZ\dhc b__\heZlbevghklvx dhlhju_ y\eyxlkydhj
j_ebjh\Zggufb
Fgh]hnZdlhjgZyfh^_ev\j_f_gghckljmdlmju
©kd\Z^jZlgufdhjg_fª
A^_kvij_^iheZ]Z_lkyqlhf]gh\_ggZydjZldhkjhqgZyijhp_glgZy
klZ\dZy\ey_lkykmffhcg_aZ\bkbfuoi_j_f_gguokhklhygbybebnZd
lhjh\
¦
W]WU
>bgZfbdZi_j_f_gguokhklhygbyijbgbfZ_lkydZd\fh^_ebK,5
G]
W
T
D
]
W
GW
V
W]
G
<
W
beb\\_dlhjghcnhjf_
G=
W
T
:
=
W
GW
9
¸
¸
¸
¹
·
¨
¨
¨
©
§
W]
W]
G
<
W
AZf_lbfqlh:b
9
y\eyxlky^bZ]hgZevgufbfZljbpZfb>eylh
]h qlh[u h[_ki_qblv fh^_eb \hafh`ghklv ZgZeblbq_kdh]h j_r_gby
ijbf_fqlh
T
b
9
g_aZ\bkylhl\j_f_gbWlhijb\h^bldlhfmqlh\
h[s_f kemqZ_ ijbkihkh[blv fh^_ev d ijhba\hevghc bkoh^ghc \j_
f_gghckljmdlmj_g_\hafh`ghH^gZdhlZddZdgZr_cp_evxy\ey_lky
ZgZeba baf_g_gbc \j_f_gghc kljmdlmju ihjh`^Z_fuo \gmlj_gg_c
kljmdlmjhcfh^_ebwlhg_[m^_lk_jv_agufh]jZgbq_gb_f
NhjfmeZ fh^_eb K,5 ^ey p_gu ^bkdhglghc h[eb]Zpbb k ^Zlhc
ih]Zr_gbyL\fhf_gl\j_f_gb
W
h[h[s_ggZy^eyfgh]hf_jgh]hkem
qZy^ZgZQ_ghfbKdhllhf
J
=
W
W
L :
W
L_oj^
E
W
L
=
W
`
]^_
:
W
L
$W7
^`
H[S
$W7 FZ F D 7 W
§·
¨¸
©¹
A^_kv
E
W
Ly\ey_lky\_dlhjkljhdhckdhfihg_glZfb
E
W
L
Z
_oj^k L
W
`
]^_
Z
>k
Z
_oj^k L
W
`k
Z
@ k
D
V
Imklv
a
7]
]
L
Z
V
_oj^k
L
W
`
E
W
L
]
L
V
lh]^ZhdZau\Z_lky-ZPVKLGLDQqlh
a
7]
mkeh\ghijbnbdkbjh
\Zgghf
]
W
hlghkbl_evgh \_jhylghklghc f_ju
T
hlj_]mebjh\Zgghc
jbkdhfnhj\Zj^ghcklZ\db
bf__lg_p_gljZevgh_obd\Z^jZljZkij_
^_e_gb_k
Y
kl_i_gyfbk\h[h^ubiZjZf_ljhfg_p_gljZevghklb
O
dh
lhju_aZ^ZxlkyjZ\_gkl\Zfb
Y
T
V
O
]
W
FZ
_oj^k
L
W
`
V
E
W
L
Djhf_lh]h^bki_jkbbnZdlhjh\
a
7]
aZ\bkylhl\j_f_gb
W
ijbf_j_
T
ke_^mxsbfh[jZahf
YZU
>
a
L
]
_
a
W]
@
Y
O
YZU
>
]
L
_
]
W
@
V
E
W
L
>T
E
W
L
]
W
FZ
_oj^k
L
W
`
@
KhihklZ\bfZy]Zmkkh\Zfh^_ev
Kgh\Zij_^iheh`bfqlhdjZldhkjhqgZyijhp_glgZyklZ\dZhij_
^_ey_lkyg_aZ\bkbfufbnZdlhjZfb gh l_i_jv^bgZfbdZi_j_f_gguo
khklhygbyfh^_eb[m^_lkhhl\_lkl\h\Zlvh[h[s_gghcfh^_eb<Zkbq_dZ
G]
W
T
W
D
]
W
GW
V
G
<
W
d
M
d
i
H^gh b ^\monZdlhjgu_ \_jkbb wlhc fh^_eb ijhZgZebabjh\Zgu
Wev DZjmb b ^j ?O .ZUhXL _W ZO
Q
nZdlhjgZy \_jkby fh`_l
[ulv jZkkfhlj_gZ ZgZeh]bqguf h[jZahf >eylh]hqlh[uwlZfh^_ev
[ueZkhihklZ\bfhck fh^_evx©k d\Z^jZlgufdhjg_fªk^_eZ_fke_
^mxs__ <hi_j\uo mklZgh\bf dhwnnbpb_glu \ha\jZs_gby d kj_^
g_fm
D
jZ\gufbkhhl\_lkl\mxsbfdhwnnbpb_glZf\fh^_eb©kd\Z^
jZlguf dhjg_fª <h\lhjuo \u[_j_f iZjZf_lju \heZlbevghklb
V
lZdbfh[jZahfqlh[u^_j`Zlv^bki_jkbbi_j_f_gguokhklhygby\l_
q_gb_ hij_^_e_ggh]h \j_f_ggh]h ]hjbahglZ h^bgZdh\ufb \fh^_eyo
]Zmkkh\hcb©kd\Z^jZlgufdhjg_fª<lj_lvboaZ\bkysb_hl\j_f_gb
dhwnnbpb_glu^j_cnZ
T
W
iha\heyxlkh]eZkh\Zlvbkoh^gmx\j_f_g
gmx kljmdlmjm _keb fu ijbf_f bkoh^gmx \j_f_ggmx kljmdlmjm ba
fh^_eb©kd\Z^jZlgufdhjg_fªdZdbkoh^gmx^ey]Zmkkh\ZkemqZy<
wlhcfh^_ebeh]Zjbnfp_gu^bkdhglguoh[eb]Zpbchij_^_ey_lky\u
jZ`_gb_f
OQJ
=
W
W
L
OQ
3= 7
3= W
¦
³
V
GVHH
D
@>
¦
³
V
VG:HH
D
AZf_lbf qlh aZ\bkbfhklv hl
T
W
mqblu\Z_lky \ eh]Zjbnf_ bk
oh^ghc p_gu h[eb]Zpbbk khhl\_lkl\mxs_c^Zlhc ih]Zr_gby Baf_
gyydh\j_f_gbL
nhj\Zj^gmxf_jm
T
]^_
> @
G
<
WG
<
WHGW
D
V
y\eyxlkyg_aZ\bkbfufbklZg^Zjlgufb\bg_jh\kdbfbijhp_kkZfbfu
fh`_fgZibkZlv
OQJ
=
W
W
L
OQ
W=3
7=3
¦
³
V
GVHH
D
@>
¦
³
V
GVHHH
D
@>
>@
HHG
<
V
D
V
¦
³
>bki_jkbbi_j_f_gguokhklhygbyh^bgZdh\uijbg_cljZevghcd
jbkdm b hlj_]mebjh\Zgghc nhj\Zj^guf jbkdhf f_jZo b aZ^Zxlky
jZ\_gkl\Zfb
YZU
>
]
W
@
H
D
GVH
V
V
³
<u[_j_f
V
\]Zmkkh\hcfh^_eblZdqlh[u
YZU
>
]
W
@
YDU
>
]
W
@
LZdbfh[jZahf
V
Z
0
YDU
>
]
W
@
]^_
YDU
>
]
W
@
aZ^Z_lky lZd `_ dZd \ fgh]hnZdlhjghc fh^_eb \j_
f_gghckljmdlmju©kd\Z^jZlgufdhjg_fª
>\monZdlhjgu_fh^_eb
<fgh]hnZdlhjguofh^_eyobf__lky[hevr_\hafh`ghkl_cijb
kihkZ[eb\Zlv fh^_ev d j_Zevghc jughqghc kblmZpbb h^gZdh ihem
qZ_fu_j_r_gbyklZgh\ylky^h\hevghkeh`gufbG_dhlhjufdhfijh
fbkkhfy\ey_lkybkihevah\Zgb_^\monZdlhjguofh^_e_cqbkehiZjZ
f_ljh\ihkjZ\g_gbxkh^ghnZdlhjghcfh^_evxm\_ebqb\Z_lkyZm\_
ebq_gb_ keh`ghklb ihemqZ_fh]h j_r_gby fh`_l hdZaZlvky g_agZqb
l_evguf<dZq_kl\_ijbf_jZijb\_^_f^\_qZs_^jm]bopblbjm_fu_
fh^_eb
Fh^_evEhg]klZnZ±R\ZjpZ
NEhg]klZnb?R\Zjp/RQJVWDII6FKZDUW]jZajZ[hlZeb
h[sb_ jZfdb jZ\gh\_kby ^ey hij_^_e_gby klhbfhklb nbgZgkh\uo
ijhba\h^guoqm\kl\bl_evguodbaf_g_gbyfijhp_glghcklZ\dbHgb
bkihevah\Zeb\ZjbZgl^\moi_j_f_gguokhklhygby\wdhghfbd_baf_
gyxs_ckyg_ij_ju\gh\h\j_f_gbWlbfb^\mfynZdlhjZfby\eyxlky
djZldhkjhqgZy klZ\dZ
U
b ^bki_jkby baf_g_gbc djZldhkjhqghc ijh
p_glghcklZ\db
Y
iha\heyylZdbfh[jZahfp_gZfnbgZgkh\uoijhba
\h^guo hljZ`Zlv dZd l_dmsbcmjh\_gv ijhp_glghc klZ\db lZd bl_
dmsbc mjh\_gv \heZlbevghklb ijhp_glghc klZ\db KgZqZeZ Z\lhju
jZajZ[hlZeb^bgZfbdm^\mowdhghfbq_kdbonZdlhjh\dhlhju_w\hex
pbhgbjmxlg_aZ\bkbfh^jm]hl^jm]Zbbkihevamxlky^eyoZjZdl_jb
klbdbijhp_kkZhibku\Zxs_]hj_ZebaZpbx^hoh^ZgZbg\_klbpbx
G[
J
G
[
GW
[
G
<
G\
K
I
\
GW
\G
<
J
G
K
b
I
±iZjZf_lju hlj_]mebjh\Zggh]h jbkdhf ijhp_kkZ ^ey g_
dhjj_ebjh\Zgguoi_j_f_gguokhklhygby
Hkgh\gh_^bnn_j_gpbZevgh_mjZ\g_gb_\qZklguoijhba\h^guo
^eyklhbfhklbG
\k_ok\h[h^guohlg_mieZlunbgZgkh\uoijhba\h^
guohlijhp_glguoklZ\hdbf__l\b^
oG
mG
J
G
[
+
K
I
\
+
D
[
E
\
+
+
DjZldhkjhqgZy ijhp_glgZy klZ\dZ b ^bki_jkby baf_g_gbc wlhc
klZ\db^ZxlkydZd\a\_r_ggu_kmffui_j_f_gguokhklhygby
[
b
\
\