Медведев Г.А. Математические основы финансовой экономики. Часть2
Подождите немного. Документ загружается.
Bkihevamy
mjZ\g_gb_
b
\ujZ`_gb_
^ey
ijhp_glghc
klZ\db
fh`_f
aZf_lblv
qlh
hkgh\gh_
mjZ\g_gb_
p_gu
J ^bkdhglghc
h[eb]Zpbb
m^h[g__
aZibkZlv
dZd
w
w
O
w
w
w
w
T
w
w
V
U3
U
3
U
W
3
U
3
UN
U
3
U
k
]jZgbqguf
mkeh\b_f
J
U
7
7
I_j\u_
ljb
qe_gZ
\
mjZ\g_gbb
kh]eZkgh
nhjfme_
Blh
hij_^_eyxl
h`b^Z_fh_
baf_g_gb_
p_gu
h[eb]Zpbb
LZdbf
h[jZahf
h`b^Z_fZy
^hoh^ghklv
h[eb]Zpbb
jZ\gZ
U
3
3
U
U
w
wO
F]gh\_ggZy
ij_fby
^hoh^ghklb
h[eb]Zpbb
ijhihjpbh
gZevgZ
weZklbqghklb
__
ijhp_glh\
Fgh`bl_ev
O
U
y\ey_lky
dh\ZjbZ
pb_c
f_`^m
baf_g_gb_f
ijhp_glghc
klZ\db
b
baf_g_gb_f
^heb
hilb
fZevgh
bg\_klbjh\Zggh]h
[h]Zlkl\Z
©
jughqgh]h
ihjln_ey
ª
LZd
dZd
ih
wdhghfbq_kdhfm
kfukem
ijhba\h^gZy
w
J
w
U
ij_fbb
[m^ml
ih
eh`bl_evgufb
_keb
wlZ
dh\ZjbZpby
hljbpZl_evgZy
O
Ba
mjZ\g_gby
fh`gh
m\b^_lv
qlh
p_gu
h[eb]Zpbb
aZ\bkyl
lhevdh
hl
h^ghc
kemqZcghc
i_j_f_gghc
l_dms_c
kihl
ijhp_glghc
klZ\db
dhlhjZy
kem`bl
\
dZq_kl\_
bgkljmf_glZevghc
i_j_f_gghc
^ey
hkgh\ghc
l_ogheh]bq_kdhc
g_hij_^_e_gghklb
Ohly
ij_^iheh`_gb_
h
lhf
qlh
l_dmsb_
b
[m^msb_
ijhp_glgu_
klZ\db
b]jZxl
\Z`gmx
jhev
\
hij_^_e_gbb
\j_f_gghc
kljmdlmju
\
h[s_f
ih^l\_j`^Z_lky
h^gZdh
wlh
kljh]h
\_jgh
lhevdh
ijb
hij_^_e_gguo
mkeh\byo
<
jZfdZo
wlh]h
ZgZebaZ
gZb[he__
\Z`gu_
h[klhyl_evkl\Z
^hklZlhqgu_
^ey
lh]h
qlh[u
p_gu
h[eb]Zpbb
aZ\bk_eb
lhevdh
hl
kihl
ijhp_glghc
klZ\db
ke_^mxsb_
bg\_klhju
bf_xl
ihklhyggh_
hlghkbl_evgh_
g_ijb
ylb_
jbkdZ
l_ogheh]bq_kdZy
g_hij_^_e_gghklv
fh`_l
[ulv
hibkZgZ
_^bgkl\_gghc
i_j_f_gghc
b
ijhp_glgZy
klZ\dZ
y\ey_lky
fhghlhgghc
nmgdpb_c
wlhc
i_j_f_gghc
l_ogheh]bq_kdb_
baf_g_gby
g_klhoZk
lbq_kdb_
b
ijhp_glgZy
klZ\dZ
±
fhghlhggZy
nmgdpby
[h]Zlkl\Z
<uqbkeb\
khhl\_lkl\mxs__
fZl_fZlbq_kdh_
h`b^Zgb_
kf
]e
ihemqbf
p_gm
h[eb]Zpbb
\
\b^_
J
U
W
7
$
W
7
H[S>
%
W
7
U
@
]^_
$
W
7
{
@H[S>
@H[S>
»
¼
º
«
¬
ª
JJOJ
JOJ
W7N
W7N
<
W
7
{
JJOJ
J
@H[S>
@H[S>
W7N
W7
J{
VO
N
P_gZ
h[eb]Zpbb
[m^_l
m[u\Zxs_c
\uimdehc
nmgdpb_c
ijhp_gl
ghc
klZ\db
b
\hajZklZxs_c
m[u\Zxs_c
nmgdpb_c
\j_f_gb
kjhdZ
ih]Zr_gby
IZjZf_lju
ijhp_kkZ
ijhp_glghc
klZ\db
\ebyxl
ke_^mx
sbf
h[jZahf
P_gZ
h[eb]Zpbb
y\ey_lky
m[u\Zxs_c
\uimdehc
nmgd
pb_c
kj_^g_]h
mjh\gy
ijhp_glghc
klZ\db
T
b
\hajZklZxs_c
\h]gmlhc
m[u\Zxs_c
\uimdehc
nmgdpb_c
iZjZf_ljZ
kdhjhklb
mklZgh\e_gby
N
_keb
ijhp_glgZy
klZ\dZ
[hevr_
f_gvr_
q_f
T
H[Z
wlb
j_amevlZlZ
g_ihkj_^kl\_ggh
ke_^mxl
ba
lh]h
dZd
wlb
iZjZf_lju
\ebyxl
gZ
h`b
^Z_fmx
[m^msmx
ijhp_glgmx
klZ\dm
P_gZ
h[eb]Zpbb
y\ey_lky
m\_
ebqb\Zxs_cky
\h]gmlhc
nmgdpb_c
iZjZf_ljZ
©
jughqgh]h
ª
jbkdZ
O
Bglmblb\gh
wlh
\
hkgh\ghf
h[tykgy_lky
l_f
qlh
[he__
\ukhdb_
agZ
q_gby
O
^Zxl
[he__
\ukhdmx
dh\ZjbZpbx
ijhp_glghc
klZ\db
k
[h]Zl
kl\hf
LZdbf
h[jZahf
ijb
[hevr_f
O
[he__
\_jhylgh
qlh
p_gZ
h[eb
]Zpbb
[m^_l
\ur_
dh]^Z
[h]Zlkl\h
gZ
gbadhf
mjh\g_
b
ke_^h\Zl_ev
gh
bf__l
[hevrmx
fZj]bgZevgmx
ihe_aghklv
P_gZ
h[eb]Zpbb
±
\ha
jZklZxsZy
\h]gmlZy
nmgdpby
^bki_jkbb
ijhp_glghc
klZ\db
V
A^_kv
bf__lky
g_kdhevdh
wnn_dlh\
GZb[he__
\Z`guf
y\ey_lky
lh
qlh
[hevr__
agZq_gb_
V
k\b^_l_evkl\m_l
h
[hevr_c
g_hij_^_e_gghklb
hlghkbl_evgh
[m^msbo
\hafh`ghkl_c
j_Zevgh]h
ijhba\h^kl\Z
b
h
[hevr_c
g_hij_^_e_gghklb
[m^ms_]h
ihlj_[e_gby
GZ
lZdhf
jugd_
hl\_j]Zxsb_
jbkd
bg\_klhju
p_gbeb
[u
]ZjZglbjh\Zggmx
hl^Zqm
h[
eb]Zpbb
[he__
\ukhdh
>bgZfbdZ
p_gu
h[eb]Zpbb
hij_^_ey_lky
klhoZklbq_kdbf
^bnn_
j_gpbZevguf
mjZ\g_gb_f
G3 U
>
O
<
W
7
@
3GW
<
W
7
3
V
U
G]
>ey
wlhc
fh^_eb
k
h^ghc
i_j_f_gghc
khklhygby
^hoh^ghklv
h[eb]Z
pbb
kljh]h
hljbpZl_evgh
dhjj_ebjh\ZgZ
k
baf_g_gbyfb
ijhp_glghc
klZ\db
>hoh^ghklv
baf_gy_lky
f_gvr_
dh]^Z
ijhp_glgZy
klZ\dZ
gba
dZy
>_ckl\bl_evgh
hgb
klZgh\ylky
^Z`_
^_l_jfbgbjh\Zggufb
dh]^Z
ijhp_glgZy
klZ\dZ
^hklb]Z_l
gmey
lZd
dZd
lh]^Z
baf_g_gby
ijhp_gl
ghc
klZ\db
klZgh\ylky
^_l_jfbgbjh\Zggufb
Bglmblb\gh
h`b^Z_lky
qlh
dZdb_
[u
agZq_gby
g_
ijbgbfZeb
^jm]b_
i_j_f_ggu_
baf_gqb
\hklv
^hoh^ghklb
mf_gvrZ_lky
dh]^Z
h[eb]Zpby
^hklb]Z_l
ih]Zr_
gby
GZ
kZfhf
^_e_
iha\heyy
W^hklb]Zlv
7
b
h[hagZqZy
7
W
q_j_a
W
gZoh^bf
qlh
h`b^Z_fZy
^hoh^ghklv
jZ\gZ
U
W
2
W
b
^bki_jkby
^h
oh^ghklb
bf__l
ihjy^hd
2
W
Z
g_
2
W
dZd
[ueh
[u
\
kemqZ_
^hoh^
ghklb
gZ
bg\_klbpbx
\
ijhba\h^kl\_gguc
ijhp_kk
\
l_q_gb_
dhjhldh
]h
bgl_j\ZeZ
<
wlhf
kfuke_
^hoh^ghklv
gZ
hq_gv
djZldhkjhqgmx
h[
eb]Zpbx
klZgh\blky
^_l_jfbgbjh\Zgghc
H[eb]Zpbb
h[uqgh
dhlbjmxlky
\
l_jfbgZo
^hoh^ghkl_c
Z
g_
p_g
>ey
[_kdmihgguo
h[eb]Zpbc
\k_]^Z
dhlbjm_lky
^hoh^ghklv
^h
ih]Z
r_gby
\LHOGWRPDWXULW\
5
U
W
7
dhlhjZy
hij_^_ey_lky
ba
\ujZ`_gby
J
U
W
7
_oj
>
7
W
5
U
W
7
@
LZdbf
h[jZahf
5
U
W
7
>
U<
W
7
OQ
$
W
7
@
7
W
Dh]^Z
ijb[eb`Z_lky
ih]Zr_gb_
^hoh^ghklv
^h
ih]Zr_gby
ijb
[eb`Z_lky
d
l_dms_c
ijhp_glghc
klZ\d_
g_aZ\bkbfh
hl
lh]h
dZdb_
agZq_gby
ijbgbfZxl
^jm]b_
iZjZf_lju
?keb
`_
jZkkfZljb\Zlv
m\_
ebq_gb_
\j_f_gb
^h
ih]Zr_gby
^hoh^ghklv
^hklb]Z_l
ij_^_eZ
dhlh
juc
g_
aZ\bkbl
hl
l_dms_c
ijhp_glghc
klZ\db
5
U
W
f
OJ
T
N
N
Dh]^Z
kihl
klZ\dZ
f_gvr_
^he]hkjhqghc
^hoh^ghklb
\j_f_ggZy
kljmdlmjZ
jZ\ghf_jgh
m\_ebqb\Z_lky
Ijb
ijhp_glghc
klZ\d_
ij_
\urZxs_c
N
T
N
O
\j_f_ggZy
kljmdlmjZ
ihgb`Z_lky
>ey
ijhf_
`mlhqguo
agZq_gbc
ijhp_glghc
klZ\db
djb\Zy
^hoh^ghklb
bf__l
wdk
lj_fmf
>jm]mx
kjZ\gbl_evgmx
klZlbdm
^ey
djb\hc
^hoh^ghklb
ihemqZ_f
ba
\b^Z
nmgdpbb
p_gu
h[eb]Zpbb
<hajZklZgb_
l_dms_c
ijhp_glghc
klZ\db
m\_ebqb\Z_l
^hoh^ghklb
^ey
\k_o
kjhdh\
ih]Zr_gby
gh
_]h
\ebygb_
kbevg__
^ey
dhjhldbo
kjhdh\
ih]Zr_gby
:gZeh]bqgh
\hajZk
lZgb_
mklZgh\b\r_]hky
kj_^g_]h
T
m\_ebqb\Z_l
\k_
^hoh^ghklb
gh
\
wlhf
kemqZ_
\ebygb_
[hevr_
^ey
ijh^he`bl_evguo
kjhdh\
ih]Zr_gby
>hoh^ghklv
^h
ih]Zr_gby
m[u\Z_l
dh]^Z
V
b
O
\hajZklZxl
\
lh
\j_
fy
dZd
\ebygb_
baf_g_gby
N
fh`_l
[ulv
jZaebqguf
\
aZ\bkbfhklb
hl
l_dms_]h
agZq_gby
ijhp_glghc
klZ\db
<k_]^Z
agZqbl_e_g
bgl_j_k
d
g_kf_s_gghfm
ij_^kdZaZgbx
[m^m
sbo
ijhp_glguo
klZ\hd
<
gZklhys_c
kblmZpbb
fu
fh]eb
[u
jZ[hlZlv
k
mjZ\g_gb_f
dhlhjh_
^Z_l
h`b^Z_fu_
agZq_gby
[m^ms_c
ijh
p_glghc
klZ\db
q_j_a
l_dmsmx
klZ\dm
b
iZjZf_lju
N
b
T
H^gZdh
\
kdhgkljmbjh\Zgghc
gZfb
fh^_eb
jZpbhgZevguo
h`b^Zgbc
\ky
bgnhj
fZpby
dhlhjZy
bf__lky
\
l_dmsbc
fhf_gl
h
[m^msbo
baf_g_gbyo
ijhp_glguo
klZ\hd
g_y\gh
kh^_j`blky
\
l_dmsbo
p_gZo
h[eb]Zpbc
b
\j_f_gghc
kljmdlmj_
?keb
fh^_ev
ijZ\bevgZy
lh]^Z
ex[hc
hl^_ev
guc
iZjZf_lj
fh`gh
hij_^_eblv
ba
\j_f_gghc
kljmdlmju
b
agZq_gbc
^jm]bo
iZjZf_ljh\
Wlhl
f_lh^
hkh[_ggh
\Z`_g
dh]^Z
fh^_ev
jZkrbjy_lky
qlh[u
^himkdZlv
aZ\bkbfhklv
hl
\j_f_gb
nmgdpbb
^j_cnZ
T
W
Lh]^Z
fu
fh
`_f
bkihevah\Zlv
bgnhjfZpbx
kh^_j`Zsmxky
\h
\j_f_gghc
kljmd
lmj_
qlh[u
ihemqblv
T
W
b
h`b^Z_fu_
[m^msb_
kihl
klZ\db
g_
bk
ihevamy
Zijbhjguo
h]jZgbq_gbc
gZ
bo
nmgdpbhgZevguc
\b^
>Ze__
[m^msb_
h`b^Z_fu_
kihl
klZ\db
aZ^Z\Z_fu_
nhjfmeZfb
k\h^ylky
d
ke_^mxs_fm
?
U
7
_
U
W
U
W
H
N
³
T
GVHV
NhjfmeZ
^ey
p_gu
h[eb]Zpbb
\
k\hx
hq_j_^v
ij_h[jZam
_lky
d
\b^m
J
U
W
7
$
W
7
H[S>
%
W
7
U
@
]^_
$
W
7
_oj
¸
¸
¹
·
¨
¨
©
§
T
³
GV7V%VN
qlh
ij_\jZsZ_lky
\
jZ\_gkl\h
dh]^Z
nmgdpby
T
W
klZgh\blky
dhgklZglhc
Ij_^iheZ]Zy
^ey
ijbf_jZ
qlh
^jm]b_
iZjZf_lju
ijhp_kkZ
ba
\_klgu
fh`gh
bkihevah\Zlv
\j_f_ggmx
kljmdlmjm
^ey
hij_^_e_gby
g_kf_s_ggh]h
ijh]ghaZ
[m^msbo
ijhp_glguo
klZ\hd
Kh]eZkgh
nhj
fme_
$
W
7
y\ey_lky
gZ[ex^Z_fhc
nmgdpb_c
i_j_f_gghc
L
ijb
aZ^Zgghc
\j_f_gghc
kljmdlmj_
b
ba\_klghf
\b^_
nmgdpbb
%
W
7
klZg^Zjlguc
f_lh^
fh`gh
ijbf_gblv
^ey
bg\_jkbb
b
ihemq_
gby
\ujZ`_gby
^ey
T
W
q_j_a
$
W
7
b
%
W
7
MjZ\g_gb_
l_
i_jv
fh`gh
bkihevah\Zlv
^ey
ihemq_gby
ij_^kdZaZgby
h`b^Z_fuo
agZq_gbc
[m^msbo
kihl
klZ\hd
g_y\gh
kh^_j`Zsboky
\
l_dms_c
\j_
f_gghc
kljmdlmj_
AZf_lbf
qlh
ihemqZxlky
g_
l_
`_
agZq_gby
dhlhju_
aZ^Z\Zebkv
[u
ljZ^bpbhggufb
ij_^iheh`_gbyfb
h[
h`b^Zgbyo
qlh
h`b^Z_fu_
agZq_gby
[m^msbo
kihl
klZ\hd
kh^_j`Zlky
\h
\j_f_gghc
kljmdlmj_
\
\b^_
ih^jZamf_\Z_fuo
nhj\Zj^guo
klZ\hd
<
fh^_eb
g_ij_ju\gh]h
\j_f_gb
nhj\Zj^gZy
klZ\dZ
7U
aZ^Z_lky
\ujZ`_gb_f
7
3
3
w
w
Lh]^Z
iml_f
^bnn_j_gpbjh\Zgby
jZ\_gkl\Z
ihemqbf
7U
7
7WU3
7WU3
w
w
³
w
w
T
w
w
GV
7
7V%
VN
7
7W%
U
KjZ\gb\Zy
\ujZ`_gby
b
fu
\b^bf
qlh
hgb
bf_xl
h^bgZdh\mx
kljmdlmjm
H^gZdh
\
ljZ^bpbhgghf
ijh]gha_
nhj\Zj^ghc
klZ\db
bkihevam_lky
\_kh\hc
dhwnnbpb_gl
%V7
H
7
w
z
w
qlh
ijb\h^bl
d
kf_s_gguf
ij_^kdZaZgbyf
JZkkfhljbf
jy^
^jm]bo
dhgdj_lbaZpbc
\j_f_gghc
aZ\bkbfhklb
iml_f
g_[hevrhc
fh^bnbdZpbb
fh^_eb
QZklguf
kemqZ_f
fh`_l
kem
`blv
ij_^iheh`_gb_
qlh
ijhp_glgZy
klZ\dZ
bf__l
\b^
WJWU
]^_
WU
aZ^Z_lky
mjZ\g_gb_f
Z
J
W
±
nmgdpby
h[_ki_qb\ZxsZy
iheh`bl_evghklv
gb`g_c
]jZgbpu
ijhp_glghc
klZ\db
Kms_kl\_gguf
fhf_glhf
\
wlhf
kemqZ_
y\ey_lky
lh
qlh
\
fh^_eb
jZpbhgZevgh]h
h`b^Zgby
l_dmsZy
\j_f_ggZy
kljmdlmjZ
hebp_l\hjy_l
bgnhjfZpbx
lj_[m_fmx
^ey
hij_^_e_gby
jughqgh]h
jZkij_^_e_gby
\_jhylghkl_c
[m^ms_]h
dmjkZ
ijhp_glghc
klZ\db
Djhf_
lh]h
\j_f_ggZy
kljmdlmjZ
fh`_l
[ulv
bg\_jlbjh\ZgZ
^ey
gZoh`^_gby
wlbo
h`b^Zgbc
>jm]b_
fh^bnbdZpbb
l_ogheh]bq_kdbo
baf_g_gbc
k
_^bgkl\_g
ghc
i_j_f_gghc
[m^ml
\
k\hx
hq_j_^v
\uau\Zlv
^jm]b_
klhoZklbq_
kdb_
k\hckl\Z
ijhp_glghc
klZ\db
E_]dh
ijh\_jblv
qlh
\
gZr_c
fh
^_eb
_keb
D
b
**
c
ijhihjpbhgZevgu
g_dhlhjhc
nmgdpbb
K
<
W
lh
]^Z
ijhp_glgZy
klZ\dZ
[m^_l
lZd`_
ijhihjpbhgZevgZ
wlhc
nmgdpbb
Iml_f
m^h[gh]h
\u[hjZ
nmgdpbc
K
<
W
P
<
W
b
6
<
W
fh`gh
ij_^m
kfhlj_lv
rbjhdbc
^bZiZahg
Zijbhjguo
k\hckl\
baf_g_gbc
ijhp_gl
ghc
klZ\db
^ey
ihkljh_gby
iheghklvx
khklhyl_evghc
fh^_eb
HIJ?>?E?GB?KLHBFHKLB:DLB<H<
K<UIE:LHCA:<BKYS?C
HLIJHP?GLGHCKL:<DB
JZajZ[hlZggmx
ko_fm
hij_^_e_gby
klhbfhklb
fh`gh
ijbf_gblv
d
^jm]bf
P;
\uieZlu
dhlhjuo
aZ\bkyl
hl
ijhp_glghc
klZ\db
d
lZdbf
dZd
hipbhgu
gZ
h[eb]Zpbb
b
nvxq_jku
gZ
h[eb]Zpbb
WlZ
]b[dhklv
iha\hey_l
kha^Z\Zlv
fh^_eb
ij_^kdZaZgby
hlghkbl_evgh
p_g
Zdlb\h\
h^gh\j_f_ggh
gZ
g_kdhevdbo
nbgZgkh\uo
jugdZo
Ke_^h\Zl_evgh
ijb
f_g_gb_
d
^jm]bf
P;
fh`_l
^himkdZlv
[he__
fhsgu_
wfibjbq_kdb_
l_klu
q_f
l_
dhlhju_
ijbf_gyxlky
lhevdh
d
h^ghc
h[eb]Zpbb
<
dZq_kl\_
ijbf_jZ
hij_^_e_gby
klhbfhklb
^jm]h]h
khjlZ
Zdlb
\h\
aZ\bkbfuo
hl
ijhp_glghc
klZ\db
jZkkfhljbf
hipbhgu
gZ
h[eb
]Zpbb
H[hagZqbf
q_j_a
K
U
W
7
V
.
klhbfhklv
\
fhf_gl
W
hipbhgZ
dhee
gZ
^bkdhglgmx
[_kdmihggmx
h[eb]Zpbx
k
^Zlhc
ih]Zr_gby
V
p_ghc
bkiheg_gby
.
b
^Zlhc
bkl_q_gby
L
LZd
dZd
e_`Zsbc
\
hkgh\_
Zdlb\
^bkdhglgZy
h[eb]Zpby
g_
^_eZ_l
ieZl_`_c
\
l_q_gb_
kjhdZ
^_c
kl\by
hipbhgZ
ZgZeba
F_jlhgZ
kf
q
]e
ihdZau\Z_l
qlh
ij_`^_\j_f_ggh_
bkiheg_gb_
gbdh]^Z
g_
y\ey_lky
hilbfZevguf
b
ke_^h\Zl_evgh
Zf_jbdZgkdbc
b
_\jhi_ckdbc
dheeu
bf_xl
h^bgZdh
\mx
klhbfhklv
P_gZ
hipbhgZ
m^h\e_l\hjy_l
hkgh\ghfm
mjZ\g_gbx
hij_^_e_gby
klhbfhklb
k
djZ_\uf
mkeh\b_f
K
U
W
7
V
.
PD[>
3
U
7
V
±
.
@
Ihgylgh
qlh
V
t
L
t
W
b
.
g_
ij_\urZ_l
:
7
V
fZdkbfZevgh
\hafh`ghc
p_gu
h[eb]Zpbb
\
fhf_gl
\j_f_gb
L
lZd
dZd
\
ijhlb\hih
eh`ghf
kemqZ_
hipbhg
gbdh]^Z
g_
[m^_l
bkiheg_g
b
[ue
[u
[_kihe_
a_g
Kgh\Z
iml_f
\uqbke_gby
khhl\_lkl\mxsbo
fZl_fZlbq_kdbo
h`b
^Zgbc
ihemqbf
ke_^mxsmx
nhjfmem
^ey
p_gu
hipbhgZ
K
U
W
7
V
.
J
U
W
V
u
u
F
> @
NUH
U%7V
%7 V
§·
TI
I\
¨¸
VI\
©¹
.J
U
W
7
F
> @
NUH
U
§·
TI
I\
¨¸
VI\
©¹
]^_
J{
VO
N
V
J
{I
H
V
JO
{\
N
OQ
V7%
.
V7$
U
»
¼
º
«
¬
ª
¸
¹
·
¨
©
§
{
F
±
\\_^_ggZy
jZg__
nmgdpby
g_p_gljZevgh]h
ob
d\Z^jZl
jZkij_^_
e_gby
U
±
djblbq_kdh_
agZq_gb_
ijhp_glghc
klZ\db
gb`_
dhlhjh]h
[m^_l
ijhbkoh^blv
bkiheg_gb_
l
_
.
J
U
7
V
Klhbfhklv
hipbhgZ
dhee
±
\hajZklZxsZy
nmgdpby
kjhdZ
bkl_q_
gby
dh]^Z
^ZlZ
ih]Zr_gby
e_`Zs_c
\
hkgh\_
h[eb]Zpbb
hklZ_lky
nbd
kbjh\Zgghc
Klhbfhklb
hipbhgh\
dhee
gZ
Zdpbb
±
\hajZklZxsb_
nmgdpbb
ijhp_glghc
klZ\db
ihkdhevdm
m\_ebq_gb_
klZ\db
kgb`Z_l
gZklhysmx
klhbfhklv
p_gu
bkiheg_gby
H^gZdh
a^_kv
m\_ebq_gb_
ijhp_glghc
klZ\db
[m^_l
lZd`_
mf_gvrZlv
p_gm
e_`Zs_c
\
hkgh\_
h[eb]Zpbb
Qbke_gguc
ZgZeba
ihdZau\Z_l
qlh
ihke_^gbc
wnn_dl
kbevg__
b
qlh
klhbfhklv
hipbhgZ
y\ey_lky
m[u\Zxs_c
\uimdehc
nmgdpb_c
ijhp_glghc
klZ\db
KJ:<G?GB?KHIJ?>?E?GB?FP?GU
H;EB=:PBB:J;BLJ:@GUFB
F?LH>:FB
DjZldh
kjZ\gbf
jZajZ[hlZggmx
f_lh^heh]bx
k
g_dhlhjufb
^jm
]bfb
kihkh[Zfb
hij_^_e_gby
p_gu
h[eb]Zpbb
\
g_ij_ju\ghf
\j_f_gb
Ihe_agh
k^_eZlv
wlh
l_i_jv
Z
g_
iha`_
ihkdhevdm
fh^_ev
ij_^klZ\
e_ggZy
\
]e
y\ey_lky
b^_Zevguf
klZg^Zjlhf
^ey
kjZ\g_gby
GZqg_f
k
^_lZevgh]h
hibkZgby
e_`Zs_c
\
hkgh\_
wdhghfbdb
Hgh
iha\hey_l
gZf
b^_glbnbpbjh\Zlv
ke_^mxsb_
khklZ\eyxsb_
ijhp_^m
ju
hij_^_e_gby
p_gu
h[eb]Zpbb
Z
i_j_f_ggu_
hl
dhlhjuo
aZ\bkbl
p_gZ
h[eb]Zpbb
[
klhoZklbq_kdb_
k\hckl\Z
e_`Zsbo
\
hkgh\_
i_j_f_gguo
dhlh
ju_
hij_^_eyxlky
wg^h]_ggh
HQGRJHQRXVO\
\
y\guc
\b^
nZdlhjguo
jbkdh\uo
ij_fbc
IDFWRUULVNSUHPLXP
J
F_jlhg
ihdZau\Z_l
qlh
_keb
gZqbgZlv
\f_klh
wlh]h
lhevdh
k
ijbgylby
ij_^iheh`_gbc
Z
b
[
lh]^Z
nhjfmem
Blh
fh`gh
bkihevah\Zlv
qlh[u
mklZgh\blv
ij_\ur_gb_
h`b^Z_fh]h
^hoh^Z
gZ
h[
eb]Zpbx
\
lhf
`_
\b^_
qlh
b
e_\Zy
qZklv
mjZ\g_gby
?keb
nmgd
pbhgZevguc
\b^
ijZ\hc
qZklb
mjZ\g_gby
ba\_kl_g
lh]^Z
fh`gh
ihemqblv
mjZ\g_gb_
^ey
hij_^_e_gby
p_gu
h[eb]Zpbb
GZijbf_j
_keb
ijhba\hevgh
ij_^iheh`blv
qlh
p_gZ
h[eb]Zpbb
aZ\bkbl
lhevdh
hl
l_
dms_c
ijhp_glghc
klZ\db
U
dhlhjZy
ke_^m_l
ijhp_kkm
m^h\e_l\hjyx
s_fm
mjZ\g_gbx
b
qlh
ij_\ur_gb_
h`b^Z_fh]h
^hoh^Z
gZ
h[eb
]Zpbx
k
^Zlhc
ih]Zr_gby
L
jZ\gh
<
U
W
7
lh]^Z
ihemqZ_f
7WU<U3
W
3
U
3
UN
U
3
U
w
w
w
w
T
w
w
V
?keb
bf__lky
dZdh_
eb[h
e_`Zs__
\
hkgh\_
jZ\gh\_kb_
m^h\e_
l\hjyxs__
ij_^iheh`_gbyf
Z
b
[
lh]^Z
^he`gZ
kms_kl\h\Zlv
g_dh
lhjZy
nmgdpby
<
^ey
dhlhjhc
p_gZ
h[eb]Zpbb
aZ^Z_lky
mjZ\g_gb_f
H^gZdh
dZd
aZf_qZ_l
F_jlhg
wlhl
\u\h^
kZf
ih
k_[_
g_
h[_k
i_qb\Z_l
gbdZdh]h
kihkh[Z
hij_^_eblv
nmgdpbx
<
beb
hlg_klb
__
d
e_`Zsbf
\
hkgh\_
i_j_f_gguf
:j[bljZ`guc
ih^oh^
hij_^_e_gby
p_gu
h[eb]Zpbb
[ue
jZajZ[h
lZg
\
klZlvyo
F
%UHQQDQ
?
6FKZDUW]/'RWKDQ0*HU
PDQ65LFKDUG9DVLþHN
Ijb
_]h
ijbf_g_gbb
Zj
]mf_glu
ih^h[gu_
l_f
dhlhju_
[ueb
\
^hdZaZl_evkl\_
l_hj_fu
]e
bkihevamxlky
qlh[u
ihdZaZlv
_keb
g_
bf__lky
Zj[bljZ`guo
\hafh`ghkl_c
nmgdpby
<
^he`gZ
bf_lv
\b^
<
U
W
7
\
U
W
U
7WU3
w
w
]^_
\
U
W
y\ey_lky
nmgdpb_c
aZ\bkys_c
lhevdh
hl
dZe_g^Zjgh]h
\j_
f_gb
b
g_
aZ\bkys_c
hl
^Zlu
ih]Zr_gby
h[eb]Zpbb
Wlh
gZeZ]Z_l
g_
dhlhju_
h]jZgbq_gby
gZ
\b^
ij_\ur_gby
h`b^Z_fh]h
^hoh^Z
lZd
dZd
g_
\k_
nmgdpbb
<
[m^ml
m^h\e_l\hjylv
h^gh\j_f_ggh
mjZ\g_gbyf
b
H^gZdh
bf_xlky
g_dhlhju_
ihl_gpbZevgu_
ijh[e_fu
\
^Zev
g_cr_f
ijh^\b`_gbb
b
bkihevah\Zgbb
Zj[bljZ`gh]h
ih^oh^Z
^ey
hi
j_^_e_gby
iheghklvx
dhgdj_lbabjh\Zgghc
fh^_eb
\j_f_gghc
kljmd
lmju
KZf
ih^oh^
g_
kh^_j`bl
gbdZdh]h
kihkh[Z
]ZjZglbjmxs_]h
gZ
ebqb_
g_dhlhjh]h
e_`Zs_]h
\
hkgh\_
jZ\gh\_kby
^ey
dhlhjh]h
ij_^
iheh`_gby
Z
b
[
y\eyxlky
khklhyl_evgufb
HklZ\eyy
wlm
ijh[e_fm
\
klhjhg_
klZedb\Z_fky
k
^jm]hc
ljm^ghklvx
ijhbkl_dZxs_c
ba
lh]h
nZdlZ
qlh
Zj[bljZ`guc
ih^oh^
g_
ij_^iheZ]Z_l
qlh
\kydbc
\u[hj
\
\
khhlghr_gbb
ijb\_^_l
d
p_g_
h[eb]Zpbb
dhlhjZy
g_
^himkdZ
_l
Zj[bljZ`guo
\hafh`ghkl_c
>_ckl\bl_evgh
hij_^_e_gb_
fh^_eb
ihkj_^kl\hf
dhgdj_lbaZpbb
nmgdpbhgZevgh]h
\b^Z
\
fh`_l
ijb\_klb
d
\gmlj_gg_c
g_khklhyl_evghklb
<
dZq_kl\_
ijbf_jZ
ihl_gpbZevguo
\hafh`ghkl_c
f_lh^Z
jZk
kfhljbf
mjZ\g_gb_
k
nmgdpb_c
<
hij_^_ey_fhc
khhlghr_gb_f
Wlh
^Z_l
mjZ\g_gb_
hij_^_e_gby
klhbfhklb
\
\b^_
w
w
w
w
T
w
w
V
U3
W
3
U
3
UN
U
3
U
\
U
W
U
7WU3
w
w
dhlhjh_
b^_glbqgh
mjZ\g_gbx
k
lhqghklvx
^h
dhgdj_lbaZpbb
nmgdpbb
\
Fu
^he`gu
l_i_jv
dhgdj_lbabjh\Zlv
fh^_ev
iml_f
ij_^
iheh`_gby
h
lhf
qlh
\
y\ey_lky
ebg_cghc
hlghkbl_evgh
l_dms_c
ijhp_glghc
klZ\db
\
U
W
\
O
ULh]^Z
j_r_gb_
mjZ\g_gby
bf__l
\b^
@H[S>@>
7WU%7W$7WU3
Z
^bgZfbdZ
ih\_^_gby
p_gu
h[eb]Zpbb
aZ^Z_lky
mjZ\g_gb_f
G3
>
U
\
O
U
%
W
7
@
3GW
%
W
7
V
U
3G]
Ebg_cgZy
nhjfZ
jbkdh\hc
ij_fbb
hdZau\Z_lky
jZamfghc
b
[ueZ
[u
ih^oh^ys_c
^ey
\u[hjZ
ijb
wfibjbq_kdhc
jZ[hl_
gh
gZ
ijZdlbd_
hgZ
ihjh`^Z_l
g_`bag_kihkh[gmx
fh^_ev
Wlh
ijhs_
\k_]h
m\b^_lv
dh]^Z
U
<
lZdhf
kemqZ_
^hoh^ghklv
h[eb]Zpbb
\
ihke_^mxsb_
fh
f_glu
\j_f_gb
y\ey_lky
[_ajbkdh\hc
l_f
g_
f_g__
hgZ
ih\urZ_lky
\
p_g_
ijb
klZ\d_
\
%
W
7
dhlhjZy
hlebqZ_lky
hl
ijhp_glghc
klZ\db
ij_\urZxs_c
gme_\hc
mjh\_gv
DZd
[ueh
mklZgh\e_gh
jZg__
gme_
\hc
mjh\_gv
^hklb]Z_lky
_keb
V
!
N
T
Fh`gh
bkihevah\Zlv
g_dhlh
ju_
[he__
keh`gu_
Zj]mf_glu
qlh[u
ihdZaZlv
qlh
fh^_ev
g_`bag_
kihkh[gZ
^Z`_
_keb
gme_\hc
mjh\_gv
g_^hklb`bf
LZdbf
h[jZahf
fu
bf__f
fh^_ev
dhlhjZy
]ZjZglbjm_l
Zj[bljZ`gu_
\hafh`ghklb
Z
g_
bo
ij_^hl\jZs_gb_
Ljm^ghklvx
dhg_qgh
y\ey_lky
lh
qlh
g_l
e_`Z
s_]h
\
hkgh\_
jZ\gh\_kby
dhlhjh_
m^h\e_l\hjyeh
[u
ij_^iheZ]Z_fuf
ij_fbyf
LZdbf
h[jZahf
jZajZ[hlZgguc
\
wlhc
]eZ\_
jZ\gh\_kguc
ih^oh^
bf__l
^\Z
\Z`guo
ij_bfms_kl\Z
i_j_^
^jm]bfb
f_lh^Zfb
hij_^_e_
gby
p_gu
h[eb]Zpbb
\
g_ij_ju\ghf
\j_f_gb
<h
i_j\uo
hg
Z\lhfZ
lbq_kdb
kljZom_l
qlh[u
fh^_ev
iheghklvx
hij_^_eyeZkv
[_a
ihl_jb
\gmlj_gg_c
khklhyl_evghklb
\h
\lhjuo
h[_ki_qb\Z_l
kihkh[
ij_^
kdZaZgby
lh]h
dZd
baf_g_gby
e_`Zsbo
\
hkgh\_
j_Zevguo
wdhghfbq_
kdbo
i_j_f_gguo
[m^ml
\ebylv
gZ
\j_f_ggmx
kljmdlmjm
FGH=HN:DLHJG:YFH>?EV<J?F?GGHC
KLJMDLMJUBBKIHEVAH<:GB?P?G
D:DBGKLJMF?GL:EVGUOI?J?F?GGUO
<
fu
dhgdj_lbabjh\Zeb
ko_fm
h[s_c
jZ\gh\_kghc
fh^_eb
kf
]e
^ey
jZajZ[hldb
iheghc
fh^_eb
hij_^_e_gby
p_gu
h[eb]Z
pbb
Fu
ki_pbZevgh
\u[jZeb
ijhklhc
kemqZc
^ey
lh]h
qlh[u
ihdZ
aZlv
\
^_lZeyo
dZd
lZdZy
fh^_ev
fh`_l
[ulv
ihkljh_gZ
<
fh^_eb
p_
gu
h[eb]Zpbb
\k_o
kjhdh\
ih]Zr_gby
aZ\bk_eb
hl
_^bgkl\_ggh]h
kem
qZcgh]h
\hafmsZxs_]h
nZdlhjZ
l_dms_c
kihl
ijhp_glghc
klZ\db
Ohly
j_amevlbjmxsZy
\j_f_ggZy
kljmdlmjZ
fh`_l
ijbgbfZlv
jZaebq
gu_
nhjfu
^ey
fh^_eb
k
_^bgkl\_gguf
\hafmsZxsbf
nZdlhjhf
oZ
jZdl_jgh
lh
qlh
baf_g_gby
p_g
h[eb]Zpbb
\k_o
kjhdh\
ih]Zr_gby
kh
\_jr_ggh
dhjj_ebjh\Zgu
LZdZy
fh^_ev
lZd`_
ih^jZamf_\Z_l
qlh
p_
gu
h[eb]Zpbb
g_
aZ\bkyl
hl
ljZ_dlhjbb
dhlhjhc
ke_^h\ZeZ
kihl
klZ\dZ
ij_`^_
q_f
^hklbqv
l_dms_]h
agZq_gby
<
g_dhlhjuo
kemqZyo
wlb
k\hckl\Z
fh]ml
h]jZgbqblv
ijbf_g_gb_
fh^_eb
H^gZdh
[he__
h[sb_
ZgZeblbq_kdb_
\hafh`ghklb
[m^ml
\
k\hx
hq_j_^v
ih^jZamf_\Zlv
[he__
h[sb_
fh^_eb
hij_^_e_gby
p_g
h[eb]Z
pbc
IhemqZ_fu_
\
j_amevlZl_
fgh]hnZdlhjgu_
\j_f_ggu_
kljmdlmju
[m^ml
[he__
]b[dbfb
q_f
h^ghnZdlhjgZy
fh^_ev
gh
hgb
g_ba[_`gh
[m^ml
lZd`_
[he__
]jhfha^dbfb
b
[he__
ljm^gufb
^ey
ZgZebaZ
>ey
beexkljZpbb
\hafh`ghkl_c
jZajZ[hlZgghc
fh^_eb
fu
jZk
kfhljbf
^\Z
__
g_ihkj_^kl\_gguo
h[h[s_gby
Ij_^iheh`bf
qlh
\
gZr_f
hibkZgbb
l_ogheh]bq_kdh]h
baf_g_gby
\
mjZ\g_gbb
b
kh
hlghr_gbyo
kZf
iZjZf_lj
mklZgh\b\r_]hky
kj_^g_]h
T
fh`_l
baf_gylvky
kemqZcguf
h[jZahf
kh]eZkgh
mjZ\g_gbx
G
T
Y
<
T
GW
]^_
Y
y\ey_lky
iheh`bl_evghc
dhgklZglhc
Wlh
agZqbl
qlh
fu
iheZ]Z
_f
T
{
<
b
P
Y
<
<
LZdbf
h[jZahf
agZq_gb_
T
\
ex[hc
fhf_gl
\j_f_gb
[m^_l
bgl_]jZehf
wdkihg_gpbZevgh
\a\_r_gguo
ijhreuo
agZq_gbc
<
Fh`gh
ijh\_jblv
qlh
lh]^Z
ijhp_glgZy
klZ\dZ
U
kgh\Z