x6ex3c Rossx42x6fx70x52x53x63x6a(APT)x4fx6bx6cx52x53x43x44x52x63
x57x58x7fx59x20 x2bx2c Ross x20x47x40x43x16x5cx4f (APT)x29 x21x2c APT x1x52x25 x5ex57x70x47x40
x3cx4dx18x37x3ax43x16x52x28x20x5cx28x29x4ex4fx34x72x42x25x7ex2bx68xbxcx5cx20x48x35x43x16x60x2ex43x5cx29 x21
x2cx59x43x5cx5dx3bx56x58x59x5ex11x7fx18x18x48x35x43x16x60x2ex43x5cx23x14x20x27x28x29x20x26x1cx3fx3bx14x3ex3f
x19x5x4dx5cx20x48x35x43x16x60x2ex43x5cx65x17x4ax4dx43x16x29
x5ax2ex51x5bx5cx5dx20 x37x3ax11x32x29x5cx33xex41x4f (x58x53x62x3bx20x32x33x55x13x25 x1x32x25 x44x1x32
x33)x29x5cx33x28x77x33x3ex2cx4dx32x5x36x6cx5cx13x20x74x2cx36x6c)x29
x66x5ex20
? 5.1x5ex57x70x47x40x3cx4dx34Rossx20APTx1x52x29
? 5.2x26x2bx5x7fx18x18x58x53x35x2ax2bx5x29
? 5.3x25x7ex2bx68xbxcx5cx20x48x35x43x16x60x2ex43x5cx29
? 5.4x41Arrow–Debreu x72x71x2cx24x4dx77x78x48x35x43x16x60x2ex43x5cx29
? 5.5x48x35x43x16x60x2ex43x5cx20x72x42x29
? 5.6x7ex27x77x76x43x5cx18x48x35x43x16x60x2ex43x5cx29
? 5.7x59x43x5cx5dx20x3bx56x58x59x5ex11x34x48x35x43x16x12x22x60x2ex43x5cx29
? 5.8x2dx42x48x35x43x16x60x2ex43x5cx20x3bx14x3ex3fx19x5x29
? x1fx4x20 x32x33x47xdx64x443x29
xdx6dx3cx62x4ax69x63xfx2Arbitrage Pricing Theoryx54x5cx3ax48x17x13x1ex67x2
APT.x3ax3exbx4bx3bx1cx1dx62x4ax55xex27x1x50x62xbx21x62x4ax7x8x70x67x2x70x64x6dx3c
x62x4ax69x63x48x7bx1x1cx1dx62x4ax55xex71x72x44x2x11x70xex6dx54x33x6dx3cx61xdx78xfx2
x70x70x14APT,x7dx3ex19x19x0x1x25x2Rossx54xdx22x3cxfx78x58Rossx54APTxex2
x5dx1ex6fx1ex37x62x4ax55x56(CAPM)x54x70x64x43x4ex5x48x10x49x40x26x44x2x5dCAPM
x54x6dx7bx14x55x56x2ax1x70x2bx2ex7bx14x55x56x78
5.1 Ross x66 1976 x46x20x8x54 APT ([13]) x15x1bx5ax2x7ex3bx72xd Sharpe
x63x2cCAPMx54x69x55x48x4x17x2cx2x6ex3ax3bx15x4ex5cx4x70x71x57x58x72x73x55x56x78xf
x2x62xdx6fx61x72x6x64x69x7dxbx3ax4xdx42x43x14x25xfx54x25x22x48x20x8x61x72xdx1cx1dx62
x4ax55xex54x5ex55x78x26x66x62x39x28x29x20x21x8x5fx27x47x48x5fx60x48x7fx75x7ex1fx25x27x63
x54x4ex68x62x3x27x39x8x72x6x20x21x48x39x58x5dx5fx60x30x31x1x32x26x3bx51x2ax64x2cx68x27
x10x33x2ax64x2cx68xdx5dxdxfx62x4ax78x15x13x49x70xbx7bx17x6fx70x54x61x62x56x48x2cx68x61x70
x2bx1bx5dx31x32x78x13x27Huberman [8]x5fx1ax48x1x1fx68APTx69x55x73x47x75xdx7dx5d
x33x6dx3cx61xdxfx48x25x67x53APTx54x6fx60x21x1x23x8x78x17x71x48x21x22x7dx5dx33x6dx3c
106
x61xdx67x2x49x1cx1dx62x4ax55xex2cx48x75x39x62x4ax1cx1dx65x68x7fx0x78x25x70x51x48x3ax3e
x6cx79x53x3bx25x70x76x77x27x76x29Hubermanx54APTx69x55x63x2cx78
x3ax3ex54x8x5fx77x1cx7ax2x50x62xbx21 Hilbert x72x76M. x61x62x17x2cx45x6ex33
x69x6ax2cx681x48x41 2 M, x51x6cx17x44x51x1cx1dx62x4ax65x68p:! M (x1ax18x2ex61x62
x10x54x7fx0x1d)x78x33x69x6ax3cx27rf = 1=p(1) > 0. x7fx61x62x49x21x44x58x54x50x62xbx21
x42x43x2cx51x33x2ax64x2cx68x48x17x20x21x27x33x3fx1x28x29x2ax6cr1;r2;:::;rk, ::: 2 R1.
x10x18x48x7fx61xdx51 K x64x40x6fx7bx46 (x28x29x2ax6cx48x71x72x7x3bx18x10x3ex23x25x2x74
x64x2cx68x54x20x21x27x48x74x64x2cx68x42x43x5dx68x54x54x3dx27x48x74x64x5cx76x57x58x5dx38x54
x54x3dx27x48x24x5ex7ex50x7fx0x27x48x7dx5bx8x36x27x9x9) f1;f2;:::;fK,x53x68x56x5cx5d
xdx9x26x41x7dx2a
rj ?rf =
KX
k=1
?jk(fk ?rf)+"j; j = 1;2;:::; (1)
x17x2c"j x2x70x4cx5cx28x29xdx41x1dxfx48x10x3ex9xa
Cov["i;"j] = 0; i 6= j; (2)
Var["j] 6 2; j = 1;2;:::: (3)
x25K x2bx40x6fx7bx46x48x79x7ax70x71x5bx2ex70x62x2x42x43x2cx54x2cx68x6fx2cx68x14x25x48xf
x2x39x77x44x54x76x77x27x3cx48x10x3ex5bx75x2ex1Mx54x20x21x27 (x4R1 x54x38x46)x27x73
x69x78x10(1)x54x78x14x47x68x4fx3ex2bx48x23x68
E[rj]?rf =
KX
k=1
?jk(E[fk]?rf)+E["j]; j = 1;2;:::: (4)
x31x32Mx2x70x2bx26x25K x2bx40x6fx7bx46x21x0x41x54x51x2ax75x72x76x48x33x34(1)
x2cx23x47x21x51"j = 0. x7ax58x48x31x32Mx2x33x2ax75x72x76x48x6fx31x17x75x68x7fx4ex66
K,x33x34(1)–(3)x67x2x70xbx6x68x63x2cx54x61xdx78x17x2cx61x62x51x49x45x66jx54xdx6f
x7dx66xfx48x51x6cx2ex10x2cx68x76x54xdx6fx7dx66xfx2x2ex7bx3x54 (x4 (2))x57x58x21x51x54
xdx6fx7dx66xfx54x69x7dx2x70x2ax51x5bx54(x4(3))x78x10x60x27x21x51x2cx68x54x20x21x27x5bx23
x3bKx2bx7bx46x4x70x2bx69x7dx51x2ax3x7bx25x2ex7bx3x54xdx6fx7dx66xfx27x44x62x78x2ex1fx25
xbx5bx2x3ax3ex5fx60x54x61xdx48x58x2ex2x1fx68x54x31x63x78x5fx60x49x66x48x31x32x25xbxdx6f
x7dx66xfx10x20x21x54x6bx12x13x14x24x4ex48x33x34x25x26x54x55x56x2x33x3bx54x78x58APTx69
x55x54x3x1dxex2x5dx8x25xbxdx6fx7dx66xfx54x13x14x4dx28x42x47x48x54x7bx46x4bx27x4bx2ex58
x4bx27x4bx16x78
1x3x5cx20x4ex4fx35x7ex3dx5bx74x73x1axex2bx2cx6x70x3dx30x72x71x20xbx69x29 x35x7eRossx20x58x1cx4fx2e
x7x23x59x3cx43xbx1x29
107
x49x44x70x61xdx2cx48 (2)x4(3)x71x72x44x70x68x49x55x56x2cx66x49x33x2ax64x20x21x27
x25x2ex7bx3x3x58x69x7dx70x2ax51x5bx54x2cx68x14x25x78x10x66x25x26x54x2cx68x14x25x48x3ax3e
x23x7ex1fx10x10x3ex54x13x14x25x48x53x10x3ex20x21x27x69x7d(x69x6a)x55x24x66x7dx78x2bx71x44x48
x10x66x69x7dx51x56x5cx9x26x41x7dx2a
Var
?z
1 +z2 +￠￠￠+zn
n
?
= Var[z1]+Var[z2]+￠￠￠+Var[zn]n2 ;
x17x2cz1, z2;:::;znx1x25x2ex7bx3x54x28x29x2ax6cx78x31x32x10x3ex54x69x7dVar[zi]x5bx2e
x4ex66 2x48x33x34x44x26x54x1fx14x53x2ex4ex66 2=n. x17n !1x18x48 2=n ! 0. x3ax3e
x19x57x1bx2ax48x31x32x1cx1dx62x4ax55xex41x7dx48x33x34x33x69x6ax3cx27x73x51x70x2bx78xfx2
x69x6ax4bx27x4bx16x54x2cx68x14x25x48x17x20x21x27x2x35x5ax55x24x66x33x69x6ax3cx27x75x7ex25
x51x43x2x74x7ax54x2bx78x49Hubermanx54x63x64x2cx48x62x5dx25x70x77xcx2exdx7dx5dx33x6d
x3cx61xdxfx27x0x1x78x25x18x48x3ax3ex53x6cx79x5dx8x48x25x70x61xdx17x71x57x75x39x1cx1dx62
x4ax65x68x7fx0x2x9x4ax54x78
x36x3f 5.1 x20Mx1dx1ex62x43x12Hilbertx44x45x0 Mx7fx60x61x18x19x1axdxex6b
x6c1 2M. p:M!Rx1dMx7cx79x75x76x62x63x64x65x6bx2p(1) > 0, rf = 1=p(1).
R1 = fr 2Mjp(r) = 1:gx1dx11x12x13x5bx10x0x5dx5ex21x7fx0xcx1x2x26x63x2a
1. px1dx5fx60x64x65x75
2. (x53x54x2cx2dx20x2ex2f)x57x58x11x12x42x7ffrng ‰ R1 xaxbVar[rn] ! 0,x5dx5e
krn ?rfk2 = E[(rn ?rf)2] ! 0.
xdx27 x61xd p x1 M x44x54x7fx0x65x68x78x31x32x20x21x28x5c frng ‰ R1 x9
xa Var[rn] ! 0, x33x34x12 "n = rn ? E[rn], x3ax3ex51 k"nk2 = E["2n] ! 0. x7b
x7ex48 p("n) ! 0;x4p(rn ?E[rn]) = p(rn)?E[rn]p(1) = 1?E[rn]p(1) ! 0:
x25x26x48x3ax3ex68x19E[rn] ! rf. x4dx70x69x4bx48x26Mx2cx54x5ax68x54x60x3ax2ex9x26
(kx+yk6kxk+kyk),x7fx23x68
krn ?rfk = E1=2[(rn ?rf)2] 6krn ?E[rn]k+kE[rn]?rfk
= Var1=2[rn]+jE[rn]?rfj! 0:
x7bx7ex48 E[(rn ?rf)2] ! 0.
x7ax75x48x12xdx7dx5dx33x6dx3cx61xdxfx41x7dx78x31x32px2ex7fx0x48x33x34x66x49x77x5c
fxng ‰ M,x9xaxn ! ˉx (x4kxn ? ˉxk = E1=2[(xn ? ˉx)2] ! 0),xfp(xn)x2e
x55x24x66p(ˉx). x2ex40x61xdx66x49– > 0,x53x68x10x66x21x51nx48x51jp(xn)?p(ˉx)j > –
(x35xex23x7ex1fx10 fxng x47x14x5cx27x54x19x25x70x77)x78x25x18x48x23x47 rn = (xn ?
ˉx)=(p(xn)?p(ˉx)) 2 R1. x10x66x25x2bR1 x2cx54x77x5cfrng,x3ax3ex51
Var[rn] = Var
? x
n ? ˉx
p(xn)?p(ˉx)
?
6 Var[xn ? ˉx]–2 ! 0:
108
x39x58x26x61xdx48x7x8x51E[(rn ?rf)2] ! 0;x4krn ?rfk! 0. xfx25x2x2ex23x25
x54x78x25x2x7bx1
krnk2 = E[r2n] = E
"
xn ? ˉx
p(xn)?p(ˉx)
?2#
6 kxn ? ˉxk
2
–2 ! 0;
x26x24x2ax54x1dx70x1dx48 rn x2ex23x25x13x20x4ex66x43x7dx54rf. x25x67x7ax2cx61px54x7fx0
x1dx78 2
x1ax49x3ax3ex67x49x62x4ax65x68px2x7fx0x1cx1dx65x68x6fxdx7dx5dx33x6dx3cx61xdxfx54
x38x3dx56x48x27x2cx68Rossx54APTx54x74x75x31x63x78
x36x3f 5.2 x7x62x4bx4cx18x4dx5fx7x20x71(1)–(3)xaxbx0x5dx5e
limn!1
nX
j=1
(E["j])2 < +1: (5)
xdx27 x3ax3ex3bx7ax2cx55x27x2cx68x78x61x62(5)x2ex41x7dx78x33x34
1X
j=1
(E["j])2 = +1:
x2ex40x61x62xbK+1x64x2cx68x54x20x21x27x67x2rf, f1, f2;:::;fK,x4r1 = f1;:::;rK =
fK,x51x6cn > K +1. x12
wni = E["i]Pn
j=K+1(E["j])2
; i = K +1;K +2;:::;
wnk = ?
nX
i=K+1
?ikwni ; k = 1;:::;K; wn0 = ?
nX
i=1
wni +1:
xex10x66x15x1fnx51Pni=0 wni = 1,x51x6c
nX
i=0
wni ri = wn0rf +
KX
k=1
wnkfk +
nX
i=K+1
wni ri
= rf +
KX
k=1
wnk(fk ?rf)+
nX
i=K+1
wni (ri ?rf)
= rf ?
KX
k=1
nX
i=K+1
?ikwni (fk ?rf)+
nX
i=K+1
wni (ri ?rf)
109
= rf ?
nX
i=K+1
wni
? KX
k=1
?ik(fk ?rf)
!
+
nX
i=K+1
wni (ri ?rf)
= rf +
nX
i=K+1
wni "i;
x25x18x54x15x13x70x57x2x16x5e(1)x1fx68x54x78x10x15x13x70x26x54x78x14x39x68x4fx3ex2bx48x4
x68
nX
i=0
wni E[ri] = rf +
nX
i=K+1
wni E["i]:
xfx2x26x66wni x10x66i = K + 1;K + 2;:::;x54x62x7ax48x26x44x26x53x1fx68x10x66x21
x51nx51
nX
i=0
wni E[ri] = rf +1; (6)
x58
Var
? nX
j=0
wnj rj
!
=
nX
i=K+1
(wni )2Var["i]
6 2
nX
i=K+1
(wni )2
= 2 1Pn
i=K+1(E["i])2
! 0:
x26x66x10x15x1fn,x51?rn = Pnj=0 wnj rj 2 R1,x26x7dx5dx33x6dx3cx61xdx48 Pni=0 wni E[ri] !
rf. x57(6)x5dx23x78x25x26x48x62x69x68x2cx78 2
x59x40 x61(1)–(3)x71x4bx4cx18x4dx5fx7x20x21x6bx6dx6ex6fx70x68x65– > 0, x4fx30
x50x36x51x52x65N–,x4x5x3j > N– x4x6b
(E["j])2 < –: (7)
x25x2x26(5)x26x54x7ex66x55x66x7dx58x18x38x68x19x54x31x63x78
x26x7ex23x4fx48 (1)x54x33x2ax2bx9x26x2cx48x35x61x51x2ax2bx24x19x48x5bx2x43x7fx28x54
x5dxdx9x26x78x1ax49x54x5fx60x2x25x33x2ax2bx9x26x2x35x51x23x25x11x52x2cx78x31x32x7ex7f
x75x15x67x4bx54x68x4fx79x7ax27x52x2cx48x33x36x7ax2x2ex23x25x54x78x6cx79x1ax71x4cx5bx2cxf
xfx5cx12x8x33x2ax64x2cx68x27x48x17x6dx2x5dxdx9x26x75x39xdx35x12x51x2ax2bx24x19xfx78x41
x7dx48x58x25xdx51x2ax2bxfx23x25x2x70x2bx43x7fx4ex54x68xax78x31x7ex9x9x78xfx2x70x2bx68
110
x4fx55x56x2x35x4ex25x71x72x39x27x5bx2ex2x15x67x4bx54x68x4fx79x7ax27x3cx54x48x58x2x3cx10
x2x35x57x1ax71x1dx33x38x5d(x25x18x7fx47x75x11x64Friedmanx20x37x74x7ax27x2ex1x69x26x48
x2bx71x44x48x3x66 APT x25x35x11x7dx52x54x1ax63x5ax2x25x26x36x6ax54)x78x49x25x70x79x7a
x56x48x2dx2ex71x2cxcxdx5dx8x48 APTx2ax36x54x5dxdx9x26x2x7bx17x4ex25x71x72x54x48x2f
x5ex23x24x75x39"j x57fk x2ex7bx3x24x58E["j] = 0, x4x49x11x64x79x7ax56x48x5dMx17
x2ex75x68xfx16x54xdx51x2ax75x72x76xfx5ax2x5dxdx41x7dx54x78
x25x26x70x27x48x3bx3bx49x71x2cx33x14x2cx7x3bx54APTx69x63x17x71x67x2x70x2bx2ex7b
x14x1cx1dx55x56x78x10x23x24x44x2e
rj ?rf =
KX
k=1
?jk(fk ?rf)+"j; j = 1;2;:::; (8)
Cov["i;"j] = 0; Cov[fi;fj] = 0; i 6= j; (9)
Cov[fk;"j] = 0; k = 1;:::;K; j = 1;2;:::; (10)
E["j] = 0; Var["j] 6 2; j = 1;2;:::: (11)
E[rj]?rf =
KX
k=1
?jkE([fk]?rf); j = 1;2;:::: (12)
x25x18x38x3dCov[fi;fj] = 0 (i 6= j)x7fx2x20x54x54x78x25x70x38x3dx51x2exfx28x23x78x70
x71x5x0x1x21x47x48x54x7bx14x75x76x2x2ex7bx3x54x78x4x53x10x3ex2ex9xax25x70x38x3dx48
x5ax23x7ex1fx7bx14x14x54x24x17x54x1cx1dx2ax67 (x4x3bx7bx14x54x1cx1dx14x25x4ex43x6ax27x54
x7bx14)x27x53x17x9xax78x49x25x64x74x75x56x48x10(8)x54x78x14x16x44fl ?E[fl]x51x47x68
x4fx3ex2bx48x3ax3ex68x19
E[(rj ?rf)(fl ?E[fl])] =
KX
k=1
?jkE[(fk ?rf)(fl ?E[fl])]+E["j(fl ?E[fl])]:
x7bx1rf x4E[fl]x2x7fx68x48x3ax3ex51
E[rf(fl ?E[fl])] = E[E[fl](fl ?E[fl])] = 0:
x39x58
E[(rj ?rf)(fl ?E[fl])] = E[(rj ?E[rj])(fl ?E[fl])]?E[rf(fl ?E[fl])]
= Cov[rj;fl]:
x10x69x23x2cx48
E[(fk ?rf)(fl ?E[fl])] = Cov[fl;fk]; E["j(fl ?E[fl])] = Cov["j;fl] = 0:
111
x26x7ex23x68x48
?jk = flrj;fk = Cov[rj;fk]Var[f
k]
; k = 1;2;:::;K; j = 1;2;::::
x16x17x2x48x17K = 1x18x48x12rm = f1, flj = ?1j,x3ax3ex51
rj ?rf = flrj;rm(rm ?rf)+"j; j = 1;2;::::
E[rj]?rf = flrj;rm(E[rm]?rf); flrj;rm = Cov[rj;rm]=Var[rm]:
x25xdx15x7fx1bx19x1ex6fx1ex37x62x4ax55x56(CAPM)x78xfx2x67x31APTx51x43x2x28x6d
x54x2ex7bx14x1cx1dx55x56x70x26x48 CAPM x5ax2ex70x2 APT x54x40x26x76x63x78x3ax3ex29
x2fx47x4fx44x4bx54 APT x54x76x1fx1fx6ax48x67x4dx5fx1ax48x25x2bx40x26x44x54 CAPM x57
x24xbx65x63x54CAPMx49x6ex7ax44x2xfx2ex70x26x54x78
5.2 x3ax3ex4bx57x49xbx4bx65x63x1fCAPMx57x28x29x13x1ax7bx14x69x63(x1cx1dx62
x4ax55xe)x75x76x54x9x4ax1dx78x49x44x70x51x54x15x13x48x3ax3ex5dx8x61APTx49x40x26x44
x23x1fx8x72xdx66CAPMx54x60x54x26x78x25x67x23x20x8x25x26x54x70x2bx5fx60x2ax31x32x51
x70x2bxfx70x71x54APTx40x26x54x60x54x26x41x7dx48x33x34x10x57x28x29x13x1ax7bx14x69x63x51
x37x34x3x4cx7ex3bx31x3ax3ex49x65x63CAPMx18x33x26x48x3ax3ex7x8x5ax51x70x2bx28x29x13
x1ax7bx14 m x57 APT x2cx54x7bx14x75x76x54x3x4cx78x1x7ex48x3ax3ex5dx8x56x5cx70x71x2e
x7bx14x55x56x57x28x29x13x1ax7bx14x75x76x54x3x4cx78
x36x3f 5.3 x20Mx1dx1ex62x43x12Hilbertx44x45x0 p:M !Rx1dx7ex5fx60x75
x76x62x63x64x65x6b m 2 Mx1dx7ex25x6bx79x39x3ax2ax74x26x46x6bx6cx6dx6ex6fx70x 2 M,
x73p(x) = E[mx]: rf = 1=E[m] > 0x1dx7ex25x6bx79x18x19x1ax5fx13x0 R1 = fr 2
Mjp(r) = E[mr] = 1:gx1dx7ex25x6bx11x12x2bx72x1cx0 g1;g2;:::;gK 2 M;x1dx50
x51x22x23x79x39x3ax3bx3cx6bx2E[g1] = E[g2] = ￠￠￠ = E[gK] = 0:x5dx5ex60x61x15x65
a1;:::;aK 2 Rx4x5 m = E[m] + a1g1 + ￠￠￠ + aKgK x3x2x68x3x6dx6ex6fx70
r 2 R1,x73
E[r]?rf = fl1r?1 +fl2r?2 +￠￠￠+flKr?K;
x7ex7f
flir = Cov[gi;r]=Var[gi]; ?i = ?airfVar[gi]; i = 1;2;:::;K: (13)
xdx27 x2bx71x44x48x31x32m = E[m]+a1g1+￠￠￠+aKgK;x33x34x10x66x15x1fx20
x21 r 2 R1,x51E[mr] = E[m]E[r] + Cov[m;r] = 1. x7bx7ex48x26rf = 1=E[m],
x23x68
E[r] = rf ?rfCov[m;r] = rf ?rfCov[a1g1 +￠￠￠+aKgK;r]
= rf +fl1r?1 +￠￠￠+flKr?K;
112
x17x2c flir;?i x31 (13) x21x62x7ax78x7ax75x48x31x32x44x26x41x7dx48x3ax3ex5ax23x47 ai =
??i=rfVar[gi], i = 1;:::;K;x53x68m = E[m]+a1g1 +￠￠￠+aKgK x41x7dx78 2
x62x69 5.3 x70x68x48x31x32x50x62xbx21x54x3ex2bx20x21x23x3bx70x2bx2ex7bx14x55x56x27
x23x34x48x33x34x25x9x4ax66x17x28x29x13x1ax7bx14x23x3bx70x2bx2ex7bx14x1cx1dx14x25x27x23x34x78
x1bx64x44x70x51x15x13x21x29x71x72x53x3bx54APTx55x56(8)–(12)x48x10x17x71x5ax23x24x30
x31x1x25x64x2ex7bx14x55x56x78x2bx71x44x48x3ax3ex49x44x4bx19x57x1fx68
E[rj]?rf =
KX
k=1
flrjfkE([fk]?rf); j = 1;2;::::
x25x18x54fk x57x44x4bx54gk x54x48x3fx49x66x10x2ex70x62x9xaE[fk] = 0. x10x18x48x25x2b
x60x54x26x51x50x75x39x10x66x21x51x20x21x27 rj 2 R1 x9xax78xfx2x31x32x9xax8x55x56
x54rj x19x57x4dx41R1 x2cx54x70x2bxdx40xfx48x4x59x2bx20x21x27 r 2 R1 x5bx23x60x27x1
rj x54x74x7ax14x25x6fx31x10x3ex54x24x2ax18x48x3ax3ex5ax23x0x1x44x29x60x54x26x10x66x21x51
r 2 R1 x9xax78x25x18x48x3ax3ex12gk = fk ?E[fk],x33x34Var[gk] = Var[fk],x51x6c
x10x66x15x1frx51Cov[r;gk] = Cov[r;fk]:x26x7ex23x68x48
E[r]?rf =
KX
k=1
flkr(E[fk]?rf); flir = Cov[gi;r]=Var[gi]:
x57x44x4bx54x60x54x26x7bx77x77x48x4x68
?i = ?airfVar[gi] = E[fi]?rf; i = 1;2;:::;K:
x7bx7ex48x44x29xdAPTx2ex7bx14x55x56xfx71x72x44x7bx17x66x62x7ax61x28x29x13x1ax7bx14
m = 1r
f
+
KX
i=1
(rf ?E[fi])(fi ?E[fi])
rfVar[fi] :
x13x1bx19x40x6fx62x4ax6ex26p(x) = E[mx],x3ax3ex7dx4x3cx19
p(x) = E[m]E[x]+Cov[x;m] = E[x]r
f
+
KX
i=1
(rf ?E[fi])flxfi;
flxfi = Cov[x;fi]Var[f
i]
; i = 1;:::;K:
x4x25K x2bx7bx14x23x34x61x50x62xbx21x54x69x6ax4ax6x48x51x6cx17x4ex16x2x7bx7x54flx54
x1cx1dx14x25x78x25x2bx31x32x2fx5ex10x66K = 1x18(x7bx17x66CAPMx54x74x40)x5axfx51
x79x7ax78
113
5.3 Rossx49x20x8x62x54APTx69x63x24x13x48x4ex70x57x7fx31x25Black–Scholes
x3exbx62x4ax69x63x54x5fx3fx48x661978x46x49[14]x2cx20x8x70x38xfx70x71x54x62x69x78x25
x38x62x69x13x27x11x7dx3excx1x1ex37x62x4ax40x6fx62x69x78x10x5dx8x7ex1ex54x33x6dx3cx61xd
x9x4ax66x3bx1cx1dx62x4ax55xex78x17x18x48x31x3ax3exbx4bx21x76x29x54xex4cx4x1cx1dx62x4a
x55xex78x2ex1x7dx3ex21x69x1ex4x1ax72x78x7bx7ex48x25x38x1ex37x62x4ax40x6fx62x69x10x3dx3e
x57x58x4fxex4cx54x40x41x48x71x72x44x14x61x44x62x1dx54x2ex3bx78x3bx31x48 Ross x49x62x54x63
x64x54xbx1x2cx21x70x2a xdx49x70x2bx36x51x50x11x6fx5fx54x6dx3cx29x4dx54x1ex37x42x43x2cx48x66
x49x70x2bx1cx1dx4x6x12x14x48x10x23x24x2cx2ex6ex24x1ex24x7ex6ex54x42x43x43x4ex27x1x20x21
x59x62x4ax48x6fx31x10x7ex1fx42x43x14x25x5bx62x54x1ax3dx59x27x5bx62x17x6x78x3bx2ex19x4ex70
x57x61x62x48x73x75x1x6bx54x20x21x23x24x7ex1fx17x70x70x2bx42x43x1ex37x14x25x54x3cx62x54x5a
x18x33x34x27x1x10(x6fx5bx62)x48x25x2x23x25x54x78x25xbx31x32x19x11x2cx68x48x51x6cx11x3bx27
x28x5cx4x12x70x2dx2ex3dx3ex57x58x4fx2cx54x63x29x48x17x2cx45x46x66xax4x6x48 Modigliani-
Millerx69x63x48x7fx3ex62x4ax48x32x67x26x25x6x40x3dx67x63x24x58x51x3ax42x43x69x63x78 xf
x1ex37x62x4ax40x6fx62x69x49x68x4fx44x44x58x70x38x22x23x54x68x4fx62x69x2ax26x69x33x5b
x62x69x78x1x66x66x69x1ex48x3ax3ex53x79x5dx3ax3ex54x55x56x28x5cx2ax61x62x50x62xbx21x49x50
x27x73x23x25x47x51x2ax2bx6x57x5ax67x2x70x48x50x27x73x23x25x5fx36x51x2ax54 S x64x70x71x48
x58x59x2bx28x29x2ax6cx5ax67x73x25x47 S x2bx6x78x25x26x48x49x2ex5dx62x25 S x64x70x71x21
x5fx36x54x25x27x18x48x70x2bx28x29x2ax6cx5ax67x57x70x2bS x75x24x6cx9x10x14x27x78x25x64x61
x62x50x27x73x51x51x2ax64x70x71xfx7fx2ex5dx62x10x3ex21x5fx36x54x25x27x54x65x63x69x26x49x62
x63x44x2 Arrow x4 Debreu x49x62x3ex54x57x4fx54x70x71x57x58x72x73xcxdx2cx6cx79x3b
x54x78x49x25x26x54x55x56x2cx48x2ex10x18x76x3x2ex10x70x71x56x54x10x70x64x45x46x11x3cx2ex2e
x10x54x45x46x78x26x7eArrow–Debreux67x23x7ex1fx4bx4ex45x46x72x76x75x68x54x69x55x5dx3c
x62x1dx54x42x43x54x70x71x57x58x72x73x69x63x76x77x19x1cx2ex3cx62x1dx54x42x43x74x40x78x25x26
x54x76x77x79x7axbx51x76x5fx1dx48xfx51x50x2fx2fx3dx3ex42x43x54x2ex3cx62x1dx6fx60x78x2bx71
x44x48x3bx13x7dx54x3fx27x70x48x62x3ex54x25x64x56x55x7bx17x66x10x59x70x64x2ex3cx62x70x71x5b
x0x4ex61x70x64x51x6dx6ex4ax6x54x2cx68x48x39x58x53x59x70x64x50x62xbx21x5bx23x60x27x1x25
x64x2cx68x54x1cx1dx14x25x78x25x26x54x42x43x70x62x2x7ex7fx42x43x48x10x79x41x42x42x43x2cx36
x51x33xdx2ex61x54x69x6ax78x58x10x3dx3ex57x58x4fx27x70x48x21x45x75x54x2x2ex7ex7fx42x43x48x4
x66x49x2ex25x11x40x6fx2cx68x54x1cx1dx14x25x21x1x10x54x50x62xbx21x54x42x43x78x22x23x31x7ex48
Arrow–Debreux54x79x46xcxdx1x3dx3ex57x58x4fx64x67xdx56x61x78x2bx45x75x7bx11x78x70
x2x21x22xdArrow–Debreux38x39xfx78x49x68x4fx44x48x10x3ex67x2x70x2bSx75x24x6cx72
x76x2cx54x6dx6ex24x6cx78x10x3ex4ex60x73x49x70x64x70x71x56x471x48x17x62x70x71x56x470x54x50
x62xbx21x78x4dx70x2bx2x21x22xdx40x36x68x69 (contingent market)xf (x4fx45x31 [12])x48
x6fxdx50x62xbx21x42x43 (contingent claim market)xf (x4fx45x31 [2]x48x2ex1fx3ax3ex2e
x55x53x3bx25x13x70x2bx7bx11x48x24x1ex57x3ax3ex54xdx50x62xbx21x72x76xfx76x30)x78x25x78x2bx7b
x11x44x2ex25x39x10x3ex54x79x4bx79x5ex12x69x1ex48x10x3ex17x71x5bx2x5dx70x2bx50x27x73x51x51
x2ax64x70x71x54x8x3ex2cx68x42x43x55x56x78x67x9x3fx70x48x50x62x42x43x67x2x50x62xbx21x3b
(x51x2a) S x75x24x6cx27x23x34x54x42x43x48x58x7ex7fx7fx2ex5dx62x25S x64x70x71x21x5fx36x54
x25x27x78
114
x10x50x27x23x25x5fx36x54x70x71x2ex5dx62x25x27x54x65x63x49x57x58x4fx44x14x17x66x49x0
x4ax57x58x4fx2x54x79x46x31F. H. Knight (1885-1972), x62x4bx57x68x3cx1ex5dx1cx25x27
x33x6cx54x2ex3cx62x1dx57x33x55x5dx62x25x27x33x6cx54x2ex3cx62x1dx48x33x6fx27x48x51x6cx5dxb
x31xcx1xdx69x6a(risk)xfx48x13x31x78xcx1xdx2ex3cx62x1d(uncertainty)xfx78x79x7ax13x7d
x36x51x67x4bx15Knightx54x74x0x27x56x48xfArrow–Debreux74x7ax2x11x19x61Knight
x54x13x14x78x25x64x2ex1cx25x27x33x6cx54x2ex3cx62x1dx70x71x73x25x10x66x51x2ax70x71x54x74x40
x27x65x63x48x58x25x64x65x63x17x7ax10x7dx3ex0x4ax3dx3ex1ax71xfx51x28x73x78x2bx71x44x48x49
x2dx2ex3dx3ex71x72x5fx60x44x48x10x50x27x2bx3dx5fx36x54x23x25x1dx19x19x2x74x51x74x54x4x6bx48
x6fx31x70x10x21x44x58x54x28x29x2ax6cx74x51x74x54x25x27x33x6cx4x6bx78x25x64x74x36x36x4fx62
x7ax54x25x27xcx1x41x31x32x21x78x31x32x3ax3ex61x62x50x27x73x51S x64x23x25x1dx48x33x34x59
x70x64(x74x76)x25x27x51x3bx23x24x10x59x64x70x71x5fx36x54x25x27x4x6bx51x21x2ex10x48xfx17
x63x10x77x2x25Sx64x70x71x5fx36x54x25x27x5bx2ex1x7dx48x51x6cx10x3ex54x5x4x21. x21x51
x25x26x54x49Sx64x70x71x44x62x7ax54x25x27x51x3bx5bxcx1x25x2bSx64x70x71x54x25x27x72x76
x44x54x4dx28x32x21x33x37x78x61x62x50x27x73x51S x64x70x71x53x68x68x4fx44x73x47x75x6x4fx25
x27x63x48x58xdx1ex61x2dx2ex68x4fxexfx78xfx2x10x1cx7ax25x68x19x2dx2ex3dx3ex57x58x4fx44
x54x51x79x7ax54x31x63x78x25xbx31x63x54x7bx17x32x33x5bx2ex70x62x25x76x77x19x7fx0x2ax5cx54
x28x29x2ax6cx74x40x78x10x66x39x2bx71x2cx33x14x54x3dx3ex57x58x4fx59x27x70x48x6fx2dx25x64x45
x10x51x2ax70x71x54x31x63x19x57xax63x48xfx2x10x66x39x2bx69x63xcxdx54x3dx3ex57x58x4fx59
x4x68x4fx59x27x70x48x67x51x2dx2ex2fx29x54x68x4fx5fx60x47x75x29x2fx76x2dx78
x3ax3ex56x4bx54x65x63x53x2x49x25x26x54xex4cx2cx2cx68x1ex37x62x4ax40x6fx62x69x2ax7e
x1ex54x33x6dx3cx61xdx9x4ax66x62x4ax65x68x70x62x2x3bx1cx1dx65x68x48x51x6cx10x23x24x3bx70
x64x9x4ax25x27x51x3bx27x60x27(x3ax3ex49x44x51x2cx10S = 2x54x15x28x6dx54x55x56x19x57x68
x19x1fx25x64x9x4ax25x27x51x3b)x78x1x7ex48x3ax3ex79x27x4ex70x57x68x3cxdx50x62xbx21x72x76
Mxf. x49xaxbx54x74x40x56x48x3ax3ex23x61x62Mx67x2S x75x24x6cx72x76RS. x49x25x2b
M =RS x2cx48x51K x64x40x6fx2cx68x48x10x3ex54x50x27x54x4ax4bx5bx51S x64x23x25x78x3a
x3ex1cx24xi x27x60x27x65ix64x2cx68x50x27x54x4ax4bx48x10x11x61x62x1x70x2bS x75x4fx24x6c
xi = (x1i;x2i;:::;xSi ) 2RS,x17x2cx44x38s = 1;2;:::;S x4cx4cx2x49x49x48x58x2ex2
x34x48x10x3ex4ex60x65sx64x70x71x18x54x2cx68x4ax4bx78x5ax23x24x70x48 xix2x70x2b1￡Sx7bx20
x21x78x25xbx2cx68x54x50x27x4ax4bx54x7fx1fx1cx7ax23x24x60x27x1X = (x1;:::;xK)T,xf
x2x10x71x72x44x2x70x2bK￡Sx7bx20x21x78 Xx7fx11xcx1x35x36x26x27(payoff matrix)x78
x14x25 = ( 1;:::; K)x21￡K x7bx20x21x48x4x1cx7ax2x70x2bK x75x4fx24x6cx48xf
x2 x57X x54x16x2
￠X = 1x1 +￠￠￠+ KxK 2RS
x53x2x70x2b1￡S x7bx20x21 (x4fx24x6c)x48x60x27x25x70x2cx68x49x50x27S x64x70x71x56x23
x25x51x54x6x78x7ex19x48x57xbx4bx70x26x48x62x4ax5fx60x1cx7ax30x31x1x3cx62x70x2bx62x4ax65
x68p,xfx2p:RS !Rx53x2x70x2bS x75x72x76x44x54x65x68x48x51x6cx0x1x10x49K x64
x40x6fx2cx68x44x54x6p(xi), i = 1;2;:::;K;x19x57x3cx62x78
x25x26x48x3ax3ex54x8x5fx77x2x2ax50x62xbx21x72x76M = RS x1S x75x72x76x48x17
115
x44x51K x64x40x6fx2cx68x48x10x3ex54x50x27x4ax4bx26x3fx2bx20x21 X = (x1;:::;xK)T x27
x23x34x48x25x18xi = (x1i;x2i;:::;xSi ) 2RS,x58x62x4ax65x68px19x57x49x25K x64x2cx68
x44x51x62x4ax2a p(X) = (p(x1);p(x2);:::;p(xS))T. x3ax3ex44x25x26x54x2cx68x42x43x1
(RS;X;p(X)). x3ax3ex10x25x2bx42x43x20x8x56x5cx33x6dx3cx61xdx2a
(RS;X;p(X)) x9x10x2cx2dx20x2ex2fx1c
1. x75x76x62x63x8x9xaxbx6bx6c p x67x7axcM = RS x7cx79x75x76x64x65x0 x26x13x6b
x6dx6ex6fx70xfx10 = ( 1;:::; K),x7ex3x1bx63x1cx1d
p( ￠X) = p( 1x1 +￠￠￠+ KxK) = 1p(x1)+￠￠￠+ Kp(xK):
2. px6dx6ex47x4cx37x1ex62x43x12y = ￠Xx67x68x75x76x64x65x0x6cx57x58y = ￠X 2
RS xaxby > 0,x5dx5ep(y) > 0:x77x35y > 0x36x37yx79x49x3cx22x38x6bx1x2
x38x39x73x7axcx1dx68x0
x25x70x33x6dx3cx61xdx6cx79x2x10x3fx2bx20x21 X x4x62x4ax24x6cp(X)x2ex8x61x2a
x10x57x4x10K x64x40x6fx2cx68x54x17xbx4ax4bx2ex8x2ax10x78x45x31x48x65ix64x2cx68x54x50
x27x4ax4b xi > 0, x33x34x10x54x17xbx4ax4b p(xi) xcx2cx5ax4ex66x7dx78xfx4cx4cx25x26x58
x2ex63x78x58x75x47x48x74x64x40x6fx2cx68x17xbx4ax4bx75x76x54x32x50x78x35xex23x25x16x6fx2e
x66x49x9xax44x29x33x6dx3cx61xdx54x62x4ax65x68x78x17x71x48x3ax3ex49x44x70x51x2cx19x57x49
x70x2bx77x28x6dx54x55x56x2cx65x63x1fx25x2bx5fx60x78x49x33x18x48x3ax3ex73x51x70x64x69x6ax2c
x68x48x4x6ax73x48x17x2cx61x62x17xbx6ax4aS0 x19x1bx48x58x50x27x6ax4ax6fx2x2ax41aS0,x6f
x2x2ax41bS0. x4dx70x64x2cx68x2x33x69x6ax2cx68x48x10x54x50x27x4ax4bx4x17xbx4ax4bx7cx52
x11. x33x6dx3cx61xdx49x33x18x23x1fx68a < 1 < b. x1ax49x54x5fx60x2x17K > 2x18x48
x74x64x2cx68x54x17xbx4ax4bx57x50x27x4ax4bx7x8x9xax37x34x38x3dx48x78x57x33x6dx3cx61xd
x2ex5dx23x78x25x70x5fx60x67x2Rossx491978x46x21x75x1ex44x54x48x10x67x2x3ax3ex75x65x63
x54x1dx35x36x28x37x38x36x3fx78
x36x3f 5.4 (RS;X;p(X)) x7cx79x18x4dx5fx7x20xaxbx79x62x49x63x4ex5fx60x1d
x60x61S xcx68x65?1;:::;?S > 0,x4x5
p(xi) = ?1x1i +￠￠￠+?SxSi ; i = 1;:::;K: (14)
x25x38x62x69x70x68(RS;X;p(X))x44x54x33x6dx3cx61xdx79x41x42x2cx68x54x17xbx4a
x4bx2x2cx68x54x50x27x74x64x23x25x54x4ax4bx54x3bx1cx1dx14x25x78x16x17x2x17x651x64x2cx68
x2x33x69x6ax2cx68x48x17x50x27x4ax4bx1 x1 = 1 = (1;1;:::;1) x18x48x31x32 p(x1) =
p(1) = 1=rf > 0, x33x34 1=rf = PSs=1 ?s. x12 ps = ?srf, s = 1;:::;S. xeP
S
s=1 ps = 1. x39x58x48 ps x23x24x3cx2ex65sx64x70x71x49x50x27x5fx36x54x25x27x78x25x26x48
(14)x26x7fx2ax1
p(xi)rf = p1x1i +￠￠￠+pSxSi ; i = 0;1;:::;K:
116
x44x26x1fx14x2x2cx68x50x27x4ax6x10x66x25x27p1;:::;pS x54x72x6(x68x4fx3ex2b)x48x1ex14
x2x2cx68x54x17xbx4ax6x54x33x69x6ax5bx3cx78x66x2x44x29x62x69x7fx23x60x54x1
x36x3f 5.4’ x57x58x3a1x67xdxex67x18x19x1axdxex6bx7ex1ex1fx63x7x1dx1 = 1 =
(1;1;:::;1), x7ex3x1bx63x7x1d p(x1) = p(1) = 1=rf > 0. x5dx5e (RS;X;p(X))
x7cx79x18x4dx5fx7x20x26x63x6ex60x61x3bx67x26x63x3dx13x3cx25x6bx4x5x3dx7ax67x1ex1fx63x7
x1dxi x79x3ex7xdxex79x11x12x13(xi=p(xi))x79x65x66x8x9x24x26x6ex18x19x1ax5fx13rf.
x25x38x62x69x54x1dx33x1dxfx28x2cx68x78x2bx71x44x48xd (14) x26x41x7dx78x31x32 y =
￠X > 0,x33x34
p( ￠X) =
KX
i=0
ip(xi) =
KX
i=0
SX
s=1
i?sxsi
=
SX
s=1
?s
? KX
i=0
ixsi
!
:
x26x66x21x51?s > 0,x46x26x1fx14x46x49x2cx54x66x5bx43x50x3x6cx5ex5fx51x70x66x1x3bx48x23
x1fx68x1ex14x1x3bx48x4x44x29x33x6dx3cx61xdx41x7dx78
xfx2xcx75x1dx54x2cx68x49x68x4fx44x44x58x70xbx77x77x22x23x54x31x32x48x17x2cxcx2c
x3bx19x26x69x33x5bx62x69x6fx17x9x4ax31x32x78x10x7ex48x3ax3ex47x75x70x62x54x2cx74x78x25x18
x3ax3ex79x27x63x29x70xbx17x62x54x5fx60x48x24x66x66x69x1ex78
5.4 x3ax3ex49x44x4bx4bx57x20x19Arrow–Debreux2cx68x54x25x22x78x10x3ex54x50x27
x4ax4bx67x2x1ax49x44x58x54x50x62xbx21x72x76RS x2cx54x6dx6ex24x6cx78x39x68x4fx44x27x3cx48
x31x32x40x6fx2cx68x67x2Arrow–Debreux2cx68x7fx1fx48x33x34x62x4ax5fx60x54x1ex2x70xa
x61x7ax54x78x5ax67x2x70x48x70x2bx62x4ax65x68x31x32x19x57x10x66x59x70x6dx6ex24x6cx5bx51x3cx62
x54(x3b)x6x48x33x34x10x10x15x1fx24x6cx54x47x6x5ax67x7ex7fx3cx62x78x25x2x7bx1x15x1fx24x6c
x5bx23x24x3bx25xbx6dx6ex24x6cx27x1cx1dx60x27x78x58x1ex37x62x4ax40x6fx62x69x71x72x44x2x5d
x8x48x59x70x64x4ex25x33x6dx3cx61xdx54x62x4ax55xex5bxcx2cx2x10x21x51Arrow–Debreu
x2cx68x47x3bx6x54x62x4ax55xex78x67x9x3fx70x48x10x59x70x64Arrow–Debreux2cx68x5bx47
x3bx6x54x62x4ax65x68x70x62x9xax33x6dx3cx61xdx57x58x9xax33x6dx3cx61xdx54x62x4ax65x68
x5ax70x62x53Arrow–Debreux2cx68x47x3bx6x78x3bx25x26x54x69x26x27x60x54x1ex37x62x4ax40
x6fx62x69x53x68x25x38x62x69x2ax68x24x1x36x7ax48x2fx5ex49x7dx70x64x6ex3fx48xdx15x1ex37x62
x4ax40x6fx62x69x2x2ex2cx36x68x54x48x3bx2ex19x37x34x26x69x33x5bx62x69x75x72x78x17x71x25x2
x7bx1x3ax3ex61x62x40x6fx2cx68x67x2Arrow–Debreux2cx68x21x0x14x54x78x70x71x74x40x36
x51x33x34x28x6dx78
xfx2x39x24x6cx72x76x54x76x77x27x3cx48x70x71x54x1ex37x62x4ax40x6fx62x69x33x43x67x2
x75x12x7bx40x6fx2cx68x14x4Arrow–Debreux2cx68x14x75x76x54x3x4cx78x25x2x78x2bx24x6c
117
x14x78x13x70x14x2x24x6cx72x76x54x6dx6ex24x6cx14x48x15x1fx24x6cx5bx23x24x3bx10x3ex27x1cx1d
x60x27x48x7bx7ex48x40x6fx2cx68x14x2cx54x59x70x2bx24x6cx5ax5bx23x3bx10x3ex27x1cx1dx60x27x78x7a
x75xex2ex70x62x48x7bx1x40x6fx2cx68x14x2ex70x62x4dx41x24x6cx72x76x54x40x78x31x32x40x6fx2c
x68x14x4dx41x24x6cx72x76x54x40x48x33x34Arrow–Debreux2cx68x14x2cx54x59x70x2bx24x6cx5a
x5bx25x3bx40x6fx2cx68x14x2cx54x24x6cx27x1cx1dx60x27x78x49x25x64x74x40x56x48x1ex37x62x4ax40
x6fx62x69x54x2cx68x67x43x7fx28x6dx78x17x2cx68x54x4ex79x23x76x29x31x56 (x46x3cx13x4bx54x76
x29)x2ax26x66x21x51 Arrow–Debreu x2cx68x5bx9x4ax66x11x64x40x6fx2cx68x54x14x25x48x58
x10x66Arrow–Debreux2cx68x69x27x70x48x33x6dx3cx61xdx67x9x4ax66x62x4ax65x68x10x21x51
Arrow–Debreu x2cx68x47x3bx6x78x7bx7ex48x1ex37x62x4ax40x6fx62x69x41x7dx78x25x18x58x2e
xfx3cx8x48x62x695.4x2cx54?i x67x2x65ix2bArrow–Debreux2cx68x54x4ax4bx78x7bx7ex48
x10x3ex58x7fx11xcx1x57x58x28x4fx78x26x66x40x6fx2cx68x69x4dx41x24x6cx72x76x40x54x74x40x73
x69x14x27xcx3fx28x6dx48x25x67x51xcx75x13x6dx25x50x70x2bxcx3fx54x3dx3ex4fx25x22x78x10x67
x2x49x4ax68x69x54x25x22x78x49x25x64x74x40x56x48x59x70x2bS x75x24x6cx5bx23x24x3bx40x6fx2c
x68x69x2cx54x24x6cx27x1cx1dx60x27x78x3cx3bx24x6cx72x76x69x63x2cx54x19x1bx31x63x48x23x24x73
x62x48x25x18xcx2cx51K > S,x4x2cx68x54x64x72x68x75x66x1fx50x27x70x71x54x64x72x68x78x49
x1ax71x4cx5bx2cx48x25x26x54x74x40x2x2ex23x25x3bx3bx5fx36x54x78x7bx7ex48x7ex7fx42x43x73x2
x70x64x69x55x74x40x78x49x25x70x69x55x74x40x56x48x44x29x68x4fx38x3dx5cx3ax41x3dx3ex11x1x48x67
x2ax41x2ax59x70x64x50x62xbx21 (x1ex37x3x3exbx3x1ax36x2cx68) x5bx23x3bx40x6fx2cx68 (x38
x54x1ex37)x27x1x10(x1x40x6fx2cx68x54x14x25)x78
x33x34x2ex7ex7fx42x43x54x1ex37x62x4ax40x6fx62x69x25x35x7ex1fArrow–Debreux2cx68
x27x63x2cx75x7ex25x17x7ax23x24x4ex4fx3fx76x78x2ex1fx33x0x33x14x67x4dx5fx1ax48x26x66x40x6fx2c
x68x24x6cx2ex25x0x41x7fx72x76x48xcx75x1dx54x2cx68x2cx5x4dx51x70xbx2ax52x66x49x78x3cx3b
Arrow–Debreu x2cx68x27x2cx68x1ex37x62x4ax40x6fx62x69x17x71x2x23x4fx54x78x2bx71x44x48
x3ax3ex73x47x75x49x40x6fx2cx68x69x2cx13x0x44x40x41Arrow–Debreux2cx68x48x53x4bx4ex13
x54x40x6fx2cx68x69x40x41x7ex7fx42x43x4x23x78x3ax3ex1bx2ax70x14x24x6cx31x32x2ex4dx41x24x6c
x72x76x54x40x48x33x34x5x25x0x44x40x41x2bx57x10x3ex1cx1dx33x3x54x24x6cx48x53x4bx4ex13x54
x24x6cx14x4dx41x40x78x58x17x42x43x2ex7ex7fx18x48x3ax3ex5x25x60x19x70x2b Arrow–Debreu
x2cx68x48x53x68x10x54x50x27x4ax4bx2ex1x24x6cx57x40x6fx2cx68x69x2cx54x7bx7x24x6cx7fx1fx1c
x1dx33x3x78x31x32x0x70x2bx2ex63x48x33x34x58x23x24x13x0x48x70x18x0x19x42x43x7ex7fx1x1bx78
x25x67x2x70x48x15x1fx40x6fx2cx68x69x48x5x25x7ex1fx0x1x40x41 Arrow–Debreu x2cx68x48
x53x68x42x43x7ex7fx5cx78x5fx60x49x66x31x1fx1x25xbx20x0x1x54Arrow–Debreux2cx68x62
x4ax48x53x68x33x6dx3cx61xdx1cx7ax9xax78x2cx33x34x5fx48x25xbx2cx68x54x17xbx4ax4bxcx2c
x2x3bx54x57x35xex33x6dx3cx61xdx19x57x11x3bx70x78xfx2x2x35x23x24x47x15x1fx3bx68x7ex25
x67x2ex70x62x78x45x31x48x49x3ax3ex19x57x4fx1fx54x15x28x6dx54x8x70x71x74x40x2cx48x31x32x40
x6fx2cx68x69x2cx67x73x51x70x2bx33x69x6ax2cx68x48x10x54x17xbx4ax4bx21,x58x50x27x4ax4bx5a
x7cx52x21,x33x34x3bx31x3ax3ex24xbx19x57x3cx19x54x48x13x0x1x70x64Arrow–Debreux2c
x68(x4x17x78x64x50x27x4ax4bx33x3fx20x41)x18x48x8x2cx68x54x4ax4bx73x25x490x41x75
x76x78x35xex67x4dx48x77x33x6dx3cx61xdx78x22x23x31x7ex48x23x24x5dx8x48x10x66x15x1fx2ex7ex7f
x54x40x6fx2cx68x69x48x3ax3ex5x23x24x10x10x3ex0x1x40x41x24x17x62x4ax54Arrow–Debreu
118
x2cx68x48x53x68x42x43x7ex7fx5cx78x1x2cx68x25x70x77(x4fx56x70x51)x48x47x3bx7x3bx70xbx39x68
x4fx44x27x70x57x26x69x33x5bx62x69x6fx60x44x2x9x4ax54x26x27x78xfx2x25x26x54x70x38x5ex7e
xdx15x51x77x77x68x3cx54x57x58x79x7ax78
5.5 x1ax49x3ax3ex3cx3b Arrow–Debreux2cx68x27x2cx68x1ex37x62x4ax40x6fx62x69x78
x25x18x3ax3ex73x47x2cx68xcx75x1dx78x24x56x76x29x2cx54x33x6dx3cx61xdx5bx2x5d(RS;X;p(X))
x44x54x33x6dx3cx61xdx78
1. x7ex7fx42x43x74x40x2ax25x18x40x6fx2cx68x69x54x50x27x4ax4bfxigx4dx41Sx75x24x6c
x72x76x54x40x78x2ex40x61xdx40x6fx2cx68x54x2bx68x1K = S,x51x6cx1;x2;:::;xS x4dx41
x24x6cx72x76x54x40x48x17x62x54x24x6cx5bx2x10x3ex54(x1dx70)x1cx1dx14x25x78x16x17x2x21x51
Arrow–Debreux2cx68
ei = (0;:::;0; 1|{z}
x68 i x69
;0;:::;0); i = 1;2;:::;S;
x5bx2x10x3ex54(x1dx70)x1cx1dx14x25x48x4
ei = a1ix1 +a2ix2 +￠￠￠+aSi xS; i = 1;2;:::;S: (15)
x10x18x48x74x7ax5ax51
xi = x1ie1 +x2ie2 +￠￠￠+xSi eS; i = 1;2;:::;S: (16)
x16x5ex33x6dx3cx61xdx48x26 (15) x23x1bx48 ei x54x17xbx4ax4b p(ei) x23x26fxjgx54
x17xbx4ax4bfp(xj)gx27x3cx62x48x4
p(ei) = ?i = a1ip(x1)+a2ip(x2)+￠￠￠+aSi p(xS); i = 1;2;:::;S:
x51x6cx13x26x33x6dx3cx61xdx23x68x48x21x51?i > 0. x4dx70x69x4bx48x26(16)x23x1bx48
p(xi) = x1ip(e1)+x2ip(e2)+￠￠￠+xSi p(eS) = ?1x1i+?2x2i+￠￠￠+?SxSi ; i = 1;2;:::;S:
x4x62x69x68x2cx78
2. x2ex7ex7fx42x43x74x40x2ax25x18x40x6fx2cx68x69x54x50x27x4ax4bfxigx2ex4dx41Sx75
x24x6cx72x76x54x40x78x2ex40x61xdx40x6fx2cx68x54x2bx68x1N < S,x51x6cx1;x2;:::;xN
x1cx1dx33x3x78x39x58x48x26fxigx54x17xbx4ax4bfp(xi)gx73x25x10x25N x2bx24x6cx21x0
x41x54N x75x72x76XN x21x4ex60x54x2cx68(x1dx70)x62x4ax78x58x10x66XN x24x19x54x2cx68
x33x55x62x4ax78x25x5ax67x2x70x48x10x66x15x1f y 2 XN, x3ax3ex62x7ax61x70x2bx1cx1dx62x4a
x65x68pN:XN !Rx48x53x68x10x66x15x1fy = 1x1 +￠￠￠+ NxN,x51
pN(y) = 1p(x1)+￠￠￠+ Np(xN):
119
x51x6cx26x33x6dx3cx61xdx48x58x23x68x19x2ax31x32y > 0, xepN(y) > 0: (x2ex1fx48x25x26
x54yx5ax51x23x25x49XN x2cx60x2ex19x78 )
x26x66 XN x4cx4cx2 N(< S) x75x72x76x48x33x34x5ex5fx51x70x2b Arrow–Debreu
x2cx68x2ex49x17x2cx78x2ex40xdx10x2 ej, x10x54x62x4a e0j = fi x26x33x6dx3cx61xdxcx2cx1
x3bx6x48x4fi > 0. x62x7aXN+1 = fy + aej jy 2 XN; a 2Rg. x25x2x2bN + 1
x75x72x76x48x17x44x54x62x4ax65x68pN+1 x23x62x7ax1
8y 2 XN; a 2R; pN+1(y +aej) = pN(y)+afi:
x25x2bx65x68x74x7ax2x1cx1dx65x68x48xfx10x66x15x79x47x54x3bx68fi > 0,x2ex70x62x25x7cx2c
x10x9xax33x6dx3cx61xdx48x4x2ex25x7cx2c y + aej > 0 x18x48x51 pN+1(y + aej) > 0.
x3ax3ex5dx8x48x17fix49x11x2bx48x76x2cx47x6x18x48x25x70x75x39x70x62x25x9xa(x24x56x54x65
x63x49x15x28x6dx54x73x51x70x64x33x69x6ax2cx68x4x70x64x69x6ax2cx68x54x74x40x56x48x7bx17x66
x5dx8x48x19x1bx69x6ax2cx68x50x27x54x78x64x23x25[S = 2]x54x4ax6x48x33x34x10x17xbx54x62
x4ax73x75x49x25x78x2bx4ax6x75x76x48x67x9xax33x6dx3cx61xd)x78
x2bx71x44x48x10x66x15x1fy 2 XN,x3ax3ex51
pN(y) =
‰ > 0; y > 0;
x6fx16, y 6> 0:
x25x2x70x2bx38x3dx2ex9x26x78x1x53x10x60x27x1xdx33x38x3dx2ex9x26xfx78x3ax3ex0x4ex70x2b
x62x7ax49x1ex2bS x75x72x76x2cx54x77x7ax71x6x65x68V:RS !Rx31x56x2a
8x 2RS; V(x) =
‰ 0; x > 0;
?1 x 6> 0:
x33x34x44x26x5ax23x60x27x1
8y 2 XN; y 6= 0; pN(y) > V(y):
x2exfx52x2cx48x65x68V x9xa
8x;y 2RS; V(x+y) > V(x)+V(y);
8? > 0; V(?x) = ?V(x):
xbx70x1dx60xcx1V x54x66x23x0x1dx48x13x70x1dx60xcx1V x54x3bx5x6dx1dx78x39x58x10x66
x15x1fy;z 2 XN,x4x 2RS,x51
pN(y)?pN(z) = pN(y ?z) > V(y ?z) > V(y +x)+V(?z ?x);
x4
?V(?z ?x)?pN(z) > V(y +x)?pN(y):
120
x47x = ej,x51x49x1ex14x10z x39x56x3cx5bx48x58x49x1fx14x10yx39x44x3cx5bx48xex23x68
c = inf
z2XN
(?V(?z ?ej))?pN(z)) > sup
y2XN
(V(y +ej)?pN(y)) = b;
x23x24x3cx8x48 bx2x56x5cx5fx60x54x6x2a
8<
:
max(?pN(y))
y 2 XN
yj >?1; yi > 0; i 6= j:
x58cx2x56x5cx5fx60x54x6x2a
8
<
:
min(?pN(z))
z 2 XN
zj 6?1; zi 6 0; i 6= j:
x74x7ac > b > 0. x10x18x48xcx2cx51c > b. x25x2x7bx1x2exfx3cx8x44x29x78x2bx5fx60
x5bx2x51x1ex54x57x31x32c = b,x33x34x67x66x49 ˉy; ˉz 2 XN,x9xa
ˉyj >?1; ˉyi > 0; i 6= j; ˉzj 6?1; ˉzi 6 0; i 6= j:
x24x58pN(ˉy) = pN(ˉz) = ?b = ?c. xfx2x26x44x26x23x1bx48
ˉyi ? ˉzi > 0; i = 1;2;:::;S; ˉy 6= ˉz:
x25x4cx17 ˉy ? ˉz > 0x18x78x51x23x25x78x58pN(y ?z) = 0. x25x57x33x6dx3cx61xdx5dx23x78
x7bx7ex48 c > b.
x25x26x67x40x41x70x2bx68x6x48x76(b;c)x3ax3ex47fi 2 (b;c),xefi > 0. x4dx70x69
x4bx48x10x66x15x1fy 2 XN, a 6= 0,x26fix54x62x7ax48x3ax3ex51
?V
?
?ya ?ej
·
> pN+1
?y
a +ej
·
= pN
?y
a
·
+fi > V
?y
a +ej
·
;
x1fx79x19V x54x3bx5x6dx1dx48x23x24x3cx8x48x2ex23ax2x3bx54x48x58x2x50x54x48x3ax3ex5b
x51
pN+1(y +aej) > V(y +aej):
x16x17x2x17y + aej > 0x18x48 pN+1(y + aej) > 0. x25x70x68x10Arrow–Debreux2c
x68ej x54x62x4afix1cx25x53x20x54x40x6fx2cx68x69x9xax33x6dx3cx61xdx78
x15x13x48x31x32x20x54x40x6fx2cx68x69x1cx7ax53x42x43x2ex7ex7fx48x3ax3ex58x23x24x4x0
x3bx10x26x54x69x55x0x1Arrow–Debreux2cx68x78x70x18x19x68x19x70x2bx7cx1dx6ax51x62x4ax3
x51x40x41x7ex7fx42x43x54x40x6fx2cx68x69x1x1bx78x26x7ex30x31x1x44x29x74x40x78x62x69x68x2cx78
2
121
5.6 x1ex37x62x4ax40x6fx62x69x54x7fx33x2cx68x2x3cx3bx70x38x68x4fx62x69x2ax26x69x33
x5bx62x69x78x3cx3bx26x69x33x5bx62x69x54x2cx68x7ex7fx2ax41x68x4fx65x63x78x17x1fx6axfxfx13
x57x57x58x79x7ax7bx61x4cx78xfx2x26x69x2x2bx49x57x58x4fx2cx43x7fx51x3bx54x25x22x48x3ax3e
x4dx49x2dx2ex17x62x1ex69x3bx19x10x78x7bx7ex48x3ax3ex10x7ex5ax7x8x51x21x61x1ex78
x1ax49x3ax3ex3bx26x69x33x5bx62x69x27x2cx68x1ex37x62x4ax40x6fx62x69x54xcx75x1dx2a
x49RS+1 (x25x2x17xbx70x71x54x4ax6x57x50x27x54S x64x70x71x54x4ax6x21x40x41x54
x72x76)x2cx47x48x69x25
M =
(
z 2RS+1
flfl
flflz = (z0;z1;:::;zS) > 0;
SX
s=0
zs = 1
)
;
(x25x2x17xbx4ax6x1x7dx54 Arrow–Debreu x2cx68x57x50x27x4ax6x1x7dx3x17xbx4ax6
x11x54x2cx68x7fx1fx21x40x41x54x26x69x78x25x70x69x25x2cx54x2cx68x2x17xbx4ax6x57x50x27
x4ax6x5bx43x50x54x43x7dx24x6cx78 )x4x69x25
L = fy 2RS+1jy = (? ￠x0; ￠x1;:::; ￠xS); 2RK+1g
x25x18 xs = (xs1;:::;xsK)T; s = 1;:::;S, x0 = (p(x1);:::;p(xK))T. (L x2x14
x25 x54x0x44x50x49x24x13x54x17xbx4ax6x57S x64x50x27x4ax6x21x40x41x54x24x6cx7fx1f)x78
x33x34x26x33x6dx3cx61xdx48x10x3ex2x78x2bx2ex7bx66x54x67x26x69 (x31x32x7bx66x48x33x34x79
x41x42x51x70x64x43x7dx14x25x54x17xbx4ax6x43x3bx48x50x27x4ax6x43x50)x48x51x6cx2exfx52x2c
M ?Lx2x67x69x78x39x58x66x49? = (?0;?1;:::;?S) 2RS+1 x53x68
8y 2 L; 8z 2 M; (?;z) > (?;y);
xfx26x66Lx71x72x44x2RS+1 x2cx54x14x72x76x48x44x26x54x1fx14x73x23x25x1x7dx48x35xex10
x23x25x33x2ax54x4ex48x24x5ex2ex9x26x2ex23x25x41x7dx78x4dx70x69x4bx48x26x66 z x23x47x73x51
x70x2bx33x6cx1x70x3x17x62x33x6cx1x7dx54x6dx6ex24x6cx48 ?x54x59x70x33x6cx5bxcx2cx1x3bx48
x35xex44x29x67x4bx2ex9x26x2ex23x25x41x7dx78x7bx7ex48
8 2RK; ( ;??0x0 +?1x1 +￠￠￠+?SxS) = 0;
x24x5e
??0x0 +?1x1 +￠￠￠?SxS = 0:
x12?s = ?s=?0,x51x1fx79x19x0 = (p(x1);:::;p(xK))T,x4x68(14)x26x78 2
x39x62x69x54x2cx68x2cx3ax3ex23x24x3cx8x48x26x7ex3cx62x54x9x4ax25x27x51x3bx70x71x51
x2ex1dx70x78x2bx71x44x48x10x2x26x45x6eLx54x1cx1dx14x72x76x27x44x62x54x78x31x32Lx6fx50
x2ex2Sx75x14x72x76x48x33x34x7ex1fLx54x9xax62x69x38x3dx54x14x72x76x67x51x33x2ax2ex2bx48
122
x39x58x5ax23x51x33x2ax2ex2bx9x4ax25x27x51x3bx4ex25x62x69x75x39x78x49x25x64x74x75x56x48x3a
x3ex33x55x3cx3bx25x26x54x9x4ax25x27x51x3bx27x10x62x4ax5fx60x2ex8x1ax62x54x1bx1cx78x6fx31
x5ax23x39x10 ?1;?2;:::;?S x39x1ex69x6a (15) x27x3cx78x25x2x70x14x1cx1dx69x6ax14x48x10
x2ex70x62x51x1ex48x51x1ex5ax2ex70x62x51x1dx70x1ex78x49x51x2ex2bx2ex10x54x1ex18x67x70x62x51
x33x2ax2ex2bx1ex48x39x58x67x51x33x2ax2ex2bx7bx7x54x9x4ax25x27x51x3bx78x4dx70x69x4bx48 (15)
x2ex1x69x6ax33x1ex18x70x68x33x6dx3cx61xdx70x62x2ex9xax78x25x79x41x42x48 x0x1 (x37x38)
x38x39x36x28x57x22x3fx32x40x41x63x64x2dx20x2bx41x78
x31x32(15)x41x7dx48x33x34Lx2cx54x24x6cx54x65x70x2bx33x6cx7ex7fx26x13x4bSx2bx33
x6cx21x44x62x78x7bx7ex48x24x6cx72x76Lx54x75x68x5ax7ex7fx26x17x13x4bx54S x2bx33x6cx21x44
x62x78x7bx7ex48 Lx2S x75x14x72x76x54x1dx33xcx75x38x3dx1
RS = fz 2RS jz = ( ￠x1;:::; ￠xS); 2RK+1g:
x25x2bx38x3dx4cx17K +1 > Sx18x78x51x23x25x9xa(xfx51x43x70x62x9xa)x48x25x18(15)
x54x69x6ax2bx68x2ex77?s x54x2bx68x5fx78x1bx64xbx4bx20x19x54x25x22x48x21x22x1ax36x2cx68x6f
x50x62xbx21x67x2RS x2cx54x24x6c(x39x3dx3ex42x43x54x3ax3bx27x3cx48x10x3ex7x8x2x43x50
x24x6cx48xfx25x51x2ex13x14x24x56x54x68x4fx65x63)x78x66x2x44x4bx54x9x26x53x79x41x42x2a x3
x4x40x36x31x6x75x5dx42x31x43x44x38x39x3dx22x41x21x1bx39x25x26x54x2cx68x42x43x67x2xbx4b
x19x57x20x19x54x49x4ax68x69x78x39x58x44x4bx54x65x63x71x72x44x19x57x5dx8x48x64x49x4ax68x69
x44x32x45x44x40x36x31x6x75x5dx46x18x36x28x39 x25x2x7bx1x25x18x54x9x4ax25x27x51x3bx2x1d
x70x54x78x17K < S x18x48x42x43x70x62x2x2ex7ex7fx54x78x10x23x24x69x1ex1x36x51xax63x2e
x54x2cx68x64x72x27x7x2bx74x64x23x25x5fx36x54x74x75x78x10x66x1ax71x4cx5bx27x70x48x42x43x2e
x23x25x2x52x10x7ex7fx54x78x7bx7ex48x7ex7fx42x43x54x25x22x73x2x70x2bx69x55x25x22x78
x44x4bx54x65x63x5bx2x10x66x51x2ax75x50x62xbx21x72x76x74x40x4ex4fx54x78x58Rossx49
x621978x46x54x57x4fx63x64[14]x2cx71x2x1x24x7x3exbx62x4ax69x63x54x47x75x70x6fx7cx67
x39x33x2ax75x72x76x8x5fx48x51x6cx5ax7x3bx61x26x69x33x5bx62x69x78x2ex1fx62x54x68x4fx55x56
x4x2cx68xdx15x2ex25x12x7dx9x79x78x13x27x78x41x7dx5fx1ax48x33x2ax75x72x76x44x54x1ex37x62
x4ax40x6fx62x69x75x77x51x2ax75x74x40x56x54x62x69x1x2x68x2ex78x70x71x27x70x48x33x6dx3cx61
xdx2ex13x57x7fx0x3bx1cx1dx62x4ax65x68x9x4ax78x17x2cx51x2dx2exfx2fx29x54x68x4fx26x27x5f
x60x47x75x1ex44x78x51x62x5bx54x26x31x23x46x3cx45x31x15x5dx5fx60x54Clarkx54x63x64[2]x78x4d
x19x70xbx51x3x54x5fx60x46x46x3cx13x4bx54x70x68x78
x5ex66x49x50x62xbx21 Hilbertx72x76x54xex4cx2cx48x3ax3ex75x16x5dx8x48x17x28x29x13
x1ax7bx14mx2x67x4bx3bx28x29x2ax6c(x4x10x4ex66x7dx54x25x27x11)x18x48x26x > 0x23
x1fx8p(x) = E[mx] > 0. x7ax58x48x17x50x62xbx21x72x76x4cx4cx2x26x21x51x69x7dx51x2a
x54x28x29x2ax6cx21x14x41x54Hilbertx72x76x54x3bx14x72x76x18x48x3ax3ex2ex25x2cx68x28x29x13
x1ax7bx14 m xcx2cx2x67x4bx3bx28x29x2ax6cx78x17x2cx58x47x75x13x61x62x70xbx20x54x38x3dx78
x2ex1fx25x64x68x4fx44x54x2fx1x7dx3fx10x3dx3ex57x58x4fx27x70x48x23x25x51x2exfx45x75x78
5.7 x25x70x51x3ax3ex39x4dx70x2bx3ax3bx27x65x63x1ex37x62x4ax40x6fx62x69x78x3ax3ex47
x48x70x2bx15x6dx4fx1ex64x34x35x5fx60x78x57x24xbx70x26x48x3ax3ex1cx7ax61x62x73x51x17xbx4
123
x50x27x78x2bx18x23x48x17xbx2x3cx62x54x48xfx50x27xex51 S x64x23x25x57x4x25x2x21x22x50
x62x42x43x74x40x48x7bx7x54x50x62xbx21x72x76x1RS. x10x18x48x61x62x42x43x2cx51 K x64
x40x6fx2cx68x48x17x50x27x4ax4bx1S x75x4fx24x6cx1 :::;xK 2RS;x4x17x3fx2bx20x21x1
X = (x1 :::;xK)T; x17x17xbx4ax4bxex1p(x1);:::;p(xK),x25x18px2x50x62xbx21
x72x76RS x44x54x62x4ax65x68x78x58x75x61xd(RS;X;p(X))x44x54x33x6dx3cx61xd1. x41
x7dx48x4x2a
1. x75x76x62x63x8x9xaxbx6b px67x7axcM =RS x7cx79x75x76x64x65x0 x26x13x6bx6d
x6ex6fx70xfx10 = ( 1;:::; K),x7ex3x1bx63x1cx1d
p( ￠X) = p( 1x1 +￠￠￠+ KxK) = 1p(x1)+￠￠￠+ Kp(xK):
x49x25x70x55x56x56x48x57x58x2fx30x31(x24x13x2ex40xcx62x1x4fx1ex31)x54x44xex33x14
x57x3cx62x70x71x56x54x44xex33x14x36x51x6fx60x48x3fx78x3ax3ex1cx7ax23x24x7ex1fx4fx1ex31x54
x3ax3bx65x68x27x4ex4fx44xex48x73x2ex1fx25x70x4fx1ex31x10x17x5bx68x54x3ax21x54x72x73x2exf
x75x3cx17xbx4ax6x48x58x75x3cx50x27x54x2ex3cx62x54x4ax6x78x5ax67x2x70x48x62x54x3ax3bx65
x68x2x17xbx4ax6x4x50x27S x64x2ex10x70x71x56x54x4ax6x54x65x68u:RS+1+ !R. x25x18
x3ax3ex1ax18x5ax2excx0x4ex25x27x48x58x3ax3bx65x68x67x2x70x2bS+1x75x24x6cx72x76x44x54
x65x68x48x6fx31x70x48x67x2x70x2bS +1x2bx2ax6cx54x65x68x48x17x2cx650x2bx2ax6cx2x4fx1e
x31x1dx51x54x17xbx4ax6x48x13Sx2bx2ax6cx2Sx64x70x71x56x54x50x27x4ax6x78 +x49x4ex60
x3ax3ex73x47x48x17xbx4ax6x4x50x27x4ax6x43x50x54x74x40x48x4RS+1+ x2x21x51x33x6cx43x50
x54S +1x75x24x6cx7fx1fx78x10x66x25x26x54x3ax3bx65x68x48x3ax3ex61x62x56x5cx61xdx41x7dx2a
x47x29x48x2ex2f
1) u:RS+1+ !Rx67RS+1+ x7cx79x5fx60x64x65x75
2) ux6dx6ex3dxcx3bx3cx24x67x49x7x4axbx79x6bx6cx6dx6ex6fx70x;x0 2RS+1+ ,x57x58
x > x0,x5dx5eu(x) > u(x0).
x25x70x61xdx79x41x42x48x2ex23x73x66x37x34x70x71x48x5bx5x2x4bx2ex4bx28x78x25x18x >
x0 x2x5dxx54x59x2bx33x6cx5bx2ex16x66x0 x54x7bx7x33x6cx48x51x6cx 6= x0.
x1ax49x3ax3ex27x47x48x25x70x4fx1ex31x54x15x6dx2cx68x14x25x7x8x5fx60x48x4x49x70x62
x54x4ax4bx1fx4cx56x48x62x7x8x31x1fx27x7x8x2cx68x14x25x48x53x62x49x17xbx4x50x27x54x34
x35x3ax3bx15x4ex78x25x18x13x70x9x3fx54x68x4fx60x54x67x2x2ax53x62x54x3ax3bx65x68x15x4ex78x25
x70x5fx60x57x44x70x51x2cx21x65x63x54Markowitzx5fx60x17x7ax2x66x66x10x70x72x56x54x78xf
x2 Markowitz x5fx60x2cx51x20x21x4x69x6ax78x2bxax38x75x7x8x78x25x18xex73x51x70x2b
xax38x78x24x13x48x3ax3ex53x5dMarkowitzx5fx60x5ax55x1x25x26x54xex4cx78
x3ax3ex58x61x62x8x4fx1ex31x49x17xbx4x50x27x54x74x64x70x71x56x48x5bx1dx51x70x62x54
x5b(endowment)x48x4x61x62x66x49x43x50S + 1x75x24x6c! = (!0;!1) 2RS+1+ ,x53
124
x68x4fx1ex31x7x8x54x2cx68x14x25 2RK xcx2cx9xax56x5cx38x3dx2a
z0 = !0 ? 1x01 ?￠￠￠? Kx0K > 0
zs = !s + 1xs1 +￠￠￠+ KxsK > 0
s = 1;:::;S:
x10x3ex5ax23x24x28x44x1
z0 = !0 ? ￠x0 > 0
z1 = !1 + ￠x1 > 0
x25x18xbx70x2bx38x3dx2cx45x6ex4fx1ex31x49x17xbx17x70x70x2bx2cx68x14x25 ,x7bx58x7bx7x54
x4ex49x2x50x54x57x13x70x2bx38x3dx2cx45x6ex4fx1ex31x49x50x27x8x50x8x14x25x49x2ex10x70x71
x56x21x68x19x54x4ax6x48x7bx58x7bx7x54x4ex49x2x3bx54x57x58x75x39x10x3ex49x74x64x74x75x56
x57x4fx1ex31x54x1dx51x75x4x5bx43x50x2x5dx4fx1ex31x54x7x8x11x19x62x21x3fx6ex54x1ex3dx54
x65x18x78x12
B(!;x0;x1) =
8
<
:z 2R
S+1
+
flfl
flfl
z0 = !0 ? ￠x0
z1 = !1 + ￠x1
2RK:
9
=
;;
x10xcx1x4fx1ex31x54x4bx4cx79x78x4fx1ex31x4bx2fx54x2cx68x14x25x7x8x5fx60x2
‰ max u(z)
s:t: z 2 B(!;x0;x1) (17)
x25x70x5fx60x2ex70x62x51x1ex78xfx2x31x32x7fx25x26x54x5fx60x5bx36x51x1ex48x33x34x3ax3ex67
x33x55x13x4ex70x57x2ax7dx70x71x57x58x72x73x69x63xex4cx78x56x4bx54x62x69x57x7fx11xcx1x1d
x35x36x28x17x1fx37x38x36x3f2x48x10x74x75x2x45x10(RS;X;p(X))x44x54x33x6dx3cx61xd2
x54x78
x36x3f 5.5 x61x33x69x6ax7x20x21x6bx7x2 (17) x73x4ax79x62x49x63x4ex5fx60x1dx21
x7f(RS;X;p(X))x7cx79x18x4dx5fx7x202xaxbx7dx6dx6ex47x4cx37x1ex62x43x12y = ￠X
x67x68x75x76x64x65x6bx6cx57x58y = ￠X 2 RS xaxby > 0, x5dx5ep(y) > 0:x77x35
y > 0x36x37yx79x49x3cx22x38x6bx1x2x38x39x73x7axcx1dx68x0
x38x7a x31x32x5fx60 (17) x51x1e z? = (z?0;z?1) 2 B(!;x0;x1)x48x58x33x6dx3c
x61xd2x2ex9xax48x4x66x49x14x25 ? 2RK+1 x53x68
v0 = ?? 1x01 ?￠￠￠? ? Kx0K > 0
vs = ? 1xs1 +￠￠￠+ ? KxsK > 0
s = 1;:::;S; x2(v0;v1;:::;vS) 6= 0:
2x25x18x2ex4ax7x20x48x35x43x16x12x22x60x2ex43x5cx47x21x20 x6x72x73x5cx5dx7x5 x2cx6x7x3bx20x70x47x40x43
x16x29
125
x39x58x51z?+v = (z?0+v0;z?1+v?1;:::;z?S+v?S) 2 B(!;x0;x1), z?+v > z?.
x7bx7ex48 u(z? +v) > u(z?). x57z? x2x5fx60(17)x54x1ex5dx23x78 (x24x44x54x2cx68x5ax23
x3bx77x7ex11x1x60x29x1x2ax31x32x66x49x6dx3cx29x4dx48x33x34x4fx1ex31x67x23x2ex73x3cx3bx6d
x3cx29x4dx54x0x17x3cx21x48x24x5ex2ex66x49x15x6dx2cx68x14x25x78 )
x7ax75x48x31x32 (RS;X;p(X)) x44x54x33x6dx3cx61xd 2 x41x7dx48x33x34x26x1ex37x62
x4ax40x6fx62x695.4,x66x49?1;:::;?S > 0,x53x68
p(xi) = x0i = ?1x1i +￠￠￠+?SxSi ; i = 1;:::;K:
x39x58x10x66x15x1fz 2 B(!;x0;x1)x51
z0 +?1z1 +￠￠￠+?SzS = !0 +?1!1 +￠￠￠+?S!S = ?:
x25x18x1fx14x54?x57x58x6ex7ax2x4fx1ex31x6dx6ex54x2cx68x14x25x54x17xbx1dx51x54x4ax6x57
x50x27x1dx51x54x13x1ax6x75x4x48x25x2x2bx43x50x6x45x70x71x7x8x2x3bx6)x78x26x7ex23x24
x68x19x48
0 6 z0 6 ?; 0 6 zs 6 ?=?s; s = 1;:::;S:
x7bx7ex48 B(!;x0;x1)x2x2bx51x5bx69x78x10x18x48x10x74x7ax2x70x2bx67x69x78x25x26x48x5fx60
(17) x2ax1x49x70x2bx51x5bx67x69x44x39x7fx0x65x68x54x15x4ex6x5fx60x78x7bx7ex48x10x70x62
x51x1ex78 2
x25x38x62x69x5dx4fx1ex31x54x15x6dx2cx68x14x25x7x8x5fx60x57x33x6dx3cx61xdx61x4cx14
x27x78x10x5dx8x48x31x32x4fx1ex31x54x3ax3bx65x68x9xax79x41x42xdx2ex2ex21x6exfx54x25x6dx50
x61xdx48x33x34x15x6dx14x25x7x8x5fx60x51x1ex71x72x44x57x33x6dx3cx61xdx49x70x62x79x7ax56
x2x9x4ax54x78x5ax67x2x70x48x31x32x33x6dx3cx61xdx2ex41x7dx48x33x34x2ex23x25x7ex1fx70x71
x57x58x72x73x54xex4cx27x1x2cx68x62x4ax78x25x26x48x33x6dx3cx61xdx54x45x75x1dx67x21x0x23
x8x78
x56x5cx76x63x58x23x53x15x6dx2cx68x14x25x7x8x5fx60x54x1ex4ex70x57x57x70x71x4ax4bx61
x4cx14x27x78
x59x40 x20x41x42x67x7dxbx79x6b u xaxbx33x69x6ax7x20x6bx1x2x47x6x0x57x58x7
x2(17)x73x4az? 2 B(!;x0;x1),x1x2z? x79x1xcx49x3cx24x3ex6ex23x6bx5dx5ex60x61
x22x38x15x65”,x4x5
@u(z?)
@z0 = ”;
@u(z?)
@zs = ”?s; s = 1;:::;S;
x7ex7f?s, s = 1;:::;S,x67S xcx1ex1fx4dx6cx79x4dx6cx63x7(x6cArrow–Debreuxd
xex79x63x7)x0
x38x7a x2bx71x44x48x26x44x4bx54x2cx68x2cx23x24x3cx19x48 z?x5ax2x56x5cx5fx60x54x1ex2a
‰ max u(z)
s:t: z0 ?!0 +?1(z1 ?!1)+￠￠￠+?S(zS ?!S) = 0
126
x25x2bx5fx60x2cx12x35x61zx1x43x50x24x6cx54x65x18x4 2RK+1 x54x65x18x78xbx31x2x26
x66z? x54x74x2bx33x6cx5bx4ex66x7dx48x39x58x65x18x38x3dzs > 0, s = 0;1;:::;S;x54x38
x3dx2ex14x2ex3bx78x10x18x48x26x66x42x43x2x7ex7fx54x48x10x66x15x1f
z1 ?!1 = (z1 ?!1;:::;zS ?!S);
x3ax3ex5x25x60x19x24x17x54x14x25 z,x53x68
z ￠x1 = z1 ?!1:
x7bx7ex48x3x66 x54x65x18x5ax2ex14x2ex3bx78x25x26x48x3cx3b Lagrange x16x14x55x48x47
Lagrangex16x14x1”,x33x34z? x5ax2x53Lagrangex65x68
u(z)?”[z0 ?!0 +?1(z1 ?!1)+￠￠￠+?S(zS ?!S)]
x54x19x15x4ex6x54x1ex78x26x17x74x2bx70x7bx7x1fx68x49z?x73x1x7dx67x7dx4x1fx68x44x29x31
x32x78 2
x25x70x76x63x2cx54x0x61x70xbx20x54x61xdx78x17x2cx75x70x2x5fx60(17)x54x1ex75x49
x65x70x32x2ax54x10x32x54x19x78x35xex58x75x43x0x2ex9x26x65x18x48x53x76x63x2cx54x11xbx9
x26x2ax1x2ex9x26x78x4dx70x2bx2x7ex7fx42x43x61xdx78x35xex67x75x54x0x70x2bx42x43x2ex7e
x7fx54x38x3dx48x4x60x61 2RK,x4x5 ￠x1 = z1?!1. x4dx70x69x4bx48x4x53x61x62u
x23x1x48x25x18x54”x58x23x25x1x7dx78xfx2x31x32x13x61x62ux2zx54x7dx65x68(x25x5ax2
x57x7fx2ex54x61xdx48x10x79x41x42xdx17x72x3ax3bx49x3fxf)x48x33x34x13x0x44x25x6dx50x61xdx48
x70x62x51” > 0. x25x18x48x70x71x4ax4bx57xdx17x72x3ax3bxfx75x76x67x51x77x45x3x4cx78
x44x4bx21x70x54x25xbx38x3dx57x7fx23x24x7ex1fx56x5cx68x4fx61xdx27x54x19x2a
x4ex4fx50x7cx59x2ex2f u:RS+1+ ! Rx67x49x7x51x79x64x65x6bx6cx6dx6ex6fx70x1;x2 2
RS+1+ x71x6fx70? 2 (0;1), u((1??)x1 +?x2) > minfu(x1);u(x2)g.
x25x70x61xdx3ax3ex24x13x58x4dx3bx19x78
5.7 x15x13x48x3ax3ex12x70x2bx28x6dx54x71x72x7x3bx45x14x27x70x68x1ex37x62x4ax40x6f
x62x69x2x31x1fx7x3bx54x78x61x62x51x78x59x6ex66 A x4 B, x55x56x1cx7ax2x15x28x6dx54x8
x3ex64x8x70x71x55x56x78x25x78x59x6ex66x54x6ax73x4ax4bx31x56x60x2a
x3x1bx63x7 x1ex1fx63x7
x76x77A 62 100 30
x76x77B 56 40 90
x10x18x48x49x25x26x54x38x3dx56x48x51x78x2bx10x78x59x6ex66x54x4fx1ex69x6cx9x7dx44xex2a
xdx40x2x24Ax6ex66x4fx1ex28x48x58x2x24B x6ex66x4fx1ex28x78
127
x3x1bx3x6 x1ex1fx11xb
x76x77A 10 10 12
x76x77B 8 12 6
x25x2bx28x6dx3x58x7fx46x21x4dx48x54x45x14x2x55x70x68xbx7fx3fx6fx31x3bx11x12x69x55
x27x44xex2x4dx52x6ex6fx54x78xfx68x74x48x70xax3cx12xdx15x7x8x24Ax6ex66x4fx1ex48x7b
x1x24Ax6ex66x4fx1ex2ex4dx53x78xfx25x5bx2x36x51x47x48xbx4bx54x70x2bx60x54x31x32x78x15
x16x65x70x2bx60x48 x0x1x2cx2dx20x2ex2fx30x31x48x33x34x70x71x4ax4bx67x23x3cx62x48x39x58x67
x25x10x4fx1ex6bx34x54xdx17xbx4ax6xfx62x4ax78x2bx71x44x48x26
100p1 +30p2 = 62
40p1 +90p2 = 56
x23x1ex68x78x2bx70x71x4ax4bx33x3fx1p1 = 0:5, p2 = 0:4. x25x26x48x10Ax6ex66x54x4fx1e
x69x6cx54x54x1bx29(NPV, Net Present Value)x1
NPVA = 10p1 +12p2 ?10 = 10￠0:5+12￠0:4?10 = ?0:2;
NPVB = 12p1 +6p2 ?8 = 12￠0:5+6￠0:4?8 = 0:4:
x7bx7ex48x7x8x38x11x24B x6ex66x4fx1ex54x69x6cx78
x17x7ax48x25x2bx7x3bx45x14x4cx4cx2x27x79x1dx54x78x16x5ex25x70x6ax69x48x3ax3ex2exf
x4dx48x8x21x1x2x4x21x71x3bx54x45x14x27x78x25x18x48x15x0x7dx1fxax54x2x2ax22x1ax6x54
x6bx12x2ex2x3bx50x27x4ax6x54x68x4fx3ex2b (x7ex1fx4x6bx50x27x78x2bx70x71x54x71x72x23x25
x5fx36x54x25x27)x27x6bx12x54x48x58x2x7ex1fx26x33x6dx3cx61xdx1fx8x54x70x71x4ax4bx27x6bx12
x54x78
x2fx6a xbx3bx4x1cx51x21x2cx5x4ax10x5ex57x70x47x40x3cx4dx13x4fx48x4dx50 Rossx20APTx29xbx17x20
x4fx72x1x52x471982 x2 G. Hubermanx6xex20x33x6ax4fx2e(x5bx2cxex44x12[8]) x7x2ex2cx20x29x19
x1ax6xbx53x63x6aJarrow [10]x4dx2bx2cxbxax1x52x29x24x16x20x4ex4fx4ex48x6Huang–Litzenberger
[7] x20 104–108 x74x7x5dxex29 Duffie [4], [5] x34 Ingersoll [9] x60x2exe Huberman [8]x5 x3c
x60x24x25x2bx2cxbxax1x52x29x19x1ax6xbx53x79x21x2cx5x41x42x10x5ex7bx70x47x40x3cx4dx13x4fx47x52x37x3ax43x16
x7ax32x20xfx3dx61x3ax2cx2cx29 Cochrane [2]x7x7ex61xfx4ex5bxdx47x24x16x20x30x1x29x6x1cx19x20x27x7bx48
x33x28x7x64x2fx7x5x41x4dx60x2dx2bx61APTx20x73x4dx29x3bx56x20x0x52x47x8x3bx14x25x7ex2bx68x25 x25x7ex72
x71x20x7fx18x5 x1ex26x21x2cx5x1ax43x16x2bx12x12x4fx25x47x40x53x6x29xbx35x7ex47x37x3ax43x16x52x28x20x3bxa
x10x49x19x2dx42x13x29x76Rossx4x4dx20APTx79x52x1ax33x29x2bx3bx5x2ex4x20x12x3bx1x48x3x7ax36x1cx19x20
x27x7bx48x33x28x7x64x2fx7x20x10x5cx4fx63x6ax13x29
x7ex61x0x4ax20APTx7fx18x35x7ex4fx47x3bx14x26x2bx5x43x16x7fx18x29xbx58x19x6x41x65x47x2fx26x61
x2bx5x37x4dx20xcx30x29 x3cx47x27x44x4ax58x53x35x2ax2bx5x20x30x1x4dx7ax5x6ex48x26x2bx5x7fx18x60x33x16x53
x3bx14x3fx2bx5(x13x58x53x35x2ax2bx5)x7fx18x29 x43x5c5.3x39x35x26x11x20x4ex4fx4fx21x2cx47xbx17x20xex44x29
xbx53x19x1ax7cx77x47 Cochrane [2] x20x5bxdx29x1ax1ex5x68x6cx41x56x3bx58x59x33x20x30x1x4dx77x78x43x16
x18x25x27x20x58x59x2bx43x20x27x28x5x7ex47x6fx3bx14xcx30x29x6x48x35x43x16x20x7ex72x77x4fx7x5x25x12x23x2b
128
x13x14x35x3bx6x53x5cx29 x3cx47x41x5cx4fxfx4dx2dx5 x46x2cx37x3ax43x16x52x28xax2ax5x41x25x20x43x16x7fx18x74
x43x60x47x10x3fx2bx5x7fx18x13x29
x62x27x19x1ax6x10x11x41x26x13x7x41xdx5x70x47x40x3cx4dx1cx51x47x6Modigliani–Miller 1958x2
x20x58x1cx4fx2ex7x42x7dx2ex2cx20x29x6x31x4x51x7cx20x2ex4ax7x5x70x47x40x3cx4dx1cx19x2cx4a Duffie [4],
Ingersoll [9] x20x29x43x69x7dx5 x35x7x15x47x40x53x6x34x77x37x12x3bxax47x40x53x6 (x1ax4x16x13x9x62x5
x59x4dx16x13x37x62)x18x12x22xax47x40x53x6 (x1ax4x16x13x37x16x5x59x4dx16x13x9x16)x29xbx17x3bx4dx5x32x33
xfx6x3cx20x3dx26x2bx74x2cx20x3ex3fx29x19x1ax20x0x52x24x16x53Jarrow [10]x52x70x47x40x3cx4dx20x29x43x69
x7dx5 x35x7x42x7dx2ex2cx10x43x16x7ax32x13x20xexfx5x23x44x1cx3fx28x6ex58x15x12x3bxax47x40x53x6x38x64x6ax5
x45x44x47x3bx18x3fx7bx4ex4fx29
x48x35x43x16x60x2ex43x5cx20x60x2ex45x2fx1cx51x2cx2ax6Ross 1976x2x27x53x47x40x43x16x5cx4fx20x58
x1cx2ex4a[13]x7x5 x35x7?ix46x7cx3x10x2bx68x16x17x13x20x44x33x29x42x7dx3x9x12x55x7fx18x20x69x7dx20xfxd
x48x35x43x16x60x2ex43x5cx28x2cx2ax6Ross 1978x2x24x29x20[14]x7x29 1979x2Harrisonx34Kreps
[6]x2dx15xbx36x43x5cx2x3x43x5c5.4’x7ex17x20x55x13x13x69x7dx29x53x47x4fx48x5cx28xexex41x4fx7x20x7dx20
xexf(x17x6cxex2dx5x7dx4fx47x10x59x4dx13x20x55x13x13x33x53x1ax4x13x20x58x53x3fx37)x29x26x4dKreps [11]
x2dx15x48x35x43x16x60x2ex43x5cx73x1axex3bx56xbx69x5xax35x47x59x4dx16x17x37x3dx61x58x53x62x3bx20xbx69x29
x35x32x33x72x42x20x27x3bx1dx1ex6x53x7ex27x77x76x43x5cx5 x3cx38x39x20x66x3bx60x14x47x70x7ex65x20x29x12x14xf
x20x62x15x4ex5dx5ex41x46x25x9x14x12xfx24x60xex26x14x12x55x5x42x7dx3dx61x62x15x5x16x17x20x43x16x45x2fx1d
x1ex48x3x4ax2ax41x20x32x33x63x25x4dxex4fx29xbxax1x52x33x37x7dx1x52x29x19x1ax23x6x3x26x5ax4dx7bx3bx59
x2bx2cx29
x19x1ax20x12x3bx14x72x42x7ex61xfx47x21x50x47x41x42Hahn–Banach x43x5cx20x72x42x29x27x41x34x64x5
xbx3bx43x5cx47x18x7ex27x77x76x43x5cx33x16x20x29x25x27x7ex27x77x76x43x5cx20x64x44x48x7cx7ax3bx18x32x33x7bx57
x5cx4fx7cx7ex77x4fx1x11x20x7x64x2fx29
Duffie [5]x15x48x35x43x16x60x2ex43x5cx2axex11x12x58x59x33x20x1cx2cxex6ax29x1ex7cx7ax28x20x121x6bx29
Ingersoll [9] x20x12 2 x6bx4ex47x13x50x3bx1fx20x64x65x29 Huang–Lizenberger [7] x20x25x27x64x65x6
x12 8 x6bx5xbx47x2bx37x47x2fx3x43x20x47x63x37x20x10x5ex11x43x16x13x29x5dx36x34x75x20x47 Jarrow [10] x7
x4dx1ex24x25x42x7dx2ex2cx48x35x43x16x60x2ex43x5cx29
x48x35x43x16x12x22x60x2ex43x5cx20x2dx52x2bx7x1bx3dx29x25x12xbx3bx44x33x47x21x10x72x73x5cx5dx5cx5x48
x35x48x7x3bx43x16x13x29x6x71x2ex19x4ax20x7x64x2fx7x5 x46x25Duffie [5] x2exex24x16x20xex44x29x19x1ax20
x5bxdx2ax62x57x53 Magill–Quinzii [12]x29xbx3bx43x5cx2dx42x70x47x40x3cx4dx2bx3cx47x3bx56x58x59x5ex11
x20x73x4fx5 xdx7dx47x3bx56x58x59x5ex11x20x4x2ex5x18x28x24x25x3bx14x58x59x22x34x70x35x3cx35x6fx4ax20x9x29
x20x26x20x19x5x2fx45 Copeland–Weston [3]x5 126 x74x5x6x7ex53x19x1ax79x48x7axex35xex20
x0x4ax19x5x29
x44x30x23x41x45x23
1. x37x34x2xdx7dx5dx33x6dx3cx61xdxfx7ex32x26x69x1ex25x70x61xdx7ex1x37x34x2ex25x3bx77
x7ex54x33x6dx3cx61xdx27x1fx8x10x7e
2. x3bxdx7dx5dx33x6dx3cx61xdxfx1fx8x54APTx2x32x26x54x31x63x7ex10x58x51x37x34x3f
x54x61xdx7e
3. x32x26x27x69x1ex4x7dx52x25x18x1fx8x54APTx7e
129
4. x37x34x2x1ex37x62x4ax40x6fx62x69x7ex10x2x32x26x27x23x34x33x6dx3cx61xdx54x7ex32x26
x69x1ex10x54x57x58x79x7ax7e
5. x32x26x10xdx50x62x42x43xfx74x40x3cx3bx24x6cx72x76x20x37x27x60x54x3x69x1ex24x58x2c
x68x1ex37x62x4ax40x6fx62x69x7e
6. x49x50x62x42x43x74x40x56x48x37x34x2x7ex7fx42x43x7ex10x7ax7bx61x70x64x32x26x54x1ax71
x3dx3ex42x43x54x5dxdx7ex10x54x40x6fx1dx60x2x37x34x7e
7. x37x34x21x56Arrow–Debreux2cx68x7ex1ax71x4cx5bx2cx51x25x26x54x2cx68x2x7ex1x37
x34x75x0x4ex25x26x54x2cx68x7ex10x3ex51x37x34x57x58x4fx79x7ax7e
8. x47x48x70x2bx60x3ex2cx68x42x43x55x56x48x17x2cx51xdx11x17xfx3 xdx68x17xfx3 xdx13x17xf
x60x2bx18x23x78x39x11x17x3cx68x17x48x68x17x23x25x51x78x2bx70x71x48x58x39x68x17x54x15
x1fx70x2bx70x71x3cx13x17x48x13x17x5ax23x25x51x78x2bx70x71x78x39x58x48x39x11x17x3cx13
x17x48x13x17x23x25x51x47x2bx70x71x78x49x25x26x54x55x56x2cx48x32x26x7ex1fx2cx68x13x17
x54x4ax4bx27x1x10x54x68x17x62x4ax24x58x1x10x54x11x17x62x4ax7ex25x18x48x5ex5fx75x51
x3x2bx2cx68x78x25x53x25x2bx2cx68x42x43x1x7ex7fx42x43x7ex1ex37x62x4ax40x6fx62x69x7
x8x32x26x76x29x7ex76x16x5ex25xbx2ex63x7bx5dx54x64x79x47x29x48x49x8x37x1fx54x68x4f
x47x29x48x51x5dx8x48x16x5ex13x17x1x11x17x33x6dx3cx62x4ax54x1dx33xcx75x38x3dx2x13
x17x1x68x17x62x4ax24x58x68x17x1x11x17x62x4ax5bx2x33x6dx3cx54x78
9. x32x26x69x1ex62x695.5x54x76x63x7ex25x70x76x63x5ax23xcx1x2a xdx70x71x4ax4bx9x66x17
x72x3ax3bx75x77xfx48x10x57x1x76x57x58x4fx2cx54x34x35x69x63x51x37x34x7bx10x4x2ex10
x75x73x7ex10x3ex25x2ex25x51x70x2bx63x10x54x68x4fx55x56x7e
10. x3ax25x4dx48x70x2bx575.7x51x2cx7bx72xdx54x1ex37x62x4ax54x45x14x2x7ex3bx33x6dx3c
x62x4ax27x2ex4fx1ex33x14x2x35x3bx51x2ax69x7ex46x19x29x10x54x69x26x4x2exax78
x2fx30x31x32
[1] Clark, S. A., 2000, Abitrage approximation theory, Journal of Mathe-
matical Economics, 33: 167–181.
[2] Cochrane, J. H., 2001, Asset Pricing, Princeton University Press, Prince-
ton, N. J..
[3] Coperand, T. E., and J. F. Weston, 1988, Financial Theory and Corpo-
rate Policy, Addison-Wesley.
[4] Duffie, D., 1988, Security Markets: Stochastic Models, Academic Press,
Boston.
130
[5] Duffie, D., 1997, Dynamic Asset Pricing Theory, Second ed., Princeton
University Press, Princeton, N.J..
[6] Harrison, J. M., and D. M. Kreps, 1979, Martingales and arbitrage in
multiperiod securities market, Journal of Economic Theory, 20: 318–
408.
[7] Huang, Chi-fu & R. H. Litzenberger, 1988, Foundations for Financial
Economics, Prentice–Hall, Englewood Cliffs, N. J..
[8] Huberman, G., 1982, A simple approach to Arbitrage Pricing Theory,
Journal of Economic Theory, 28: 183–191.
[9] Ingersoll, J. E. Jr., 1987, Theory of Financial Decision Making, Rowman
& Littlefield Publishers, Maryland.
[10] Jarrow, R. A., 1988, Finance Theory, Prentice-Hall, Englewood Cliffs,
N. J..
[11] Kreps, D. M., 1981, Arbitrage and equilibrium in economics with in-
finitely many commodities, Journal of Mathematical Economics, 8: 15–
35.
[12] Magill, M. & M. Quinzii, 1997, Theory of Incomplete Markets, Vol. 1,
MIT Press, Cambridge, Massachusetts.
[13] Ross, S. A., 1976, The arbitrage theory of capital asset pricing, Journal
of Economic Theory, 13: 341–360.
[14] Ross, S. A., 1978, A simple approach to the valuation of risky streams,
Journal of Business, 51: 453–475.
x5cx5dx2ax42x43x1dx1ex1fx203
x5bx79x41x5bx79x27x39x36x3fx2ax24x6cx72x76X x2cx54x69x25Axcx1x5bx79x2x5d
8x;y 2 A;8? 2 [0;1]; (1??)x+?y 2 A:
x17x3x1fx79x7ax2x69x25Ax2cx54x15x1fx78x77x54x7fx38x1cx42x5bx49Ax2cx78x26x69x33x5bx62
x69x2x26x69x54x40x6fx1dx60x48x17x3x1fx79x7ax2x78x2bx2ex7bx66x54x26x69x70x62x23x24x3bx66
x36x4bx27x33x5bx78x25x2bx1dx60x79x7ax23x24x4cx4cx49x24x6cx72x76x54x5ax52x2cx27x76x29x48xf
x1x61x28x6dx14x4fx48x3ax3ex61x62x25x2bX x51Hilbertx72x76x31x4dx78 X x2cx54x66x36x4b
131
H x2x5dX x54xdx40x75x68x11xfx54x14x72x76x54x36x77x78x40x75x68x11xfx54x14x72x76x2
x5dx10x23x24x60x27x1x57X x2cx54x70x2bx35x62x24x6c?x68x18x54x24x6cx7fx1fx48x4
L = fx 2 Xj(?;x) = 0g:
x7bx7ex48x70x2bx66x36x4bH x2ex1Lx54x36x77x48x23x24x60x27x1
H = fx 2 Xj(?;x?x0) = 0g = fx 2 Xj(?;x) = fig;
x17x2cx0 x2H x2cx54x70x2bx35x62x77x48 fi = (?;x0). x66x36x4bH x5dx1ex2bx72x76X x33
x1x78x2bx44x72x76x2a
H+ = fx 2 Xj(?;x) > fig;
H? = fx 2 Xj(?;x) 6 fig:
x70x2bx66x36x4bx5dx78x2bx2ex7bx66x54x26x69x33x5bx2x5dx78x2bx26x69x33x3fx65x49x25x78x2bx44
x72x76x2cx78x25x67x2x70x48x31x32Ax4B x2x78x2bx2ex7bx66x54x26x69x48x33x34x26x69x33x5b
x62x69x53x5dx8x48x66x49x70x2bX x2cx54x24x6c?,x53x68
8x 2 A;8y 2 B; (?;x) > (?;y);
x17x2cx44x62x66x36x4bx6ex6fx54x7fx68fix49x25x18x33x3x5fx75x78x44x26x74x7ax9x4ax66
8x 2 A;8y 2 B; (?;x?y) > 0
x6fx31
8z 2 (A?B); (?;z) > 0:
x26x66K = A?Bx5ax2x26x69x48x58Ax57Bx2ex7bx66x9x4ax66x6ax770x2ex49K x2cx48
x46Ax4B x23x3bx66x36x4bx33x5bx9x4ax660x57K x54x33x5bx78
x36x3f 1 x57x58 K ‰ X x67xax55x56x31x6d 0 x79x45x66x5bx6bx5dx5ex60x61x48x3c
? 2 X,x4x5
8z 2 K; (?;z) > 0:
xdx27 x25x2bx62x69x54x2cx68x57Hilbertx72x76x54x3bx66x33x1ex62x69x54x2cx68x5ex55
x2x70x26x54x78x26x660x2ex49x67x26x69K x2cx48x460x19K x75x76x51x70x3bx2ax5bx78x57x3b
x66x33x1ex62x69x70x26x48x23x39x8x57K x2cx54x5b0x15x5dx54x77?. x66x2x3ax3ex51
8z 2 K; kzk>k?k:
xfx2x26x66Kx2x26x69x48x46x10x66x15x1fz 2 Kx4? 2 (0;1)x5ax51(1??)?+?z 2
K. x66x2x7fx51
8? 2 (0;1);8z 2 K; k(1??)?+?zk2 >k?k2:
132
x1ex14x3fx6fx23x68
k?k2 +2?(?;z ??)+?2kz ??k2 >k?k2:
x7bx7ex48
(?;z ??) >??2kz ??k2:
x26x66x44x26x10x15x1f? 2 (0;1)x5bx41x7dx78x12? ! 0,x4x68
8z 2 K; (?;z) >k?k2 > 0:
2
x26x7ex4x68x56x5cx62x69x2a
x36x3f 2 (x5bx79x27x39x36x3f) x57x58Ax71B x67Hilbertx44x45X x7fx79x0xc
xax25x4cx79x66x5bx6bx1x2A?B x67x45x5bx6bx5dx5ex60x61x48x3c? 2 X,x4x5
8x 2 A;8y 2 B (?;x) > (?;y):
133
