Медведев Г.А. Математические основы финансовой экономики. Часть2
Подождите немного. Документ загружается.
beb
qlh
wd\b\Ze_glgh
OG
a
T GZ
^ey
gZ[hjZ
d\hl
T
«
T
b
^hihegbl_evguo
ieZl_`_c
G
«
G
Ba
kh
hlghr_gbc
b
ihemqZ_f
a
a
a
a
GZ
:
;
GZ
;
;
;G
ED
ED
ED
ED
¦
]^_
E
E
«
E
Hlkx^Z
k
ihfhsvx
h[f_gZ
gZoh^bf
qlh
a
GZ
:
G:T
;G
ED
EDD
Qlh[u
m[_^blvky
qlh
jZ\_gkl\h
kijZ\_^eb\h
gZf
gm`gh
ihdZaZlv
qlh
^jh[v
\
\ujZ`_gbb
jZ\gZ
T
JZkkfhljbf
^\Z
kem
qZy
_keb
E
z
^ey
wlh]h
gm`gh
qlh[u
T
D
G
E
E
L
«
i
_keb
E
lh]^Z
T
«
T
±
ijhba\hevgu_
d\hlu
Z
^hihegb
l_evgu_
ieZl_`b
hij_^_eyxlky
jZ\_gkl\Zfb
G
E
D
L
«
i
<
l_hj_f_
nZdlbq_kdb
ml\_j`^Z_lky
qlh
^ey
hilbfZevgh]h
ih
IZj_lh
h[f_gZ
jbkdZfb
a
a
;;
bf__lky
kemqZcgZy
\_ebqbgZ
/
lZdZy
qlh
/
N
X
c
a
O
^ey
L
«
i
LZd
dZd
O
a
O
a
Z
y\ey_lky
nmgdpb_c
h[s_]h
[h]Zlkl\Z
Z
ba
wlh]h
ke_^m_l
qlh
/
/
Z
lZd`_
[m^_l
nmgdpb_c
Z
>bnn_j_gpbjh\Zgb_
jZ\_gkl\
^Z_l
/c
N
X
s
a
O
a
O
c
>_e_gb_
e_\hc
b
ijZ\hc
qZkl_c
wlh]h
jZ\_gkl\Z
khhl\_lkl\_ggh
gZ
e_
\mx
b
ijZ\mx
qZklb
jZ\_gkl\Z
b
bkihevah\Zgb_
nhjfmeu
iha\heyxl
ihemqblv
khhlghr_gb_
a
¸
¸
¹
·
¨
¨
©
§
c
¦
;T
JZ\_gkl\h
ihdZau\Z_l
qlh
/
y\ey_lky
m[u\Zxs_c
nmgdpb
_c
ihegh]h
[h]Zlkl\Z
Kh\f_klgucihl_gpbZe
Kgh\Z
jZkkfhljbf
i
kljZoh\uo
dhfiZgbc
b
ij_^iheh`bf
qlh
bkoh^guc
gZ[hj
:
«
:
l
_
jZkij_^_e_gb_
bo
ihegh]h
[h]Zlkl\Z
:
g_
y\ey_lky
hilbfZevguf
ih
IZj_lh
GZ
kdhevdh
m\_ebqZl
k\hc
^h
oh^
dhfiZgbb
ijb
dhhi_jZpbb
"
Hl\_l
fh`_l
[ulv
ihemq_g
k
ihfhsvx
kh\f_klgh]hihl_gpbZeZ
V\QHUJ\ SRWHQWLDO
K
Hg
baf_jy_lky
gZb[hevr_c
kmffhc
o
dhlhjZy
fh`_l
[ulv
ba\e_q_gZ
ba
kbkl_fu
[_a
ms_fe_gby
dZdhc
eb[h
ba
dhf
iZgbc
l
_
lZd
qlh[u
ihke_
h[f_gZ
jbkdZfb
ijb
mkeh\bb
O
«
O
:
o
\_ebqbgu
O
«
O
m^h\e_l\hjyeb
g_jZ\_gkl\Zf
?
>
b
O
@
t
?
>
b
:
@
^ey
L
«
i
Ykgh
qlh
^ey
o
K
fu
^he`gu
bf_lv
jZ\_gkl\h
\
khhlghr_gbb
b
h[f_g
jbkdZfbO
«
O
^he`_g
[ulv
hilbfZevguf
ih
IZj_
lh
^ey
:
K
Ijbf_j
ijh^he`_gb_
ijbf_jZ
Ij_^iheh`bf
qlh
\k_
nmgdpbb
ihe_aghklb
wdkihg_gpbZevgu_
LZd
dZd
;;
a
a
y\ey_lky
hilbfZevguf
ih
IZj_lh
h[f_ghf
jbkdZfb
^ey
[h]Zlkl\Z
:
K
ba
ke_^m_l
qlh
O
a
G:
D
D
K
^ey
L
«
i
AZl_f
fu
bkihevam_f
mkeh\b_
\
\b^_
jZ\_gkl\
?
>
b
O
a
@
?
>
b
:
@
hldm^Z
\b^gh
qlh
?
>
_
@
_oj
^
D
K
D
G
` @>
H(
beb
@>OQ
@>OQ
H(
D
H(
D
G
D
D
K
Kmffbjh\Zgb_
ih
L
^Z_l
y\gh_
\ujZ`_gb_
^ey
kh\f_klgh]h
ihl_gpbZeZ
@>
@>
OQ@>OQ
@>OQ
H(
H(
H(
D
H(
D
¦
K
Ijbf_j
ijh^he`_gb_
ijbf_jZ
Ij_^iheh`bf
qlh
dhf
iZgbb
bkihevamxl
kl_i_ggmx
nmgdpbx
ihe_aghklb
i_j\h]h
jh^Z
<
khhl\_lkl\bb
k
jZ\_gkl\hf
V
O
a
T
V
:
K
Ba
?
>
b
O
a
@
?
>
b
Z
@
l_i_jv
ke_^m_l
qlh
T
(
>
V
:
K
@
(
>
V
:
@
Ba\e_q_gb_
dhjgy
kl_i_gb
k
b
kmffbjh\Zgb_
ih
L
^Z_l
(
>
V
:
K
@
¦
?
>
V
:
@
Wlh
jZ\_gkl\h
y\ey_lky
mjZ\g_gb_f
^ey
kh\f_klgh]h
ihl_gpbZeZ
K
Ijbf_j
ijh^he`_gb_
ijbf_jZ
Ij_^iheh`bf
qlh
dZ
`^uc
ba
bg\_klhjh\
bf__l
kl_i_ggmx
nmgdpbx
ihe_aghklb
\lhjh]h
jh^Z
Ihwlhfm
O
a
T
:
K
Ba
?
>
b
O
a
@
?
>
b
:
@
ihemqZ_f
T
(
>
:
K
@
(
>
:
@
_keb
k
z
b
OQ
T
(
>OQ
:
K
@
(
>OQ
:
@
_keb
k
Ba\e_dZy
dhj_gv
kl_i_gb
k
\
jZ\_gkl\_
b
kmffbjmy
ih
L
ihemqZ_f
mjZ\g_gb_
^ey
hij_^_e_gby
kh\f_klgh]h
ihl_gpbZeZ
K
\
kemqZ_
k
z
(
>
:
K
@
¦
?
>
:
@
:gZeh]bqgh
ba
jZ\_gkl\Z
ihemqbf
mjZ\g_gb_
^ey
K
\
kemqZ_
k
H[S^
(
>OQ
:
K
@`
¦
_oj
^
(
>OQ
:
@`
Ijbf_j
<
ijbf_j_
jZ\_gkl\h
h`b^Z_fuo
ihe_aghkl_c
ijb\h^bl
d
lhfm
qlh
a
O
:
(
>
:
@
b
a
O
G
]^_
G
hij_^_ey_lky
ba
mjZ\g_gby
b
G
(
>
b
:
@
LZdbf
h[jZahf
G
S
^_l_jfbgbjh\Zgghfm
wd\b\Ze_glm
:
Hl
kx^Z
ke_^m_l
qlh
K
:
a
O
S
(
>
:
@
S
Fu
fh`_f
bkihevah\Zlv
kh\f_klguc
ihl_gpbZe
^ey
ihkljh_gby
dhgdj_lgh]h
hilbfZevgh]h
ih
IZj_lm
h[f_gZ
jbkdZfb
B^_y
khklhbl
\
lhf
qlh[u
ba\e_qv
K
ba
h[s_]h
[h]Zlkl\Z
dhfiZgbc
b
aZl_f
jZkij_
^_eblv
_]h
f_`^m
dhfiZgbyfb
kh]eZkgh
khhlghr_gbx
J_amev
lbjmxsbc
hilbfZevguc
ih
IZj_lh
h[f_g
jbkdZfb
;;
a
a
^ey
[h
]Zlkl\Z
:
oZjZdl_jbam_lky
mkeh\b_f
?
^
b
>
O
:
K
@`
?
>
b
:
@
^ey
L
«
i
Ijbf_j
ijh^he`_gb_
ijbf_jZ
<
kemqZ_
wdkihg_gpb
Zevguo
nmgdpbc
ihe_aghklb
bf__f
O
a
GD:D
K
Qlh[u
hij_^_eblv
^hihegbl_evgu_
ieZl_`b
ih^klZ\bf
wlh
\u
jZ`_gb_
\
jZ\_gkl\h
b
ihemqbf
?
>
_
@
_oj
^
D
K
D
G
`
@>
H(
Ba
wlh]h
ke_^m_l
qlh
@>OQ
@>OQ
H(
D
H(
DD
D
G
K
Ih^klZ\eyy
\
wlm
nhjfmem
agZq_gb_
K
\
\b^_
ihemqZ_f
hdhgqZ
l_evguc
j_amevlZl
@>OQ
@>OQ
H(
D
H(
DD
D
G
¦
^ey
L
«
i
Ijbf_j
>ey
kl_i_gguo
nmgdpbc
ihe_aghklb
i_j\h]h
jh^Z
fu
gZreb
qlh
hilbfZevguc
ih
IZj_lh
h[f_g
jbkdZfb
a
a
;;
lZdh\
qlh
V
O
a
T
V
:
Hlkx^Z
b
ba
mkeh\by
ihemqZ_f
jZ
\_gkl\h
T
(
>
V
:
K
@
(
>
V
:
@
LZdbf
h[jZahf
@>
@>
¸
¸
¹
·
¨
¨
©
§
K
:V(
:V(
T
GZdhg_p
qlh[u
hdhgqZl_evgh
ihemqblv
y\gmx
nhjfmem
^ey
d\h
lu
bkihevam_f
mjZ\g_gb_
¦
:V(
:V(
T
@>
@>
L
«
i
Ijbf_j
>ey
kl_i_gguo
nmgdpbc
ihe_aghklb
\lhjh]h
jh^Z
gZc^_gh
qlh
O
a
T :
Ba
jZ\_gkl\Z
\b^gh
qlh
@>
@>
:(
:(
T
¸
¸
¹
·
¨
¨
©
§
K
_keb
k
z
b
@`>OQH[S^
@`>OQH[S^
K
:(
:(
T
_keb
k
Ba
mjZ\g_gbc
b
ke_^m_l
qlh
¦
:(
:(
T
@>
@>
_keb
k
z
b
¦
:(
:(
T
@`>OQH[S^
@`>OQH[S^
_keb
k
JUGHDBJ:<GH<?KB?
Kgh\Z
jZkkfhljbf
i
dhfiZgbc
dhlhju_
[ueb
\\_^_gu
\
;m
^_f
kqblZlv
qlh
dhfiZgbyf
ke_^h\Zeh
[u
hkms_kl\blv
hilbfZevguc
ih
IZj_lh
h[f_g
jbkdZfb
Ihkdhevdm
lZdb_
h[f_gu
khklZ\eyxl
rb
jhdh_
k_f_ckl\h
`_eZl_evgh
[he__
hij_^_e_ggh_
j_r_gb_
<
[ueb
ij_^eh`_gu
dhgdj_lgu_
\ZjbZglu
hilbfZevguo
ih
IZj_lh
h[f_gh\
jbkdZfb
A^_kv
jZkkfhljbf
ij_^eh`_gguc
D
;hjq_f
b
O
;xevfZghf
^jm]hc
ih^oh^
dhlhjuc
hkgh\Zg
gZ
wdhghfbq_kdbo
b^_yo
Ij_^iheh`bf
qlh
kemqZcgu_
ieZl_`b
ijhba\h^ylky
gZ
jugd_
ijbq_f
p_gZ
G
<
ex[h]h
ieZl_`Z
<
kemqZcgZy
\_ebqbgZ
\uqbkey
_lky
ke_^mxsbf
h[jZahf
G
<
?
>
<
<
@
A^_kv
<
y\ey_lky
iheh`bl_evghc
kemqZcghc
\_ebqbghc
Ij_^iheh
`bf
qlh
G
<
ij_^klZ\ey_l
kh[hc
p_gm
\
dhgp_
]h^Z
Lh]^Z
p_gZ
^_
l_jfbgbjh\Zggh]h
ieZl_`Z
^he`gZ
[ulv
dhgklZglhc
Ihwlhfm
fu
^he`gu
bf_lv
?
>
<
@
I_j_ibr_f
ijZ\mx
qZklv
jZ\_gkl\Z
\
\b^_
?
>
<
@
?
>
<
<
@
?
>
<
@
?
>
<
@
lh]^Z
ke_^m_l
qlh
p_gZ
ieZl_`Z
<
fh
`_l
[ulv
aZibkZgZ
dZd
G
<
?
>
<
@
k
RY
<
<
l
_
p_gZ
ieZl_`Z
jZ\gZ
_]h
fZl_fZlbq_kdhfm
h`b^Zgbx
fh^bnbpb
jh\Zgghfm
k
mq_lhf
jughqguo
mkeh\bc
K
^jm]hc
klhjhgu
fu
fh`_f
bgl_jij_lbjh\Zlv
p_gm
ieZl_`Z
dZd
_]h
fZl_fZlbq_kdh_
h`b^Zgb_
hl
ghkbl_evgh
fh^bnbpbjh\Zgghc
\_jhylghklghc
f_ju
4
dhlhjZy
hij_
^_ey_lky
khhlghr_gb_f
?
<
?
>
<
<
@
^ey
\k_o
<
>jm]bfb
keh\Zfb
<
_klv
ijhba\h^gZy
JZ^hgZ
±
Gbdh^bfZ
f_ju
4
hl
ghkbl_evgh
bkoh^ghc
\_jhylghklghc
f_ju
Ih
wlhc
ijbqbg_
;xevfZg
gZa\Ze
<
iehlghklvxp_gu
SULFHGHQVLW\
DhfiZgby
L
[m^_l
klj_fblvky
dmiblv
ieZl_`
<
^ey
lh]h
qlh[u
fZdkbfbabjh\Zlv
?
>
b
:
<
G
<
@
IeZl_`
<
a
y\ey_lky
j_r_gb_f
wlhc
aZ^Zqb
_keb
b
lhevdh
_keb
m^h\e_l\hjy_lky
mkeh\b_
b
c
:
<
a
G
<
a
<
?
>
b
c
:
<
a
G
<
a
@
Qlh[u
ihdZaZlv
g_h[oh^bfhklv
wlh]h
mkeh\by
ij_^iheh`bf
qlh
<
a
y\ey_lky
j_r_gb_f
mjZ\g_gby
Imklv
9
[m^_l
ijhba\hevghc
kemqZcghc
\_ebqbghc
JZkkfhljbf
iZjZf_ljbq_kdh_
k_f_ckl\h
\_eb
qbg
^
<
_
<
<
a
W9
`F
iZjZf_ljhf
W
Kh]eZkgh
gZrbf
ij_^iheh`_gb
yf
nmgdpby
I
W
?
>
b
:
<
G
<
@
ijbgbfZ_l
k\h_
fZdkbfZevgh_
agZq_gb_
\
lhqd_
W
Ke_^h\Zl_evgh
I
?
?
^
b
c>
:
<
a
G
<
a
@
9
?
>
<
9
@
`
Wlh
jZ\_gkl\h
fh`gh
i_j_ibkZlv
lZd
?
>
9
^
b
c
:
<
a
G
<
a
<
?
>
b
c
:
<
a
G
<
a
@`
@
LZd
dZd
hgh
kijZ\_^eb\h
^ey
\k_o
9
\ujZ`_gb_
\
nb]mjguo
kdh[dZo
^he`gh
[ulv
jZ\gh
gmex
ba
q_]h
ke_^m_l
mkeh\b_
Qlh[u
ihdZaZlv
^hklZlhqghklv
mkeh\by
jZkkfhljbf
ieZl_`
<
a
dhlhjuc
m^h\e_l\hjy_l
mkeh\bx
b
ex[hc
^jm]hc
ieZl_`
<
Ba
g_jZ\_gkl\Z
ke_^m_l
qlh
b
:
<
G
<
d
b
:
<
a
G
<
a
b
c
:
<
a
G
<
a
<
G
<
<
a
G
<
a
b
:
<
a
G
<
a
<
?
>
X
c
: <
a
G
<
a
@
<
G
<
<
a
G
<
a
<uqbke_gb_
fZl_fZlbq_kdh]h
h`b^Zgby
b
bkihevah\Zgb_
hij_^_
e_gby
G
iha\heyxl
gZibkZlv
?
>
b
:
<
G
<
@
d
?
>
b
:
<
a
G
<
a
@
qlh
aZ\_jrZ_l
^hdZaZl_evkl\h
AZf_lbf
qlh
hilbfZevgh_
<
a
±
_^bgkl\_ggh_
k
lhqghklvx
^h
ih
klhyggh]h
keZ]Z_fh]h
Ke_^h\Zl_evgh
jZaghklv
<
a
G
<
a
[m^_l
_^bg
kl\_gghc
?_
fh`gh
bgl_jij_lbjh\Zlv
dZd
hilbfZevguc
ieZl_`
dh
lhjuc
bf__l
gme_\mx
p_gm
b
\
^Zevg_cr_f
[m^_f
gZau\Zlv
__
qbklhc
ihlj_[ghklvx
QHWGHPDQG
dhfiZgbb
L
Ijb
aZ^Zgghf
<
kemqZcgZy
\_ebqbgZ
¦
<
a
>
G
<
a
@
y\ey_lky
ba[ulhqguf ihlj_[e_gb_f
H[FHVV GHPDQG
DhfiZgbb
fh
]ml
fZdkbfbabjh\Zlv
h^gh\j_f_ggh
k\hb
h`b^Z_fu_
ihe_aghklb
_keb
lhevdh
ba[ulhqgh_
ihlj_[e_gb_
klZgh\blky
jZ\guf
gmex
qlh
wd\b\Z
e_glgh
mkeh\bx jughqgh]h debjbg]Z
PDUNHW FOHDULQJ FRQGLWLRQ
Wlh
ijb\h^bl
d
ke_^mxs_fm
hij_^_e_gbx
Iehlghklv
p_gu
<
b
ieZl_`b
^
<
a
L
«
i
`
khklZ\eyxl
jZ\gh
\_kb_
HTXLOLEULXP
_keb
\_ebqbgZ
h[jZsZ_lky
\
gmev
b
mkeh\b_
m^h\e_l\hjy_lky
^ey
\k_o
L
«
i
AZf_lbf
jZ\gh\_kb_
ihjh`^Z_l
h[f_g
jbkdZfb
a
a
;;
lZ
dhc
qlh
O
a
: <
a
G
<
a
L
«
i
Lh]^Z
mkeh\b_
mklZgZ\eb\Z_l
qlh
b
c
O
a
<
?
>
b
c
O
a
@
L
«
i
Ba
mkeh\by
l_hj_fu
ke_^m_l
qlh
h[f_g
jbkdZfb
ihjh`^Z_
fuc
jZ\gh\_kb_f
hilbfZevguc
ih
IZj_lh
AZf_lbf
lZd`_
qlh
jZ\_g
kl\h
ih
kms_kl\m
wd\b\Ze_glgh
hij_^_e_gbx
Z
agZqbl
jZ\_gkl\h
m^h\e_l\hjy_lky
ijb
/
<
<
qZklghklb
wlh
ihdZau
\Z_l
qlh
<
±
m[u\ZxsZy
nmgdpby
h[s_]h
[h]Zlkl\Z
H[jZlgh_
kijZ\_^eb\h
\
ke_^mxs_f
kfuke_
Ij_^iheh`bf
qlh
jZkij_^_e_gb_
:
«
:
m`_
hilbfZevgh
ih
IZj_lh
Lh]^Z
:
«
:
b
<
khklZ\yl
jZ\gh\_kb_
_keb
hij_^_eblv
<
b
c
O
a
?
>
b
c
O
a
@
Ijbq_f
<
a
G
<
a
^ey
\k_o
L
«
i
Wlh
fh`gh
ihemqblv
ba
nhjfmeu
_keb
aZf_gblv
O
a
gZ
:
b
mkeh\by
Ijbf_j
ijh^he`_gb_
ijbf_jZ
Ij_^iheZ]Zy
qlh
\k_
dhfiZgbb
bkihevamxl
wdkihg_gpbZevgu_
nmgdpbb
ihe_aghklb
fu
aZ
dexqZ_f
ba
qlh
<
a
:
OQ
<
D
N
]^_
N
y\ey_lky
dhgklZglhc
Ke_^h\Zl_evgh
qbklZy
ihlj_[ghklv
dhfiZgbb
L
jZ\gZ
<
a
G
<
a
:
OQ
<
D
?
><
:
@
?
><
OQ
<@
D
Ijb
jZ\gh\_kbb
kmffZ
ih
L
^he`gZ
[ulv
jZ\gZ
gmex
Ihwlhfm
:
?
><
OQ
<@
D
N
]^_
N
y\ey_lky
dhgklZglhc
LZd
dZd
?
><@
hlkx^Z
ke_^m_l
qlh
jZ\gh\_kgZy
iehlghklv
p_gu
<
_
?
>
_
@
GZdhg_p
g_keh`guc
jZkq_l
ihdZau\Z_l
qlh
\
jZ\gh\_kbb
O
a
:
<
a
G
<
a
Z:
D
?
><
:
@
Z?
><
:
@
D
Z:
D
G
:
ZG
:
D
Ijbf_j
ijh^he`_gb_
ijbf_jZ
Ij_^iheh`bf
qlh
dhf
iZgbb
bkihevamxl
kl_i_ggu_
nmgdpbb
ihe_aghklb
i_j\h]h
jh^Z
Ih
wlhfm
b
c
o
V[V
L
«
i
b
ba
jZ\_gkl\Z
V
O
a
T
V
:
L
«
i
Lh]^Z
kh]eZkgh
mkeh\bx
jZ\gh\_kgZy
iehlghklv
p_g
<
b
c
O
a
?
>
b
c
O
a
@
V
:
?
>
V
:
@
JZ\gh\_kgu_
d\hlu
emqr_]h
\k_]h
hij_^_eylv
ba
mkeh\by
qlh
G
:
G
O
a
beb
G
:
G
V
T
V
:
V
T VT G
:
Ke_^h\Zl_evgh
T
@>
@>
:V(
:V(
:+V
:+V
<
<
L
«
i
Ijbf_j
ijh^he`_gb_
ijbf_jZ
?keb
\k_
dhfiZgbb
bk
ihevamxl
h^bgZdh\u_
kl_i_ggu_
nmgdpbb
ihe_aghklb
\lhjh]h
jh^Z
b
c
o
o
L
«
i
lh]^Z
ba
nhjfme
O
a
T :
L
«
i
Hlkx^Z
jZ\gh\_kgZy
iehlghklv
p_g
<
b
c
O
a
?
>
b
c
O
a
@
:
?
>
:
@
<
wlhf
kemqZ_
jZ\gh\_kgu_
d\hlu
emqr_
\k_]h
gZoh^blv
ba
mkeh\by
G
:
G
O
a
T G
:
LZdbf
h[jZahf
T
@>
@>
@>
@>
<
<
:(
::(
:(
:(
:+
:+
L
«
i
Ba
jZ\_gkl\Z
ke_^m_l
qlh
^ey
kemqZcghc
\_ebqbgu
<
G
<
?
<
E
G
:
?
:
]^_
E
k
RY
<
<
k
RY
:
<
Z
<
jZ\gh\_kgZy
iehlghklv
p_g
NhjfmeZ
[ebadZ
d
hkgh\ghfm
j_amevlZlm
rbjhdh
ba\_klghc
jughqghc
fh^_eb
p_ghh[jZah\Zgby
&$30
&DSLWDO$VVHW3ULFLQJ0RGHO
<
dZq_kl\_
beexkljZpbb
fu
h[
jZlbfky
d
lj_f
ij_^r_kl\mxsbf
ijbf_jZf
<
wlhf
kemqZ_
^ey
ijb
f_jZ
bf__f
E
k
RY
<
_
k
RY
:
_
^ey
ijbf_jZ
E
k
RY
<
V
:
k
RY
:
V
:
^ey
ijbf_jZ
E
k
RY
<
:
k
RY
:
:
AZf_lbf
qlh
ijb
k
d\Z^jZlbqgZy
nmgdpby
ihe_aghklb
nhj
fmeZ
k\h^blky
d
deZkkbq_kdhc
nhjfme_
&$30
E
k
RY
<
:
YDU>
:
@
HIJ?>?E?GB?P?GNBG:GKH<UO
IJHBA<H>GUO
Ijb
jughqghf
jZ\gh\_kbb
p_gZ
ieZl_`Z
<
jZ\gZ
G
<
b
hij_^_
ey_lky
ih
nhjfmeZf
b
]^_
<
±
jZ\gh\_kgZy
iehl
ghklv
p_g
H[uqgh
kemqZcgZy
\_ebqbgZ
<
y\ey_lky
klhbfhklvx
Zdlb\Z
DVVHW
beb
nbgZgkh\hc
ijhba\h^ghc
GHULYDWLYH VHFXULW\
\
dhgp_
i_