x51x12x1x52x15x16x53x54x55x3fx40x30x31
x2dx2ex7ax2fx20 x52x3bx55x58x59x5ax11x20x5cx4fx70xcx25x38x25x5ex20x5cx20x29 x47x20x44x73x4ax58x59x20x3b
x55x58x59x5ax11x20x2cx6x43x5cx3x39x28x18x11x12x5cx5dx5ax11x23x14x20x27x28x29x52x2bx72x73x11x12x5cx5dx20x3b
x55x5ax11x5cx4fx25x42x7dx20xexfx29 x47x20CAPMx34APMx65x17x41x3bx55x58x59x5ax11x20x70xcx50xex29
x30x22x48x31x32x33x20 x36x3ax11x32x29x5bx33xex41x4f (x58x52x62x3bx20x32x33x55x13x25 x1x31x25 x4ax1x31
x33)x29x5bx33x27x77x33x6dx2cx57x32x5x35x6bx5cx13x20x74x2cx35x6b)x29
x59x34x20
? 7.1x44x73x4ax58x59x20x32x33x29x43x29
? 7.2x44x73x4ax58x59x20x3bx55x58x59x5ax11x20x2cx6x43x5cx29
? 7.3x11x12x5cx5dx20x3bx55x5ax11x20x2cx6x29
? 7.4 CAPMx20x5ax11x43x16x4ex4fx29
? 7.5 APTx20x5ax11x43x16x4ex4fx29
x5cx14x19x32x17x40x2cx4fx1fx27x57x39x3ax1fx59x23x30x31x2cx3ex3fx58xbx17x40x6ex28x3e
x49x4ax77x79x7ax5fx52x75x28x6x20x3ex2ex2fx7cx7dx4dx3ex6ex62x30x31x76x77x6ax5ex3fx49x1ex27x57
x1fx23x20x7cx7dx4dx3ex30x31x2cx3ex30x31x2x7ax7bx69x65x4ax36x15x6bx45x46x6cx6dx57x45x29x36
x20x7cx7dx3ex31x0x3ex75x14x49x3bx1fx65x43x44x45x46x47x6fx78x14x76x3ex3ex45x46x47x3ax3bx49x56
x1fx6cx4ex57x65x1fx15x58x16x17x3ex45x46x15x16x77x53x1cx43x44x31x0x6cx64xex75x14x3ex57x45
x5fx1fx28x6fx18x75x14x42x46x38x0x57x46x5cx15x58x6ax59x10x57x3ex13x14x49x59x1ex57x3ex64x39
x3ax4cx4fx52x0x1x50x67x4ex57x3bx0x7dx46x6cx15x5ex4fx5cx16xax3cx50x49x1ax4bx41(x14x61)x47
x42x3ex47x46x4dx2cx1ax4bx23x9x43x44x3fx2x3ex7fx3ex2cx77x4ex57x3bx59x5ax74x5fx15x75x7ax4d
x47x5cx59x5ax69x77x43x44x31x0x3fx42x75x14x3ex3cx2cx3ex41x42x57x45x6cx5bxbx1ax43x44x31x0
x75x14x5ex3fx3ex45x46x47x5cx3cx20x1bx77x78x3ex61x62x49
x65x18x78x3bx0x3ex5ex3fx57x39x3ax5fx53x54x15x20x45x64x3ex15x6bx45x46x6cx6dx61x78x49
7.1 x45x64x3eArrow–Debreux15x16x4dx33x45x46x3ax3bx2cx2ax65x51x33x73x7ax7bx2c
x6ax46x0x2cx49x1ax39x3ax1fx20x3ex18x78x77x4ex57x39x3ax5fx54x54x25x46x0x2cx49x4bx6cx15x16
x4dx46xax20x7ax7bx2cx49x71x71x48x75x3bx39x7ax7bx2cx3ex7x47x7x5cxfx10x41x73x31x65x49x4a
x4bx45x46x4dx8x5cx46x0x57x23x45x3bx15x45x46x4dx3ex45x46x3ax3bx46xax20x7ax7bx2cx3ax58x56
x32x11x3ex41x73xbx9x49x3bx0x3ex45x46x25x65xbx10xbx64x65x49x4cx11xbx9x45x46x4dx3ex15
x6bx45x46x6cx6dx3ex74x4cx5ex3fx1fx6cx7bx69x4dx6cx10x74x4cx15x58x15x6bx45x46x6cx6dx14x24x18
xdx57x5bx29x30x15x58x7ax7bx2cx46x5cx7ax59x46x3bx15x14x24x18xdx77x8x58x7x4dx3ex41x73x29
x36x15x7x7dx57x1fx40x3bx7x7dx75x1x3cx5cx7ax3ex41x73x57x5bx29x3cx3ex7ax7bx17x40x6ex28x49
x3ax4cx39x3ax5bx3bx15x5ex3fx4fx47x12x3fx51x49x48x75x45x46Ex4dx5cLx5ex41x73x57 Ix58
x7ax7bx2cx49 Lx5ex41x73x3ex10x59x1fx40RLx4dx3eLx7ex8x10z = (z1;:::;zL)x77x72x5x57
160
x69x4dx30x15x58x2ax10x52x72x30x15x5ex41x73x3ex10x4ax45x30x58x7ax7bx2c i x46x4ax51x58x3bx68
x77x28x3cx73x15x6cx3cx67x22x5cx3ex31x65x41x73!i 2RL+,x65x72x5x7ax7bx2cix67x22x5cx3ex5d
x5ex41x73x3ex10x4ax4bx15x6cx3cx3ex17x40x2cx4fui,x65x40x77x28x3cx7ax7bx2cx3ex7ax7bx69x65x49
x3bx0x57x3bx58x45x46E x56x59x1fx3cx55x2x52x3dx72x5x65E(u1;:::;uI;!1;:::;!I) =
E(u;!).
x48x75x7cx7dx26x2dx45x5cx15x58x14x24x18xdp = (p1;:::;pL) 2RL+,x65x3ex5dx58x2a
x10x52x72x5dx5ex41x73x3ex14x24x57x74x58x5fx58xex56x14x24x59x5ax6cx5x49x39x3ax77x4bx37x7a
x7bx2c i x6cx64xex77x34x69x3cx3ex7ax7bxfx29x3ex49x3bx71x57x15x58x41x73x8x10 z x3ex14x1
x1fx6c
p￠z = p1z1 +￠￠￠+pLzL:
x45x7ax7bx2cix59x5ax3bx40x3ex31x43x56x1fx6c
p￠!i = p1!i1 +￠￠￠+pL!iL:
x3bx6ex57x7ax7bx2cix59x5ax7ax7bx3ex41x73z x15x75x7ax37x38
p￠z 6 p￠!i:
x4ax4bx39x3ax15x6bx7x48x75x17x40x2cx4fx37x38x4cx15x6bx4dx69x60x3ex3fx61x40x48x4b(x59x1ex57
x40x4cx3ex17x40x2cx4fx3ex75x54x6dx7ex4cx15x6bx4dx3ex5cx67x5fx60)x57x24x7ax7bx2cx65x4ax36x69
x6ex62x7ax7bx57x3ax6cx7ax33x7dx2fx7fx57x19x1ax3cx3ex6ex62x7ax7bx5ex3fx57x46x5cx4bx37x6x13
x36x6dx3ex73x12x49x3bx6ex57x12
B(!i;p) = 'z 2RL+jp￠(z ?!i) = 0“:
x38x53x7ax7bx2cx1bx1bx3ex1fx6cx20x70xfx29x5ex3fx73
‰ max ui(z)
s:t: z 2 B(!i;p) (1)
x3bx15x5ex3fx5fx15x75x5cx62x49x20x70x75x61x4cx4fx47x26x6cx31x0x75x14x68x70x2fx7bx75x61x3e
x60x51x73x12x57x65x7bx60x57x4cx17x40x2cx4fx3ex3fx61x40x48x4bx20x57x5ex3fx5cx62x3ex2ex2ax54
x7ax75x76x6cx5fx5ax5cx57x3ex3ex41x73x14x24x49
x56x39 7.1 x4bx3ex72x73x72x3x4x55x66x74 (1) x5bxfx64x24x25x26x27x28x29x1cp 2
RL++,x62x6fRL++ x7bx7cx56x5bx25x2fx7x1cx52x64Lx20x2ex2fx67xcx6b
x24x3a x64x4ex5cx15x5ex41x73x3ex14x24pl = 0,x38x53x12
vl = (0;:::; 1|{z}
x39l x75
;:::;0) 2RL;
x1ax4bxdxez 2 B(!i;p)x3ax5cz+vl 2 B(!i;p). x4ax3fx61x40x48x4bx57 ui(z+vl) >
ui(z). x3bx6ex57 ui x4cB(!i;p)x4dx5fx59x5ax5cx6ex28x1x49
161
x40x32x57x64x4ep 2RL++,x38x53x1ax4bxdxez 2 B(!i;p),x7x1ex5c
0 6 plzl 6 p￠!i; l = 1;:::;L:
x23x45zl 2 [0;p￠!i=pl]. x3bx4ex2x57 B(!i;p)x6cx15x58x5cx58x2ax57x1fx55x26x65x6cx58
x5fx2ax1fx25ui x6cx6bx17x2cx4fx57x5ex3f (1)x15x75x5cx62x49 2
x33x3bx75x75x61x7ex31x0x75x14x68x70x2fx7bx75x615.5x58x1bx1cx57x56x59x5bx39x3ax1ax5a
x1bx1cx48x4bx5cx34x15x4cx61x62x49x3bx75x75x61x6cx4ex57x64x4ex5cx3ex41x73x5fx7ax7dx57x45x5f
x14x2x53x41x73x57x1ax7ax7bx2cx77x4ex57x3ax6cx8x71x8x2cx57x38x53x7ax7bx17x40x6ex28x51x5e
x3fx1fx5fx59x5ax5cx62x49x7ex31x0x75x14x68x70x2fx7bx75x61x58x1bx1cx57x1fx59x1fx27x36x57x5a
x1bx1cx48x4bx58x59x4bx8x5cx5fx7ax7dx3ex41x73x49
x57x5cx15x61x5cx7ax6fx7ax3ex6cx57x4cx5ex3f (1)x4dx3ex14x24px60x3ax4cx15x58x6fx18x60
x26x6ax3fx4dx49x3bx7ax4dx47x57x64x4ex67x5cx41x73x3ex14x24x7x26x12x4dx20x13x60x0x3exbx4fx57
x38x53x65x1ax3dx77x3ex5ex3fx5fx5bx5cxdxex69x6ax49x3bx1fx6cx4ex57x48x7ax3ex7cx7cx6cx5dx5e
x41x73x14x24x32x11x3ex58x56x1bx1cx57x45x5fx6cx65x3ax3ex5ax1ax1x49x3bx6ex57x39x3ax3ax59x71
x37x1bx5ex41x3fx77x5bx14x24xax3cx51x49x71x40x3ex41x3fx5cxfx5ex49x15x5ex6cx48x75x67x5cx14
x24x32x6ax651,x3bx5ex41x3fx1bx1cx3cx1ex57x6bx6cx23x4fx47x26x77x4ex57x67x5cx59x5ax3ex14x24
x2ax77x12x13x15x58L?1x7ex3ex61x11x121x57x5cx71x5bx67x77x4fx47x26x3ex5fx41x55x4ax15x5e
x6cx48x75x67x5cx14x24x3ex36x41x6ax65 1x57x3bx71x67x5cx59x5ax3ex14x24x12x13x15x58x4bx1bx3e
x15x29x2ax57x21x14x4cx3ax3fx72x58x55x63x73x59x3bx0x77x18x61x14x24x57x6bx3bx0x7dx4cx4fx47
x26x5cx69x41x55x32x18x4ax57x5cx15x5ex41x3fx6cx48x75x68x15x5ex41x73x3ex14x24x651x57x66x67x26
x3bx6cWalrasx5ex5fx3bx0x7dx3ex57x3cx51x65x3bx6cx33x66x67x59x3ex68x15x5ex41x73x57x45x66
x67x3ex14x24x3ax6c1x49x39x3ax4cx20x1bx5fx58x1ax14x24x5fx3exax3cx51x48x75x57x45x4cx5ex3fx3f
x62x4dx57x27x77x15x5exax3cx41x3fx41x55x1fx40x77x15x5ex49
7.2 x3ax4cx39x3ax77x4bx37x45x46E(u;!)x4dx3ex15x6bx45x46x6cx6dx5ex3fx49x3bx15x5e
x3fx59x72x21x65x73x3fx14x24x18xdp? 2RL++ x6az? = (z?1;:::;z?I) 2 (RL+)I =RLI+ ,
x5bx29
i) x1ax4bxdxei = 1;:::;I;x1ax4bxdxez 2 B(!i;p?), ui(z) 6 ui(z?i);
ii) z?1 +￠￠￠+z?I = !1 +￠￠￠+!I:
x37x38x3bx0x75x76x3e (z?;p?) 2 RLI+ ￡RL+ x25x65x45x46 E(u;!) x4dx3ex18x63x66x67
(General Equiribrium, GE)x49x3ex64x39x3ax42x45x4cx4fx52x0x1x50x4dx43x44x37x3ex57x3b
x5ex33x16x3ex15x6bx6cx6dx3ex74x4cx5ex3fx57xbx3ax45x37x28x70x58x72x73x1ax2bx29x1bx1cx2cx2dx49
1x6nx68x66x3bx63x14x7x5 n+1x14x2bx6x16x3bx14n?1x68x3ex59x11(x36x3ax5x63x14x20x59x49)xf
x20x1x41x69xax20x20x55x56x26x32x37nx68x3fx44x69x29x19x27x5x22x68x63x14x7x20x13x14x2bx4ax36x20x1x41x69
xax20x3fx44x69x4fx47xbx13x14x1x69xax20x13x7ex69x29
162
x65x5bx15x6bx6cx6dx74x4cx57x39x3ax57x5cx7ax1ax17x40x2cx4fx3ex39x48x4bx49x20x1bx6cx69x4dx32
x15x49
x79x6bx7ax27x5dx4ex4f u:RL+ !Rx51x6fx1bx7bx25x4ex4fx55x56x57x58x59x5az1;z2 2RL+
x61x59x5a? 2 (0;1), u((1??)z1 +?z2) > minfu(z1);u(z2)g.
x23x24x28x2cx4fx15x75x6cx23x24xdx28x2cx4fx49x3bx6ex57x23x24xdx28x2cx4fx33x68x36x67
x5cx4fx36x42x17x40x23x24x2ex64x50x3ex17x40x2cx4fx49x40x32x57xdx28x2cx4fx5fx15x75x6cx28x2cx4fx49
x63x64x57x61x70x10x2cx4fx4dx3ex23x24x61x40x2cx4fx15x75x6cx23x24xdx28x2cx4fx57x6bx5fx15x75
x6cx23x24x28x2cx4fx49x5fx37x4cx71x70x10x2cx4fx73x12x20x57x23x24x61x40x2cx4fx5fx15x75x6cx23
x24xdx28x2cx4fx49x10x46x39x3ax1fx46x5cx7ax3fx61x40x48x4bx57x45x5fx1fx5cx7ax3bx75x23x24xd
x28x48x4bx49
x20x70x75x61x6cArrow–Debreux15x6bx45x46x6cx6dx74x4cx75x61x3ex43x43x73x12x49
x56x39 7.2 x2ex2fxexfE(u;!)x6ax64x75x4fx4ex4fx7x79x7ax3ex72x73x72x3x61x6f
x1bx7bx25x72x3x55x6cx6d!1 +￠￠￠+!I 2RL++,x1fx20E(u;!)x6ax4ax4bx65x7ex3bx10x6b
x24x3ax34x49 x23x24x16x17x3dx2ex2x3bx75x75x61x57x60x14x7bx6bx54x3ex3cx3dx49x6bx6c
x39x3ax59x1fx60x21x15x20x65x3ex2ex2x72x78x49
x5ex5fx75x54x1ax4bx30x58x7ax7bx2cixcx4bx14x24px3ex5cx3fx2cx4ffi:RL++ !RL,
x69x4dx1ax4bxdxex14x24p 2RL++, fi(p)x1fx75x54x65x5ex3f (1)x3ex62x49x1cx40x3fx61x40
x48x4bx57x59x65x3bx0x3ex62x6cx74x4cx3ex4ax45x1cx40x23x24xdx28x48x4bx57x5fx63x2ex2x3bx0
x3ex62x6cxfx15x3ex49x3bx6ex57x3bx0x75x54x5cx3fx2cx4fx6cx59x5ax3ex49
x69x26x75x54x20x45x46x3e (x19xe) x6b (x2f) x11 (x12) x36x69 (aggregate excess
demand function) Z:RL++ !RL,x65x75x54x65
Z(p) =
IX
i=1
(fi(p)?!i):
x69x53x54x6cx3ax5cx3fx7ex3ax77x7ex32x5cx49x4bx6cx15x6bx6cx6dx3ex74x4cx5ex3fx41x46x65x3bx58
x57x5cx2cx4fx5cx8x5cx5x61x49
x3ax75x65x5cx5x61x3ex15x5ex41x42x6cx5fx33x14x24xax3cx51x65
p 2 S = fp 2RL+jp1 +￠￠￠+pL = 1g:
x3bx6dx14x24px5fx1fx7ax3fx69x2ax10x7x65x3ex49x60x71x57x33Z x6bx17x67x2dx36S x26x49x60
x61x67x2dx6cx7dx5fx36x3ex57x3bx65x59x1bx15x41x73x3ex14x24x38x4bx5x71x57x3ex64x39x3ax4cx75
x617.1x4dx67x7bx60x3ex57x1ex41x73x3ex3ax5cx3fx5bx38x4bx5ax77x49x65x7ax23x3bx15x6cx63x57x39
x3ax59x1fx1ax5ex3f (1)x1fx55x77x15x49x63x64x57x7ax3fx30x5ex41x73zlx3ex5cx3fx5fx57x37x1ex41
x73x3ex3ax77x7ex49x4bx6cx30x58x7ax7bx2cx3ex5cx3fx2cx4ffi x1aS x4dx3epx7x5cx75x54x57x74
x58x6cx15x58x6bx17x1ex4x49x23x45Z x56x6cS x26x3ex6bx17x1ex4x49x5ex3fx41x46x65x15x58x6b
163
x17x1ex4Z:S ! RL x6cx10x5cx5x61x49x5cx15x75x65x2ex2x3bx15x46x4ex45x47xbx74x3ax3e
Debreu–Gale–Nika¨?dox75x61x7bx60x57x64x4ex1ax4bxdxep 2 S, Zx37x38p￠Z(p) 6 0
(x65x25x65x56x54Walrasx42x46x57x69x53x54x6cx4fx3ax13x60x5fx5ax57x37x3ax6x78x50)x57x38x53
x74x4cp? 2 S,x5bx29Z(p?) 6 0 (x3bx6cx15x58Lx7ex8x10x5fx6ax3fx57x69x53x54x6cx30x5e
x41x73x3ex5cx3fx7x5fx57x37x77x7e)x49x3bx75x75x61x7ex1x24x3eBrouwerx5fx3bx61x75x61(S
x36S x3ex6bx17x1ex4x5cx5fx3bx61)x6cx6ax14x3ex49x3bx6ex57x69x2ex2x58x59x6cx63x49x1ex27x57
x1fx59x46x3fx61x40x48x4bx59x7bx60x57x3bx58p?x52x72x3ex14x24x18xdx1fx6cx15x6bx6cx6dx14x24
x18xdx49x9x3fx26x57x4ax4bx30x58x7ax7bx2cx7x5fx59x5ax75x77x7ex57x37x5cx3fx57x6ex1ex46x4e
x15x75x6cx77x5cx58x6ax49
x4bx15x5ex3ax75x65x5cx5x61x3ex41x42x6cx5fx33x14x24xax3cx51
p 2 P = fp 2RL++jp21 +￠￠￠+p2L = 1g;
x1fx1ax17x40x2cx4fx55x26x7fx3bx18x48x4b (x2cx4fx5ax77x26x59x6a)x49x4bx6cx5ex3fx41x46x65x3f
x15x58x7fx3bx1ex4Z:P !RL x6cx10x5cx5x61x3ex5ex3fx49x3bx58Z x59x1fx61x62x65x67x36
x7fx3bx8x12 P x26x3ex8x10x7dx57x3bx65x65x37x38 p ￠ Z(p) = 0 (x65x25x65 Walras x42
x46x57x69x53x54x65x4fx3ax13x60x6ax4bx3ax6x78x50x49x3bx58x6ax3fx72x5x51x58x8x10x25xax57x3b
x6e Z(p) x4cx4bx1bx3ex61 p x26x7ex4bx1bx58x58x49 ) x49x1cx40 p x38x8x4bx36x58 (x1bx39x41
x73x3ex14x24x38x8x4bx5)x71x57x57x5cx2cx4fx4dx3ex1bx39x41x73x3ex5cx3fx38x8x4bx5ax77x57x59
x1fx7bx60x57x3bx0x3ex8x10x7dx4cxbx6fx36x58x71x57x6cx4fx26x8x50x8x10x7dx49x4bx6cx59x46x65
x59x1fx66x4fx15x58x7ex65x5cx60x0x5x61x3ex7fx3bx8x12P x26x3ex4fx3ax8x50x7fx3bx8x10x7dx49
x1cx40x67x30Poincar′e–Hopfx75x61x57x59x7bx60x3bx0x3ex8x10x7dx5cx5x61x49 2
x7ex15x6bx6cx6dx4dx31x58x6bx3ex57x5cx15x58x5ex3fx6cx67x30x4fx31x65x6ex62x14x14x50x5e
x3fx49x4cx26x21x15x16x4dx57xdxex37x38z1 +￠￠￠+zI 6 !1 +￠￠￠+!I x3eLx7ex41x73x76
z = (z1;:::;zI) 2RLI+ x25x65E(u;!)x4dx3ex15x58(x47xex3dx34)x13x14(allocation)x49
x67x30x6ex62x14x14x6cx7bx4cParetox7ax54x20x3ex6ex62x57x19x4cx5fx22x6bx5dx3ex7ax7bx2cx1c
x1cx3ex4cx69x20x57x30x58x7ax7bx2cx5fx59x5ax1fx6bx55x3cx1x3ex17x40x49x65x3ex4fx47x72x4ax64
x20x73 z? = (z?1;:::;z?I) 2RLI+ x25x65x6cE(u;!)x4dx3ePareto x40x41x13x14x57x6c
x7bx5fx74x4cx4bx15x58x14x14 z = (z1;:::;zI) 2 RLI+ , x5bx29x20x70x5fx6ax3fx4dx1dx9x5c
x15x58x23x24x5fx6ax3fx73
ui(zi) > ui(z?i); i = 1;:::;I:
x20x70x75x61x45x71x47x25x65x15x20x64x65x6ax17x18x56x39x73
x56x397.3 x4bx4cx397.2x64x28x29x4x55x2ex2f(z?;p?) 2RLI+ ￡RL++x51E(u;!)
x6ax64x65x7ex3bx10x55x1fx20z? x51E(u;!)x6ax64Paretox25x6x16x17x6b
x24x3a x64x4ez?x5fx6cParetox6ex62x14x14x57x38x53x74x4cx14x14zx37x38ui(zi) >
ui(z?i); i = 1;:::;I; x74x58x74x4c j, x37x38 1 6 j 6 I, x5bx29 uj(zj) > uj(z?j).
x3bx65 uj x4c z? x18x7x69x4c B(!j;p?) x4dx3ex6ex28x1x57x24 zj =2 B(!j;p?), x19
164
p? ￠ zj > p? ￠ !j. x4bx15x41x1bx57x4ax3fx61x40x48x4bx57x39x3ax56x5c p? ￠ zi > p? ￠ !i,
i = 1;:::;I. x3bx6cx3bx65x64x4ex1ax4bx1bx58ix5cp?￠zi < p?￠!i,x39x3ax3ax59x43x36x15x58
x57x5x8x10v 2RL+x5bx29p?￠(zi+v) = p?￠!i,x23x45ui(zi) < ui(zi+v) 6 ui(z?i),
x7ex48x4bx3ex50x49x6ex27x57x39x3ax29x36
p? ￠(z1 +￠￠￠+zI) > p? ￠(!1 +￠￠￠+!I):
x3bx7ez = (z1;:::;zI)x6cx14x14x3ex50x49 2
x3bx75x4fx2fx1cx45x46x47x68x15x2fx7bx75x61x50x3ex4fx39x75x61x50x56x13x49x57x19x57x1ax30
x15x58 Pareto x6ex62x14x14x7x74x4cx1bx5ex14x24x18xdx57x5bx29x65x3ax12x13x15x6bx6cx6dx49
x65x25x65x4fx2fx1cx45x46x47x68x70x2fx7bx75x61x50x49x69x2ex2x5cx7ax1cx40x40x2ax2ax5bx75x61x49
x3bx6dx5fx1fx31x21x49
7.3 x3ax4cx39x3ax77x18x78x5cxcx6ex62x2ex2fx76x77x78x79x3ex15x6bx6cx6dx74x4cx5e
x3fx49x39x3ax48x75x40x4cx5c I x58x30x31x2cx57x45x46x4dx8x5cx41x73x57x45x6cx64x4cx15x6bx4d
x67x18x78x3ex11x75x7cx7dx38x0x57x5cx59x4cx6ax11x77x51x58x71x28x57x11x77x5c S x5ex30x5fx57
x7cx7dx4dx5cK x5ex2ex2fx57x64x6ex6ax6ax49x30x58x30x31x2cix7ax4bx37x3ex5ex3fx1fx6cx4cx15
x6bx4dx4bx37x3ex5ex3f ‰
max ui(z)
s:t: z 2 B(!i;x0;x1) (2)
x69x4d
B(!i;x0;x1) =
8
<
:z 2R
S+1
+
flfl
flfl
z0 = !i0 ? ￠x0;
z1 = !i1 + ￠x1;
2RK:
9
=
;:
x3bx1fx6cx4ex57x40x4cx39x3ax4bx37x3ex30x31x2c i x6cx40x15x58x6dx10x3cx3ex59x4cx6ax11x77x7a
x7bx3ex17x40x2cx4fui x6ax3cx67x17x18x3ex59x4cx7ex11x77x67x22x5cx3ex31x43!i x77x28x3cx3ex49
x39x3axex1ex1cx40x60x0x3ex2ax51x57x3bx0x55x4bx7ex4cx1bx3ex18x78x1bx1cx49x6bx6cx5cx7ax6f
x7ax3ex6cx69x45x46x53x54x2dx45x5cx67x30x70x49
x40x4cx7ax4bx37x3ex15x6bx6cx6dx5ex3fx5fx1fx6cx7ax7ex41x73x75x14x57x45x6cx7ax7eK x5e
x2ex2fx3ex59x4cx75x14x49x69x4dK x5ex2ex2fx3ex11x77x14x24x46x6cx47x51x65x40x13x6dx4bx4cx7e
x75x3ex49x3bx6ex57x39x3ax3ex45x46x3ax4cx7ax72x5x65E(u;!;x1),x69x4du = (u1;:::;uI),
! = (!1;:::;!I), ui:RS+1+ !R+, !i 2R+, i = 1;:::;I,x45x1 = (xsk)k=1;:::;K;s=1;:::;S
x6cK x5ex2ex2fx3eS x5ex11x77x14x24x67x12x13x3ex13x6dx4bx4cx49
E(u;!;x1)x59x25x65x47x48x22x23x49x4cx3bx58x43x44x7cx7dx4dx57x39x3ax19x32x3ex6cx71
x37x30x58x30x31x2cx3fx69x6ex62x2ex2fx76x77x78x79x77x12x13x6cx6dx3ex2ex2fx59x4cx14x24x49x5c
x7ax6fx7ax3ex6cx57x4cx3bx6dx57x2ex2fx3ex59x4cx14x24x5cx59x5ax6cx68x3ex49x43x44x7cx7dx3ex15
x6bx6cx6dx75x54x65(z?; ?;x?0) 2RI(S+1)+ ￡RI(K) ￡RK x5bx29
i) x1ax4bxdxei = 1;:::;I;x1ax4bxdxez 2 B(!i;x0?;x1), ui(z) 6 ui(z?i);
165
ii) ?1 +￠￠￠+ ?I = 0;
ii) z?1 +￠￠￠+z?I = !1 +￠￠￠+!I:
x3bx6dx75x76 ii) x6cx7bx2ex2fxbx60x1fx4cx3bx39x30x31x2cx32x11x34x69x57x67x5cx30x31x2cx67
x17x18x3ex2ex2fx76x77x32x6ax5bx7cx7dx46x2cx49x4cx45x46x53x54x26x57x65x7ax4dx47x3bx6dx3ex2e
x2fx7x6cx18x2fx16x3ex57x45x5fx6cx72x0x16x3ex49x6bx6cx3bx74x5fx69x6ax15x16x3ex15x6bx18x49
x39x3ax56x59x4cx15x16x4dx48x4bx57x5cx15x39x30x31x2cx22x5cx3ax6ax5fx65x5x3ex2ex2fx49x63x64
x69x3ax6ax4x65 1x57x65x59x7ax4dx47x30x58x30x31x2cx7x17x18x1bx50x13x72x0x3ex15x75x7x4d
(x59x5ax65x5x4dx68x1)x49x1ax4bx3bx5ex73x2dx55x3bx60x71x37x60x61x3ex70x9x4cx4fx47x26x41
x46x65x26x21x73x12x49x5dx18x3ex4fx47x72x4ax59x61x27x20x22x49x45x75x76iii)x3fx42x26x6cx75x76
ii) x3exaxbx4dx78x49x3bx0x3ex15x6bx6cx6dx25x65x47x48x22x23x66x67 (Financial Market
Equiribrium, FME)x49
x39x3ax33x3bx15x15x16x7ex4cx1bx3ex11xbx9x45x46x15x16x58x1bx1cx57x59x1fx27x36x57x43
x44x7cx7dx4dx3exbx60x7ex11xbx9x45x46x4dx3exbx60x4cx1bx5ex7ax54x26x6cx15x0x3ex49x33x5f
x60x30x5fx20x3ex7dx27x13x5fx60x3ex41x73x57x4cx2cx58x59x4bxbx3ax4cx33x5fx60x30x5fx20x3ex7d
x58x56xbx9x57x1fx3fx29x5dx3cx3ex6ex28x17x40x49x45x2ex2fx4cx69x4dx46x76x4dx43x3ex40x49
x43x44x7cx7dx6cx6dx3ex74x4cx5ex3fx1bx76x4cx22x18x78x3ex52x75x18x41x73x7cx7dx3ex15x6b
x6cx6dx3ex74x4cx5ex3fx77x57x59x1ex3cx55x62x63x49x6bx6cx4ax4bx4cx15x6bx4dx3ex31x0x75x14x68
x70x2fx7bx75x61x3ex13x49x57x39x3ax5ex5fx59x1fx65x62x57x64x4ex43x44x7cx7dx6cx6dx74x4cx57x38x53
x4cx3bx15x7cx7dx4dx57x5ax1bx1cx48x4bx54x55x13x49x49x64x4ex9x5fx55x26x5ax1bx1cx48x4bx57x38x53
x3fx2ex2fx59x4cx14x24x3ex5ex3fx57x59x26x51x65x3fx30x5fx14x24(x4dx2cx4ex3fArrow–Debreu
x2ex2fx3ex14x24) x3ex5ex3fx49x0x78x30x5fx14x24 ? = (?1;:::;?S) 2 RS++, x39x3ax59x1f
x27x36x57x5ex3f (2)x26x51x65
‰ max ui(z)
s:t: z 2 B(!i;?;x1) (3)
x69x4d
B(!i;?;x1) =
‰
z 2RS+1+
flfl
flfl z0 ?!i0 +?1(z1 ?!i1)+￠￠￠+?S(zS ?!iS) = 0;z1 ?!i1 = ￠x1; 2RK:
:
x69x58x1dx3ex15x6bx6cx6dx56x59x33x62x75x54x49
x3ax4cx39x3ax2ax51x5ex73x12x77x18x78x49x15x5ex6cx16x20x7cx7dx73x12x4ax4bx15x5ex6cx5f
x16x20x7cx7dx73x12x49x4cx16x20x7cx7dx73x12x20 (x3bx71 K > S)x57x39x3ax59x1fx74x3ax26x1b
x3ex32x37x2aB(!i;?;x1)x4dx3ex1 x5fx76x3ex40x57x3bx65x1ax4bxdxeS x7ex8x10(x11x75
x1ax1c) z1 ?!i1, x39x3ax3ax5ax43x36x29x59x3ex76x77 , x5bx29 x3ex11x77x14x1x7ex65x15
x0x57x19z1 ?!i1 = ￠x1. x3bx0x57 B(!i;?;x1) = B(!i;?):x33x65x7ex26x15x25x22
x4dx18x78x3ex15x6bx6cx6dx58x1bx1cx57x39x3ax59x1fx27x36x57x45x37x3bx0x3ex26x51x1fx27x57x3a
166
x4cx3ex5ex3fx4cx12x3fx26x7ex4cx1bx3ex5ex3fx64x65x16x20x15x0x57x7cx5cx3ex1fx5dx23x14x10x11
x3ex7ex4fx5fx60x26x57x58x59x4bx3dx77x3ex14x24x8x10px3ex30x5fx14x24x8x10?x7ex4fx9x14
x15x7ex49x64x4ex51x65x59x4cx30x5fx3ex4fx30x5fx14x24x50 ?0 = 1,x74x33x65x7ex3dx77x3e?x77
x4cx15x76x12x13x15x58x14x24x8x10x57x38x53x65x5ax57x6cWalrasx3ex14x24xax3cx12x3fx57x69
x3cx41x1bx7ex4cx1bx1fx16x20x15x2ax14x49x34x26x67x21x57x39x3ax1fx59x29x36x20x70x75x61x73
x56x39 7.4 x2ex2fx4bx4dx4dx4e E(u;!;x1) x51x74x67x64x55x69x6ax64x75x4fx4ex4f
x7x79x7ax3ex72x73x72x3x61x6fx1bx7bx25x72x3x55x6cx6d !1 + ￠￠￠ + !I 2 RS+1++ , x1fx20
E(u;!;x1)x6ax4ax4bx3bx10x55x6cx6dx62x65x3bx10x51Paretox25x6x16x17x6b
x3bx75x75x61x3cx55x5dx18x3dx4ex2x14x39x3ax4cx1bx69x36x3ex7ax72x73x4cx16x20x43x44x7c
x7dx4dx57x43x44x7cx7dx6cx6dx7ex11xbx9x45x46x3ex15x6bx6cx6dx4cx3dx61x26x6cx16x20x15x0x3ex49
x59x10Arrowx6aDebreux56x1fx6cx3bx0x51x65x67x5fx52x75x18x3ex43x44x7cx7dx3ex6cx6dx5e
x3fx59x41x46x65x52x75x18x3ex41x73x7cx7dx3ex6cx6dx5ex3fx49x16x20x43x44x7cx7dx6cx6dx45x71x25
x65x2cx56x22x23x66x67 (Contingent Market Equilibrium, CME)x57x69x4dx4fx11x75x7c
x7d (contingent market)x50x3bx58x4dx3ex64x39x3ax2dx45x69x36x3ex57x74x8x5cx2x53x52x1b
x7ax54x49
x1ex45x57x3bx16x16x6cx4ex2x16x20x7cx7dx8x5cx40x1ex5fx52x75x18x3ex7bxfx49x45x5fx16
x20x7cx7dx3ex6cx6dx74x4cx5ex3fx7ax62x63x29x71x49x4cx16x20x7cx7dx73x12x20x57x2ex2fx3ex11x77
x14x1x13x6dx4bx4cx1x69x3fx4cx3fx6cx6dx71x8x5cx76x71x28x3ex40x49x23x14x40x4ax4ax65x77x52
x75x7cx7dx6cx16x20x3ex1fx26x57x4cx3fx6cx6dx3ex37x34x4dx57x65x5fx1fx76x3ex40x49x6ex27x65x3f
x60x6cx6dx3ex2ex2fx76x77x78x79x71x57x1ax1fx26x76x40x65x49x6bx6cx4cx5fx16x20x7cx7dx3ex73x12
x20x57x65x1ax3fx6cx6dx3ex37x34x76x55x28x3ex32x37x3ex40x57x1fx1dx3x19x77xbx3ax5fx65x51x0
x77x18x61x65x49x43x44x7cx7dx15x16x6c1972x10x4aRadner [14]x5ex5fx69x60x3ex57x74x58x3c
x4cx1ax8x10x5cx26x58 (x5fx5ax5ax77x15x3dx8x10) x3ex75x76x20x57x2ex2x14x6cx6dx3ex74x4cx49
x6bx6c1975x10Hart [7]x40x40x63x7bx60x57x5fx16x20x43x44x7cx7dx3ex15x6bx6cx6dx59x5ax5f
x74x4c2x49x3bx5bx29x3bx41x1bx3ex79x7ax3x19x60x18x5fx4cx49 1985x10x57 Duffiex6aSchafer
[5]x57 [6]x40x58x59x62x63x3ex4fx47x41x42x7bx60x57x1ax4bx4fx1ax28x71x4fx50x3ex5fx16x20x7cx7dx57
x6cx6dx57x6cx74x4cx3ex49x3bx6dx3ex4fx1ax28x71x4fx50x6cx7bx1ax4bx67x5cx59x5ax3ex70x4ax22x5c!
x7ex67x5cx59x5ax3ex2ex2fx11x77x14x1x13x6dx4bx4cx1 x67x12x13x3ex2ax77x45x1x3e(x6cx6dx5f
x74x4cx3ex2ax77x6ax4ax65x5)x49x3cx3ax60x71x57x2ex2x14x57x5fx16x20x7cx7dx3ex4fx1ax28x71x4fx50
x6cx6dx7x6cParetox5ax17x3ex57x5fx5ax4ax36x4fx31x65x6ex62x14x14x50x49x5fx16x20x7cx7dx3ex6c
x6dx5fx5ax4ax36 Pareto x6ex62x14x14x57x6cxbx3ax42x45x73x36x3ex57x3bx65x7cx7dx5fx16x20x57
x71x4x5fx5ax16x20xax1bx57x7cx7cx71x37xbx60x62x65x5fx5ax4ax36x6ex62x49x6bx6cx33x65x3ax2
x52x72x4ax65x3bx0x3ex75x61x57x38x57x6cx68x15x26x49x3bx39x79x7ax46x4ex7x1x29xbx3ax77x72x49
2x48x3x72x42x5x22x55x10x3fx32x33x13 (x46x25x10x50x13x47x3dx3bx20x3bxax32x33) x11x12x5cx5dx20x20x3bx55x5a
x11(x2bx73x5cx5dx47x18x72x73)x7fx47x2cx6x20x29 x3cx47x52x53x22x55x26x32x33(x64x47x10x50x13x3x67x5x79x25x35
x20x32x33x5x41x56x7ex18x7x48x61x10x10x55x22x79x7ax13)x2bx72x73x11x12x5cx5dx5x7cx70x13x55x3xfx20x3fx32x33
x5cx5dx5x3bx55x5ax11x4fx48x35x2bx2cx6x29 Hartx20x46x19x47x52x53x22x55x22x32x33x5cx5dx58x56x20x29xbx3bx46
x19x4ex3dx5bx74x12x56x37x52x53x13x55x3fx32x33x5cx5dx20x46x19x29x77x7aMagill–Quinzii [11]x29
167
x5fx16x20x7cx7dx3ex15x6bx6cx6d(General Equilibrium of Incomplete Markets, GEI)
x61x78x4cx6fxfx64x10x77x5cx55x28x74x75x49 Magillx6aQuinziix3e[11]x6cx6fx10x77x3bx41
x1bx60x3ax3ex3ax3bx57x71x19x73x3ex15x1x49
7.4 x20x1bx51x22x4dx57x39x3axcx1a CAPM x6a APT x40x15x6bx6cx6dx61x78x77
x18x78x49x3bx0x3ex18x78x59x1fx4cx11x77x30x5fx5cx77x3ex13x14x20x34x69x49xbx42x6cx1ax30x15
x30x5fx2x1fx4fx16x35xcx57x1fx1dx30x15x11x77x14x24x7x59x27x3ex5cx2ax5dx3ex6dx6ex70x10x49
x9x3fx26x57x4c Magill–Quinzii [11] x4dx1fx6cx3bx0x77x18x78 CAPM x3ex57x69x4dx19
x32x17x40x2cx4fx45x40 6.5 x4dx67x69x36x3ex12x3fx57x19 u(z0;z1;:::;zS) = v(z0) +
–PSs=1 qsv(zs), x45 v x46x45x40 HARA x33x2cx4fx49x4ax6ex59x1fx29x36x60x0x12x3fx3e
CAPMx49
x1ex45x57x3bx0x3ex18x78x5bx40x2dx5cx3e CAPM x3ex5cx21x1cxbx49x39x3ax4cx20x1b
xcx18x78x2ex2fx11x77x14x24x6cx15x6bx3ex6dx6ex70x10x3ex73x12x49x3bx0x3ex18x78x4cx4fx47x26
x5cx15x75x6cx63x57x6bx6cx64x4ex39x3ax1bx40x6cx6dx74x4cx5ex3fx57xcx29x36x3cxbx6fx45x64x3e
CAPM (x1fx25APT)x3ex46x4ex49
x39x3axex48x75x46x5cx59x4cx6ax11x77x51x58x71x28x57x59x4cx6cx52x75x3ex57x6bx11x77x6cx5f
x52x75x3ex49x48x75x7cx7dx4dx5cnx5ex2fx7bx71x4x2ex2fx57x69x11x77x14x24x6cnx58x6dx6ex70x10
x1;x2;:::;xn;x3bx6dx48x4bx65x3ax11x6fx18x5axcx57x23x45x69x40x41x5cx4bx4cx6ax6x1cxcx3e
x40x41x5cx4bx4cx3ex75x49x6ex26x57x680x5ex2ex2fx6cx5ax71x4x2ex2fx57x69x11x77x14x24x0 x6c
x52x75x10x49x39x3axex48x75x6fx18x75x14x42x46x13x49x57x1fx1dx74x4cx1bx58x6fx18x75x14x2cx4fp,
x5bx29x3bnx5ex2ex2fx3ex59x4cx14x24x65p(x0);p(x1);p(x2), :::, p(xn),x58x48x75x65x3a
x7x65x3ex49x3bn+1x5ex2ex2fx3ex30x31x76x77x59x40n+1x7ex8x10 = ( 0; 1;:::; n)
x77x72x5x49x38x53x30x31x76x77x3ex59x4cx14x24x65
y = 0p(x0)+ 1p(x1)+￠￠￠+ np(xn); (4)
x45x30x31x76x77x3ex11x77x14x24x65
y = 0x0 + 1x1 +￠￠￠+ nxn: (5)
x33x62x4cx1bx18x78x3ex73x12x57x12x48x4bx5cx1bx58x30x31x2cx57x3cx4cx59x4cx22x5c(x52x75
x3e) x31x43 !0, x11x77x46x22x5c (x6dx6ex3e) x3ex31x43 !1. x3cx3ex7ax7bx17x40x6cx40x1bx58
x3ex65x59x4c(x52x75x3e)x7ax7bz0 x6ax11x77(x6dx6ex3e)x7ax7bz1 x3ex2cx4fx3ex19x32x17x40
x2cx4f u(z0;z1) x77x6dx10x3ex49x3bx0x3cx1bx1bx3ex6ex62x2ex2fx78x79x5ex3fx64x20x73x3fx59
x4cx7ax7b z0 x6ax30x31x76x77 , x5bx29 E[u(z0;z1)] x4ax36x6ex28x49x3bx6d u x46x1ax52x75
x10x77x75x54x57x23x45x65x3ex19x32x1x1fx6cx1ax6dx6ex70x10x3ex19x32x17x40x49x3cx5dx18x3dx4ex57
x5ex3fx59x72x21x65x73x3fx2ex2fx76x77 ,x5bx29
8<
:
max E[u(z0;z1)]
s:t: z0 = !0 ?Pnk=0 kp(xk);
z1 = !1 +Pnk=0 kxk:
(6)
168
x3bx6dx68x15x58x6ax3fx6cx52x75x10x3ex6ax3fx57x68x70x58x6ax3fx6cx6dx6ex10x3ex6ax3fx49
x3bx15x5ex3fx6cx10x59x62x3ex18x78x7ax1bx4cx1bx5cx77x30x5fx3ex73x12x62x63x29x71x49x1d
x1ex1ax3bx6dx3ex2cx4fux39x3ax56x59x1fx55x26x3fx61x40x32x33x3ex48x4bx57x6bx6cx4ax4bx3bx6d
x57x66x25x4fx47x19x32x7dx49x57x55x63x29x36x1fx4cx38x0x3ex60xdx75x61x49x5fx37x39x3ax59x1a
x15x39x5dx18x3ex19x32x17x40x2cx4fx77x34x69x18x78x49
x1fx20x39x3ax3ex18x78x40x19x6cx73x4ax6ex60x74x27x60x31x7bx31x0x75x14x15x16(CAPM)x49
x65x6ex57x39x3ax5fx48x75x30x31x2cx4cx59x4cx57x17x18x15x58x2ex2fx76x77 0x57x12 = 1? 0,
x74x40 !1 x7x52 !1 ?Pnk=0 0kxkx57x38x53x26x21x5ex3fx26x51x65x20x70x5ex3fx73x3fx2ex2f
x76x77 1,x5bx29
8
<
:
max E[u(z0;z1)]
s:t: z0 = !0 ?Pnk=0( 1k ? 0k)p(xk);
z1 = !1 +Pnk=0 1kxk:
(7)
x3bx0x69x60x3ex5ex3fx4cx45x46x53x54x26x7ex1fx4cx3ex5ex3fx5cx67x5fx60x49x65x58x59x4bx43x44
x7cx7dx4dx5cx72x0x16x3ex2ex2fx49x30x31x2cx3dx77x5cx2ex2fx76x77 0,x4cx59x4cx33x65x1bx3ax57
x74x1fx2x1x62x3ex76x77 1. x4cx1fx4cx3ex43x44x7cx7dx6cx6dx15x16x4dx57x39x3ax7ax3fx7cx7d
x4dx67x5cx2ex2fx76x77x32x6aPIi=1 i = 0. x3bx0x3ex2ex2fxcx3cx71x3dx7ax4dx47x18x2fx4d
x30x31x2cx32x11x3ex43x44x77x32x49x45x3ax4cx7ax18x78x3ex6cx6dx15x16x4dx57x39x3ax1ax6cx6dxc
x7ax3f PIi=1( 0i? 1i) = 0,x6bPIi=1 0i = PIi=1 1i 0 ( x72x5x8x10x3ex67x5c
x2ax10x65x3e)x57x65x3axcx52x72x20x7cx7dx3ex2ex2fx76x77x49x1dx1ex4cx4fx47x26x3fxfx26x8x5c
x7bxfx30x70x57x6bx6cx45x46x53x54x26x2dx45x5cx14x70x51x49
x39x3ax48x75E[u(z0;z1)] = v(z0;E[z1];Var[z1]),x19x17x40x2cx4fx46x7ex59x4cx7a
x7bx1fx25x11x77x7ax7bx3ex6cx1x6ax41x5cx5cxcx49x7ex6ex58x10xdx3ex59x1ex6cx2cx4fx3ex11x77
x7ax7bx3cx70x10x1dx1ex7ex1bx58x4fx11x75x1ax1c Hilbert x10x11x50x5cxcx49x4cx45x46x47x3ex18
x78x4dx57x71x71x3ax48x75x19x32x17x40x2cx4fx7fx3bx1x2ex6bx1x23x24x28 (x71x4x56x7b) x6ax49
Markowitz x4cx3cx3ex2ex2fx76x77x78x79x61x78x4dx57x40x4ax71x8x5cx5bx40x19x32x17x40x2c
x4fx57x45x7cx1fx76x77x3ex6x1cxcx3ex6cx1x6ax41x5cx77x6dx10x76x77x6x1cx3ex62x7ex57x19x46
x69x60x67x30x4fx6cx1x2x41x5cx19x46x50x49x1ax4bx30x31x2cx77x4ex57x64x4ex7ax40x17x40x2cx4fx77
xfx29x57x38x53x3cx59x1fx45x40x15x58x46x7ex6x1cxcx3ex6cx1x6ax41x5cx5cxcx3ex2cx4fx77x3e
x65x17x40x2cx4fx49x3bx7ex69x6bx3ex19x32x17x40x2cx4fx5cx67x5fx60x49 Markowitz x6a Tobin
x65x14x4ex2x3bx0x3ex18x61x41x42x7ex69x6bx3ex18x61x41x42x5fx3ex50x57x42x45x7bx60x57x3bx58
x59x4bx19x32x17x40x2cx4fx6cx70x26x28x2cx4fu(x) = ax?bx2; a;b > 0. x9x3fx26x57x64x4e
ux64x26x75x54(x6fx6fx7ax57x3bx6dx3ex17x40x2cx4fx6cx1ax11x77x7ax7bx3ex14x1x77x75x54x3ex57
x45x5fx6cx1ax2ex2fx76x77x3ex6x1cxcx75x54x3e)x57x38x53
E[u(x)] = aE[x]?bE[x2] = aE[x]?b(Var[x]+E2[x]):
x40x32x57x64x4ex48x75ux5cTaylorx75x40x57x38x53x56x3bx60x7bx60x57 E[u(x)]x46x7exx3e
x6cx1x6ax41x5cx5cxcx54x75x6cx70x26x2cx4fx49x5fx37x4cx3bx5ex73x2dx20x57x64x4ex57x7ax3fx65
169
xcx4bxx6cx2ex6bx28x2cx4fx57x38x53x1axx3ex70x51x3cx3dxcx5cx67x77x15x49x6ex26x57x57x59
x27x36x57x64x4ex67x66x25x3ex6dx6ex70x10x7x6cx3ex5fx2ax5dx3ex6dx6ex70x10x57x38x53x3bx15x7a
x3fx3cx1ex37x38x49x6fx7ax36x3bx39x1fx27x57x39x3ax1fx59x51x65x57x40x4cx3ex48x75x4cx15x75x34
x4ax26x6cx77x61x3ex49x1ex45x57x3ex64x39x3ax4cx26x15x6bx18x78x6dx6ex41x62x5ex3fx71x2dx45x69
x36x57x3bx6dx7ax0x76x6fx7ax3ex6cx73 Markowitz x3ex6cx1x2x41x5cx19x46x23x59x7bx26x77
x4ex57x6cx7ex19x32x17x40x2cx4fx61x78x5fx16x20x15x2ax3ex49x65x1dx71x6cx26x21x48x75x20x3ex15
x33x43x43x2cx4fx3ex6dx6ex41x62x3ex2ex2ax75x76x57x6bx74x57x54x7ax75x76x49x3bx3fx42x26x4ex2x57
Markowitzx3ex6cx1x2x41x5cx19x46x5fx59x5ax40von Neumann–Morgensternx19x32
x17x40x2cx4fx50x61x77x28x3cx49
x4cx3bx0x3ex48x75x20x57x64x4ex1fx48x75!1 x6cx75x71x10, x38x53x5ex3f (7) x59x1fx72
x4ax29x3cx2x52x49x3bx6cx3bx65?z1 = E[z1]x6a 2z1 = Var[z1]x4cx40x4cx7x59x49x60x73
?z1 =
nX
k=0
1kE[xk];
2z1 =
nX
j;k=1
1j 1kCov[xj;xk]:
x3bx0x57x5ex3f (6)x70x65x73x3fx2ex2fx76x77 1,x5bx29
8
>><
>>:
max v(z0;?z1; 2z1)
s:t: z0 = !0 +Pnk=0( 0k ? 1k)p(xk);
?z1 = Pnk=0 1kE[xk];
2z1 = Pnj;k=1 1j 1kCov[xj;xk]:
(8)
x20x1bx57x39x3ax65x60x51x2ax51x57x2a v = v(x;y;z), x65x1axfx58x70x10x3ex35x27x4f
x2ax5dx2ax65vx;vy;vz:x68x69x6cx39x3ax7ax3f
vx > 0; vy > 0; vz < 0: (9)
x65x3ax2ax5dx7ax4dx47x73 x4fx59x4cx7ax7bx14x1x8x28x8x2cx50x4a x4fx11x77x7ax7bx14x1x8x28x8
x2cx50x4a x4fx11x77x7ax7bx14x1x3ex71x4x8x25x8x2cx50x49
x56x397.5 x66x74(8)x64xf(ˉ 1)x79x7ax4x72x5bx34x68
E[rj]?r0 +2vz(ˉz
0;?ˉz1; 2
ˉz1)
vy(ˉz0;?ˉz1; 2ˉz1)
nX
k=1
ˉ 1kp(xk)Cov[rk;rj] = 0; j = 1;:::;n: (10)
r0 = vx(ˉz
0;?ˉz1; 2
ˉz1)
vy(ˉz0;?ˉz1; 2ˉz1); (11)
x62x6f ˉz0, ˉz1 x1cx57x60 ˉ 1 x64z0, z1; r0;r1;:::;rn x25x0x1cx76x78x79x64x7cx7dx7ex6b
170
x24x3a x2ex2x59x40Lagrangex35x33x42x49x5ex3f (8)x3eLagrangex2cx4fx65
L = v
?
z0;
nX
k=0
1kE[xk];
nX
j;k=1
1j 1kCov[xj;xk]
!
+?
?
!0 +
nX
k=0
0kp(xk)?z0 ?
nX
k=0
1kp(xk)
!
:
x3bx6ex57x69x62 ˉ x6ax58x1dx3e(ˉz0;?ˉz1; 2ˉz1)x37x38x20x70x75x76x73
@L
@z0 = 0;
@L
@ 1j = 0; j = 0;1;:::;n;
@L
@? = 0:
x23x45x4ax4cx51x3fx59x29
vx(ˉz0;?ˉz1; 2ˉz1) = ?; (12)
vy(ˉz0;?ˉz1; 2ˉz1)E[xj]+2vz(ˉz0;?ˉz1; 2ˉz1)
nX
k=1
ˉ 1kCov[xj;xk]??p(xj) = 0; (13)
j = 0;1;:::;n:
x59j = 0x71x57 (13)x59x27x2a
vy(ˉz0;?ˉz1; 2ˉz1)x0=p(x0) = ?:
x1fx6fx7ax36 x0=p(x0) = r0 x6a (12), x19x29 (11). x59 j 6= 0 x71x57x60x0x59x6fx7ax36
E[xj]=p(xj) = E[rj], p(xj)p(xk)Cov[rj;rk] = Cov[xj;xk]x1fx25?x3ex26x21x72x4a
x3fx57x4a(13)x59x27x29(10). 2
x1fx26x4ex3ex6cx15x58x30x31x2cx3ex6ex62x2ex2fx76x77x78x79x49x64x4ex3ax4cx7cx7dx26x5c
Ix58x3bx0x3ex30x31x2cx57x19x3cx3ax5dx5cx5dx3ex3dx5cx31x43!0ix1x2ex2fx76x77 0ix6ax17x40
x2cx4fvi,x1fx1dx7x1bx1bx3bx0x3ex2ex2fx78x79x5ex3fx73
8
>><
>>:
max vi(z0;?z1; 2z1)
s:t: z0 = !0i +Pnk=0( 0ik ? 1k)p(xk);
?z1 = Pnk=0 1kE[xk];
2z1 = Pnj;k=1 1j 1kCov[xj;xk]:
i = 1;:::;I: (14)
x74x58x7x5dx3cx3ex60x69x6ex62x76x77x78x79 ˉ 1i, x38x53x39x3ax1fx59x4bx37x1ax3bx0x3ex2ex2f
x7cx7dx3ex6cx6dx74x4cx5ex3fx49x64x4ex29x59x3ex2ex2fx59x4cx14x24 p(x0);p(x1);:::;p(xn)
x5bx29x7cx7dx26x2ex2fx29x2cx4ax36x77x5cx36x6dx71x57x19
IX
i=1
0ik =
IX
i=1
ˉ 1ik 0; k = 0;1;:::;n; (15)
171
x38x53x25x1ex7cx7dx4ax36x66x67x49x4cx40x4cx3bx0x3ex73x2dx20x57x6cx6dx6cx10x74x4cx6cx58x3c
x55x62x63x3ex5ex3fx49x3bx6dx39x3axcx60x61x3dx4ex56x22x23x66x67x64x65x49
x20x15x75x61x4ex2x7cx7dx6cx6dx3ex15x39x43x61x57x69x4dx6ex79x7ax3ex15x61x6cx31x7bx31
x0x75x14x15x16x13x49x49
x56x39 7.6 x4bx6ex7x70x78x6ax55x2ex2fx57x58x4cx4dp(x0), p(x1), :::, p(xn)x1e
x1a, ˉ 11, ˉ 12, :::, ˉ 1I,x66x75x4dx4ex3bx10x55x1fx20
i) PIi=1 !i0 = PIi=1 ˉzi0; (x56x5bx72x73x50x64x25x6x6ex1ax1bx4ex7dx61x9x58x1cx60x1dx1e
x5bx64x73x4bx7dx61x55x56x55x5axcx1ex1ax55x6ex1ax1bx4ex6cx1dx1fx4fx78x79x4dx4ex6ax64
x73x4bx6b )
ii) ˉ 1ik > 0, k = 1;:::;n, i = 1;2;:::;I; (x39x77x72x73x50x64x25x6x78x79x72x73x26x44
x27x13x50x55x6cx6dx39x19x78x79x7x27x37x21xex4x20x68x21x78xax49x39x77x72x73x50x64
x57x7cx7dx7ex1ex1ax64x49x4ax78x79x72x73x7ax7bx7x51x65x63x64x6b )
iii) x3 r? 1i x1cx18 i x77x72x73x50x64x25x6x7ax7b ˉ 1i x6ax64x49x4ax78x79x7ax7b ? 1I =
(0; ˉ 1i1 ; ˉ 1i2 ;:::; ˉ 1in )x64x7cx7dx7ex6bx1fx20
E[rj]?r0 = Cov[rj;r? 1i]Var[r
? 1i]
(E[r? 1i]?r0); j = 1;2;:::;n:
iv) (CAPM)x3rmx1cx49x4ax78x79x64x4dx4ex7ax7bm = (0;PIi=1 0i1 ;PIi=1 0i2 ;:::;PIi=1 0in )
x64x7cx7dx7ex6bx1fx20
E[rj]?r0 = Cov[rj;rm]Var[r
m]
(E[rm]?r0); j = 1;2;:::;n:
v) x3z1 = PIi=1 z1i x1cx1dx1ex64x5ax1bx4ex55 rz1 x1cx69x8x60x64x7cx7dx7ex6bx1fx20
E[rj]?r0 = Cov[rj;rz1]Var[r
z1]
(E[rz1]?r0); j = 1;2;:::;n:
(xex6ex51x22x19x73x76x73x77x4cx4dx70x78x64x7bx7cx55x69x66x67x74x67x65x63x6b )
vi) (x23x21x6ax4bx4cx39)
nX
k=1
ˉ 1ik xk =
?
!0i +
nX
k=0
0ik p(xk)?z0i
!
rm; i = 1;2;:::;I:
(x25x6x49x4ax78x79x7ax7bxdx3x33x4dx4ex7ax7bx1ex60x4ax55x56x4dx4ex7ax7bxdx24x1x65
x19x23x21x6ax4bx6b )
172
x24x3a i)x3bx65
!0i +
nX
k=0
0ik p(xk) = z0i +
nX
k=0
ˉ 1ik p(xk); i = 1;:::;I;
x67x1fx51x1fx1aix3fx6ax74x24x34x57x59x29
IX
i=1
!0i ?
IX
i=1
z0i =
IX
i=1
nX
k=0
p(xk)(ˉ 1ik ? 0ik ) =
nX
k=0
p(xk)
IX
i=1
(ˉ 1ik ? 0ik ):
x4ax6cx6dx3ex75x54(15)x57x26x3fx65x5x57x19i)x13x49x49
ii)x4a(10),x59x29
E[rj]?r0 = Ai
nX
k=1
ˉ 1ik p(xk)Cov[rk;rj]; j = 1;:::;n; (16)
x69x4dx57x4a(9),
Ai = ?2v
i
z(ˉz
0;?ˉz1; 2
ˉz1)
viy(ˉz0;?ˉz1; 2ˉz1) > 0: (17)
x33(16)x24x13x4bx4cx12x3fx57x46x59x29
E[r]?r0e = AiV ˉ 1ip(x); i = 1;:::;I;
x69x4dE[r] = (E[r1];:::;E[rn])T, e = (1;:::;1)T, ˉ 1ip(x) = (ˉ 1i1 p(x1);:::; ˉ 1in p(xn))T,
V = (Vjk)j;k=1;:::;n = (Cov[rj;rk])j;k=1;:::;n. x3bx6ex57
Aiˉ 1ip(x) = V ?1(E[r]?r0e); i = 1;:::;I: (18)
x26x3fx2cx1fx7eix5axcx57x23x45x59x29
A1ˉ 11k p(xk) = A2ˉ 12k p(xk) = ￠￠￠ = AIˉ 1Ik p(xk); k = 1;:::;n: (19)
x4ax4bAi;p(xk) > 0,x24x1ax4bx2x75x3ek,x67x5c ˉ 1ik x60x51x49x6bx6cx1ax4bx6cx6dx77x4ex57
x4a (15), x30x5ex2ex2fx3ex3ax4fx4cx45x46x4dx3ax6cx3ex3ex57x3bx6ex57x54x55x67x5c ˉ 1ik > 0,
x19ii)x13x49x49
iii)x12
wik = ˉ 1ik p(xk)=
nX
k=1
ˉ 1ik p(xk); k = 1;:::;n: (20)
x38x53x4a(16)x59x29
E[rj]?r0 = Ai
nX
k=1
ˉ 1ik p(xk)
nX
k=1
wikCov[rk;rj] = Ai
? nX
k=1
ˉ 1ik p(xk)
!
Cov[r? 1i;rj]:
173
x39x3ax46x5cx7bx60x57x26x3fx2cx1fx3exdx4fx1fx6ciii)x4dx3exdx4fx49x9x3fx26x57x4ax26x3fx59
x29
nX
j=1
wij(E[rj]?r0) = Ai
? nX
k=1
ˉ 1ik p(xk)
! nX
j=1
wijCov[r? 1i;rj]:
x6bx6c
nX
j=1
wij(E[rj]?r0) = E[r? 1i]?r0;
nX
j=1
wijCov[r? 1i;rj] = Cov[r? 1i;r? 1i] = Var[r? 1i]:
x4ax6ex19x29
Ai
? nX
k=1
ˉ 1ik p(xk)
!
= (E[r? 1i]?r0)=Var[r? 1i]: (21)
x19iii)x13x49x49
iv)x39x3ax46x5cx7bx60x57x1ax4bx2x75x3ek,x67x5cwik x7x58x6ax57x74x58x7x6ax4bx7c
x7dx76x77x58x1dx3ex1bx63xdx4fwmk . x9x3fx26x57x4a(18),x39x3ax59x29
Ai
? nX
k=1
ˉ 1ik p(xk)
!
wi = V ?1(E[r]?r0e); i = 1;:::;I:
x69x4d wi = (wi1;:::;win)T. x6bx6cx4a (19), Ai?Pnk=1 ˉ 1ik p(xk)￠x7e i x5axcx49x3b
x6ex57 wi x7eix5axcx57x19x1ax4bx2x75x3ek,x67x5cwik x7x58x6ax49x4bx15x41x1bx57
wmk =
PI
i=1
0i
k p(xk)P
n
k=1
PI
i=1
0i
k p(xk)
=
PI
i=1
1i
k p(xk)P
n
k=1
PI
i=1
1i
k p(xk)
=
PI
i=1 w
i
k
Pn
k=1
1i
k p(xk)P
n
k=1
PI
i=1
1i
k p(xk)
= wik
PI
i=1
Pn
k=1
1i
k p(xk)P
n
k=1
PI
i=1
1i
k p(xk)
= wik:
x3bx0x57x3fx42x26x57x1ax4bxdxei, r? 1i = rm,x3bx45iv)x4aiii)x59x29x49
v)x3bx6cx3bx65
ˉz1 =
IX
i=1
?
!1i +
nX
k=0
ˉ 1ik xk
!
;
174
x65x6ax4bx7cx7dx76x77x7ex15x34x5ax71x4x31x0x32x6ax49x4a(16)x59x29
(Ai)?1(E[rj]?r0) =
nX
k=1
ˉ 1ik Cov[xk;rj]; j = 1;:::;n; (22)
x69x4dAi x4a(17)x67x75x54x49x3bx6ex57
? IX
i=1
(Ai)?1
!
(E[rj]?r0) =
IX
i=1
nX
k=1
ˉ 1ik Cov[xk;rj]
= Cov[ˉz1;rj]
= p(ˉz1)Cov[rˉz1;rj] j = 1;:::;n: (23)
x4bx15x41x1bx57 rˉz1 = Pnk=0 wˉz1k rk;x69x4dwˉz1k x74x71xax75x54x49x23x45x4a(23)x59x29
? IX
i=1
(Ai)?1
! nX
k=0
wˉz1k (E[rj]?r0) =
? IX
i=1
(Ai)?1
!
(E[rˉz1]?r0)
= p(ˉz1)Var[rˉz1]; j = 1;:::;n: (24)
x33(23)x3ex51x1fx7e(24)x3ex51x1fx58x23x57x19x29v).
vi)x9x3fx26x57
nX
k=1
ˉ 1ik xk =
? nX
k=1
ˉ 1ik p(xk)
!
(r? 1i)
?
!0i +
nX
k=0
0ik p(xk)?z0i
!
(r? 1i);
i = 1;2;:::;I:
x6bx6cr? 1i = rm, i = 1;:::;I,x24vi)x13x49x49 2
x1fx26x1fx6cx40x4fx6cx6dx75x14x78x50x77x18x78x3ex31x7bx31x0x75x14x15x16x49x39x3ax59
x1fx27x36x57x4ax6ex29x36x3ex3ax3bx1bx61x11x4ax6fx18x75x14x3dx46x60x74x6a Markowitz x3e
x6cx1x2x41x5cx2ax3x29x36x3ex3ax3bx7ax19x73x29x71x49x68x69x6cx57x3bx6dx3ex18x78x6cx76x3e
x5cx4fx45x46x47x3ax3bx50x3ex57x74x58x5ax1bx1cx48x4bx46x6cx1bx53x4cx15x6bx6cx6dx74x4cx3ex48x75
x32x4dx49x6bx6cx67x29x36x3ex46x78x4dx6ex48x7ax3ex57x6cx39x3ax4cx1bx2dx45x27x29x3ex71x71x3e
x31x7bx31x0x75x14x15x16 (CAPM)x49x4bx15x41x1bx57x39x3ax57x59x27x36x57x7cx7dx6cx6dx3e
x35x60x4cx26x21x78x21x4dx76xcx1ax3ex40x49x5fx37x57x3ex64x39x3ax4cx1bx2dx45x69x36x3ex57x3b
x6dx3ex6cx6dx6cx10x74x4cx57x6cx15x58x5ex3fx49x6ex26x57x4c Magill–Quinzii [11] x3ex5cxc
CAPM (x48x75x11x77x30x5fx5cx77)x3ex18x78x4dx7bx60x57 CAPM x6cx6dx15x75x6c Pareto
x6ex62x14x14x49x3bx6cx15x58x12xbx6fx40x3ex46x4ex49x65x4ex2x57x23x57x6cx4cx16x20x7cx7dx73
x12x20x57 CAPMx6cx6dx3ex74x4cx6cx15x5ex4fx25x22x50x3ax59x49
175
7.5 x6ex27x57x39x3ax1fx40x4fx6cx6dx75x14x78x50x77x48x62x4bx4cRossx3eAPTx61x78x49
x65x6ex57x39x3ax5fx77x18x78x15x58x7ex4cx1bx33x62x3ex6ex62x2ex2fx76x77x78x79x5ex3fx73x3fx59
x4cx7ax7bz0 x6ax30x31x76x77 1,x5bx29
8
<
:
max E[u(z0;z1)]
s:t: z0 = !0 +Pnk=0( 0k ? 1k)p(xk);
z1 = !1 +Pnk=0 1kxk:
(25)
x3bx6dx64x65x15x58x7x7ex4cx1bx15x0x57x68x69x6cxex48x4bx46x5cnx5ex71x4x2ex2fx49x6bx48
x75r1;:::, rn x32x11x6bx6cx7bx49x57x74x1ax19x32x17x40x2cx4fu = u(x;y)x5fx1fx3ex4cx1b
x38x0x3ex48x75x49x4cx3bx6dx39x3axcx48x75x73
1. u x6cx7fx3bx2cx4f (x1dx9x5cx70x72x6bx17x35x27x4f uxx;uyy;uxy)x57x74x58x3bx56x3f
x4fx47x19x32x7ex3fx35x27x4fx3ex26x8xbx9x4a
2. ux1ax51x58x70x10x7x2ex6bx57x4dx2cx4ex57x1ax51x58x70x10x3ex35x27x4fux;uy > 0;
3. u x65x23x24x28x2cx4fx57x19x69x70x72x35x27x4fx67x66x13x3e Hesse x4bx4cx68x75x57x68
x69x6cuxx;uyy < 0.
x56x397.7 x66x74(25)x64xf ˉ 1 x30x69x8x60x64 ˉz0, ˉz1 x79x7ax4x72x5bx34x68
E￡uy(ˉz0;ˉz1)(rj ?r0)? = 0; j = 1;:::;n: (26)
r0 = E[ux(ˉz
0;ˉz1)]
E[uy(ˉz0;ˉz1)]; (27)
x62x6fr0;r1;:::;rn x25x0x1cx76x78x79x64x7cx7dx7ex6b
x24x3a x2ex2xex1ex59x40Lagrangex35x33x42x49x5ex3f (25)x3eLagrangex2cx4f
x65
L = E
"
u
?
z0;
nX
k=0
1kxk
!#
+?
?
!0 +
nX
k=0
0kp(xk)?z0 ?
nX
k=0
1kp(xk)
!
:
x3bx6ex57x69x62 ˉ 1 x25x69x58x1dx3e(ˉz0;ˉz1)x37x38x20x70x75x76x73
@L
@z0 = 0;
@L
@ j = 0; j = 0;1;:::;n;
@L
@? = 0:
x23x45x4ax4cx51x3fx59x29
E[ux(ˉz0;ˉz1)] = ?; (28)
176
E￡uy(ˉz0;ˉz1)xj???p(xj) = 0; j = 0;1;:::;n: (29)
x6fx7ax36xj=p(xj) = rj, (29)x59x27x2a
E[uy(ˉz0;ˉz1)xj=p(xj)] = E[uy(ˉz0;ˉz1)(rj)] = ?:
x7j = 0, x1fx4a(28), x19x29(27)x13x49x49x1fx7j 6= 0x71x57x74x7ej = 0x3ex26x3f
x58x64x57x19x29(26). 2
x3ax4cx39x3ax77x18x78x7cx7dx6cx6dx49x6cx6dx3ex75x54x7ex4cx1bx33x62x49x3bx6dx39x3ax60
x0x4ex56x22x23x66x67x64x65x49
x20x15x75x61x4ex2x3ax4cx3ex7cx7dx6cx6dx3ex43x61x56x7ex4cx1bx33x62x49
x56x39 7.8 x4bx6ex7x70x78x6ax55x2ex2fx57x58x4cx4dp(x0), p(x1), :::, p(xn)x1e
x1a, ˉ 11, ˉ 12, :::, ˉ 1I,x66x75x4dx4ex3bx10x55x1fx20
i) PIi=1 !0i = PIi=1 ˉz0i;
ii) ˉ 1ik > 0, k = 1;:::;n, i = 1;2;:::;I.
x24x3a i)x3ex2ex2x7ex75x617.6x4dx3ex73x12x16x20x15x0x49x65x7bx60ii),x4a(26),
x59x29
Cov￡uiy(ˉz0i;ˉz1i);rj ?r0? = ?E￡uy(ˉzi0;ˉzi1)?E[rj ?r0]; j = 1;:::;n:
x23x45
E[rj ?r0] = ??E￡uy(ˉzi0;ˉzi1)?￠?1 Cov
"
uiy(ˉzi0;
nX
k=1
ˉ 1ik xk);rj
#
; (30)
j = 1;:::;n:
x3bx6dx2dx1fx7e i x5axcx49x4bx37x36 rj x32x11x58x56x7bx49x57x46x1ax4b k 6= j, xk =
p(xk)(rk) x7e rj x32x11x56x58x56x7bx49x49x3bx6ex57x4ax26x3fx59x29x57x64x4e ˉ 1ij = 0, x46
E[rj ?r0] = 0. x4bx15x41x1bx57x4ax4dx1x75x61x57
uiy
?
ˉzi0;
nX
k=1
ˉ 1ik xk
!
?uiy
?
ˉzi0;
X
k6=j
ˉ 1ik xk
!
= uiyy
?
ˉzi0;
X
k6=j
ˉ 1ik xk +?x
j
ˉ 1ij xj
!
ˉ 1ij xj:
x69x4d ?xj 2 (0;1) (x59x5ax48x49x4b xj x3ex7x1)x49x45 uiyy < 0, x24x59 ˉ 1ij 6= 0 x71x57
x4ax26x3fx59x29E[rj ?r0]x7e ˉ 1ij x60x51x49x3bx0x1fx27x29x67x5c ˉ 1ij , 1 = 1;:::;I x60
x51x4dx7x6ax4bx5x49x4ax4bx1ax4bx6cx6dx77x4ex57x5cPIi=1 ˉ 1ij = PIi=1 0ij > 0,x3bx46x59
x5ax67x5c ˉ 1ij > 0,x19ii)x13x49x49 2
177
x3ax4cx39x3ax77x47x7x18x78Rossx3eAPT.x18x78x3ex60x74x61x5ex5fxex1ex6cx1ax59
x4fx5ax77x5ex2fx7bx2ex2fx7ex60x69x6x1cxcx3ex15x16x49x7ex1fx4cx15x0x57x48x75x3bx5ax77x5e
x2ex2fx3ex6x1cxcx2ax5dx65r1;r2;:::;rk;:::,x65x3ax7x6cx6dx6ex70x10x57x45r0 x46x6cx18
x18x7x71x1x3ex5ax71x4x2ex2fx3ex6x1cxcx49x12x48x4bx5cKx5ex2fx7bx3bx68f1;f2;:::;fK
(x65x3ax7ex6x1cxcx15x0x57x69x59x4cx14x24x56x6c1)x57x5bx29x20x70x6fx62x6ax3fx13x49x73
rj ?r0 =
KX
k=1
?jk(fk ?r0)+"j; j = 1;2;:::; (31)
x3bx6dx48x4bfk x32x11x58x56x6bx6cx7bx49x57 "j x6cx15xdx70x6dx6ex4fx10x7x50x57x65x3ax11x58
x56x6bx6cx7bx49x57x7efk x6ax56x7bx49x57x1fx1dr1;r2;:::;rk;:::x32x11x58x56x7bx49(x3bx15
x7ax3fx1bx68xex6bx4dx3ex7ax19x57x38x6dx46x7ax3fx5fx58xc)x57x74x58
Var["j] 6 2; j = 1;2;:::: (32)
x39x3ax3ex40x3exex1ex6cx7bx60"j x6ax4fx55x25x50x49x3bx6dx1bx68xex6bx4dx3cx71x3ex48x4bx6cx73
rj = fj; j = 1;:::;K; (33)
"j = ?j;j+K(rj+K ?r0); j = K +1;:::: (34)
x6ex26x57x39x3ax57x1ax30x15x58x30x31x2cx1ax11x77x7ax7bx3eArrow–Prattx71x4x56x7bx4ax10
x3ex20x70x15x2ax5cx58x48x4bx73x1ax11x77x7ax7bx3eArrow–Prattx71x4x56x7bx4ax10x5cx20x70
x15x2ax3ex58x77x73
? u
i
yy(ˉz
0i;y)
E[uiy(ˉz0i;ˉz1i)] 6
i; (35)
x69x4dyx7xdx7ax1x57 i x65x5fx48x49x4byx3ex71x4fx49
x39x3ax3ex2ex2x72x78x6cx73x5fx48x75x45x46x4dx5cn > K x5ex71x4x2ex2fx57x1ex27x1a
x2x75x3enx7dx40x26x21x3ex6cx6dx46x4ex57x6ex27x1fx12n ! +1,x74x7bx60E["j] ! 0.
x56x397.9 (APT) x4bx6ex7x72x3x4x55x57x58x5bnx19x78x79x64x4dx4ex70x78x6ax55
x2ex2fx57x58x4cx4dp(x0), p(x1), :::, p(xn)x1ex1a, ˉ 11, ˉ 12, :::, ˉ 1I,x66x75nx19x78
x79x64x4dx4ex3bx10x55x4cx5fx4dx4ex7ax7bxax4f
wMk (n) =
PI
i=1
0i
k p(xk)P
n
k=1
PI
i=1
0i
k p(xk)
; k = 1;:::;n;
x1fx20x55x6e
limn!1wMk (n) = 0; k = K +1;:::;n;
178
x6fx55x5b
limn!1E
"
rj ?r0 ?
KX
k=1
?jk(fk ?r0)
#
= limn!1E["j] = 0; j = 1;2;:::;n:
(36)
x24x3a x7ex26x15x75x61x3ex2ex2x15x0x57x39x3ax4a (30), x1a uy x40x4dx1x75x61x1f
x25(35)x6a ˉ 1ij > 0,x59x27x29
E[rj ?r0] 6 iˉ 1ij p(xj)Cov[rj;rj]; j = 1;:::;n:
x23x45x4a(34),x59j > K x71x57x4a(32)x59x29
E["j] = E[?j;j+K(rj+K?r0)] 6 iˉ 1ij+Kp(xj+K) Var["j]j?
j;j+Kj
6
2 i
j?j;j+Kj
ˉ 1ij+Kp(xj+K):
x68x69x6cx4ax4bx4cx7cx7dx6cx6dx71x57x59x27x29
E["j] 6 fij?
j;j+Kj
(PIi=1 ˉ 1ij+K)p(xj+K)P
j=1(
PI
i=1 ˉ
1i
j )p(xj)
= fij?
j;j+Kj
wMj+K(n);
x69x4dfix6cx71x4fx49x4ax6ex19x59x27x29x75x61x3ex46x78x49 2
x3bx0x57x39x3ax1fx23x6cx6dx75x14x3ex49x4ax57x7ex60x14Rossx3eAPTx3ex62x78x2ex49
x7ex4cx1bx68xex6bx4dx67x29x36x3ex46x4ex58x1bx1cx57x4cx1bx29x36x3ex6c
limn!1
nX
j=1
(E["j])2 < +1;
x45x3ax4cx29x36x3ex6c
limn!1E["j] = 0; j = 1;2;:::;n:
x7x1ex3ax4cx3ex46x78x3cx3fx49x6bx6cx65x29x36x3bx15x3cx3fx3ex46x78x6cx5cx52x14x3ex49x6cx6d
x75x14x23x14x69x13x14x26x3ex56x71x15x6bx48x4bx26x57x68x69x6cx57x48x4bx4fx30x31x2cx19x32x6cxc
x18x50x4ax45x68xex6bx4dx3ex18x78x8x5cx3bx15x48x4bx57x65x59x1fx59x46x1bx15x30x31x2cx3ex58xb
x20x60(x1ax9x76x74x46x3ex35xcx3ex11x6c)x77x75x40x49x75x617.9x4dx3elimn!1wMk (n) =
0x56x6cx15x34x48x7ax48x4bx49x65x7ax4dx47x23x4cK x58x3bx33x26x57x4cx7cx7dx76x77x4dx3ex30
x15x2ex2fx67x41x3ex1bx63x7x6cx8x77x8x25x3ex49x3bx6ex57x5cE["j]x15x2ax3dx25x56x6cx5fx12
xbx15x16x3ex49x6ex26x57x4cx15x3fx3ex65x15x58x61x7bx3ex75x76x1bx1cx3bx60x3dx33x57x45x27x15
179
x3fx52x72x56x71x1ax77x3fx57x5fx4x3bx60x3dx33x49x1dx4bAPTx3ex3fx42x3dx33x79x7ax57x39x3a
x4cx4cx1bx2dx45x69x36x57x3bx6dx5fx1fx48x62x49
x23x1fx26x3ex18x78x4dx57x39x3ax57x59x27x36CAPMx6aAPTx3ex5fx60x6cx3bx65x65x3a
x3ex48x4bx5fx60x57x68x69x6cx1ax19x32x17x40x2cx4fx3ex48x4bx5fx60x49 CAPMx6cx15x58x61x3b
x33x15x16x57x74x58x3bx15x3bx33x57x47x7ax3fx65x5cx17x3ex6cx6dx7cx7dx76x77x3ex6x1cxcx4ax3b
x6cx65x47x1ax1bx65x5ax42x3dx33x3ex59x7bx26x61x49x45APTx6cx15x58x71x3bx33x15x16x57x1ax3b
x33x7bx35x3ex5cx17x18x8x5cx7ax3fx49x3bx3ex6cRossx51x65APTx6cx1bCAPMx3cx2cx3e
x69x52x71x3ex78x46x49x23x3fx42x1dx40x77x4ex57 APTx27x77x52x3fx3cx2cx49x6bx6cAPTx3ex71
x3bx33x15x16x12x3fx6cx3ex65x48x4bx0x34x3ex57x3bx0x3ex5fx33x48x4bx61x78x26x4ex5fx60x3cx71
x3ex61x4ax49x3bx6ex57x1ax4bx43x44x45x46x47x3ex61x78x79x7a(x63x64xcx4bModigliani–Miller
x61x78x3ex77x78x79x7a)x77x4ex57 CAPMx3ex13x14x57x6cx1bAPTx13x14x3cx71x40x49
x39x3a x62x27x19x1ax6x10x11x40x25x13x7x41x2dx5 Arrow–Debreu x3bx55x58x59x5ax11x2cx6x43x5c
x0x47x47x2ax11x11x12x58x59x33x20x60x21x29x70x4fx47xex1ax20x58x1cx4fx2d [1]x5x79x47 Debreu x20x58x1cx71
x36 [2]x5x7dx14x1dx1ex13x50x3bx1fx29x25x18x3ex3fx20x4ex4fx5 x48x77x7a Varian [17]x5 x35x7xax35x61x7a
Brouwerx2bx34x1x43x5cx18Debreu–Gale–Nika¨?do x43x5cx33x16x20x72x42x29x44x73x4ax58x59x7ex18x25
x1ex41x58x59x3ax5bx7ax4dx37x38x3ex3fx5 x3cx47x6ex58x61x10x3bx55xbx69x7x20x71x17x41x25x2cx4dx29x52x53x11x12
x5cx5dx5ax11x20x4ex4fx5x2ax47x41x44x73x4ax58x59x7ex18x2cx24x2ax37x1x1cx29x19x1ax20x62xdx3dx9x37x3bxfx2f
x63x45Magill–Quinzii [11]x29 Radner [14]x4x4dx2ex2cx20x7ex18x61x10x26xax32x33x5 x56x2bx47x46x25
x10x50x13(x3fx32x33)x29x53x47x7ex18x7x79x48x61x7ax55x22x79x7ax33x33x29xbxax26x32x33x20x7ex18x25x1ex2ax37x50
x6cx5 x3cx6x32x33xfx46x47x3ex3fx20x73x1ax29xbx53x20x21x2cx20x79x47x5cx5dx20x2bx72x73x3ax3cxcx30x65x6fx20
x62x15x29x31x4x4x52x25x7ex1fx6bx20x2bx72x73x5cx5dx20x3bx55x5ax11x5cx4fx4ex4fx50x37x38x61x62x29x70x7ex1fx6b
x20x2bx72x73x5cx5dx20x3bx55x5ax11x5cx4fx25x5fx26x5ax3x1x74x20x32x33x5bx5ax29
x27x53x11x12x5cx5dx3bx55x5ax11x20x4ex4fx6 Huang–Linzenberger [8] x7x5x35x12 5 x6bx49x6
Ingersoll [9]x7x5x35x128x6bx49x6Jarrow [10]x7x28x25x126x25 15x3418x6bx29x7ax4dx20x26xbx2e
x7x63x52x3bx20x21x6ex29x2bx3f Duffie x20 [3], [4] x11x47x3bx17x10x4fx7x42x3bx55x58x59x5ax11x5 x35x7 [3]
xdx7dx15x58x1cx20 Arrow–Debreu x43x5cx60xex2cxex7bx7cx47x73x11x31x32x29x19x1ax20x20x26x9x55x5x20
x62xdx37x38x62x57 Jarrow x20x2fx29x20x26x3bx5x25x27 Ross x20 APT x20x62xdx7ex61xfx18 Ross x20
x58x1cx4fx2d[15]x60x2ex3bx7cx29
Markowitz [12] x7x4ax52x1ax9x20x7ax1fx4dx4ex4fx55x13x74x4ax79x32x5x31x20x47x2cx37xex20x5a
x13x7fx1x31x77x51x6fx2ax10x58x59x33x60x21x13x29 x3cx47x35x20x43xex44x46x47x2dxex20x5cx4fx48x3x4a 7.4 x7
x7ex17x20x74x4ax79x32x4dx59xdx29x7ex61xfx5 x62x27x19x1ax6xfx3bx4x7x6ex58x2exex20x5x41x63x2exfx4dx2d
x5 Markowitz x5ax13x7fx1x31xcx28x23x2bx47x55x13x74x4ax79x32x20x54x74xbx69x29 Sharpe x20x25x27
CAPMx20x58x1cx4fx2d[15]x7x25x1ex2bx76x2exex5cx5dx5ax11x5 x3cx47CAPMx20x3bx55x5ax11x7ex18x35
x7ex47x26x4dx2ex2cx20x29x20x40x37x38x42x7dx2ex2cx20x47 Duffie [3]x29x26x4dx20x30x31x25x19x27x5 Nielsen
[13] Magill–Quinzii [11]x28x2ax47x15x28x18x2bx72x73x5cx5dx3bx55x5ax11x5cx4fx63x28x65x4dx29
x6bx6cx43x6dx6ex43
1. x2x53x6cx11xbx9x45x46x7fx65x3ex4fx47x15x16x6cx51x0x3ex7f
180
2. x2x53x6cx11xbx9x45x46x3ex15x6bx45x46x6cx6dx74x4cx75x61x6ax2fx1cx45x46x47x68x15x2f
x7bx75x61x7fx69x4dx1ax7ax7bx2cx3ex17x40x2cx4fx5cx2x53x48x4bx7f
3. x51x0x71x37x31x0x75x14x2fx7bx75x61x33x16x20x43x44x7cx7dx3ex6cx6dx74x4cx75x61x41x46
x65x11xbx9x45x46x3ex6cx6dx74x4cx75x61x7fx1bx1cx3bx51x75x4cx45x46x3ax3bx26x57x71x5f
x60x3ex75x61x57x4fx1ax16x20x43x44x7cx7dx3ex6cx6dx5cx2x53x27x42x7f
4. x2x53x6cx5fx16x20x43x44x7cx7dx7fx65x2x53x65x5fx5ax26x51x65x11xbx9x45x46x38x0x3e
x12x3fx7fx1ax4bx5fx16x20x43x44x7cx7dx3ex15x6bx6cx6dx5cx2x53x0x78x6fx40x3ex46x78x7f
5. x51x0x1cx40x6cx1x2x41x5cx16x3ex17x40x2cx4fx77x7e CAPM x69x60x15x6bx45x46x6c
x6dx13x14x7fx65x4cx61x78x26x27x60x77x39x46x78x7fx69x15x16x5cx2x53x5fx38x7f
6. x51x0x23x15x6bx45x46x6cx6dx13x14x77x27x60Rossx3eAPTx61x78x7fx65x5cx77x39x2f
x7bx48x4bx7fx69x46x78x7ex68xex6bx4dx43x44x3ex5cxex5fx60x7f
x71x6cx72x73
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