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x20x19x54x58x21954x46Arrow (1921–)x4Debreu (1921–)x54x70x71x57x58x72x73x69
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12
? Arrow–Debreux70x71x57x58x72x73x66x49x62x69
Arrow, K., and G. Debreu, 1954, Existence of an equilibrium for a
competitive economy, Econometrica, 22: 265–290.
? Markowitz (1927–)x4fx1ex14x25x7x8x69x63
Markowitz, H., 1952, Portfolio selection, Journal of Finance, 7: 77–91.
Markowitz, H., 1959, 1991 Second ed., Portfolio Selection: Efficient
Diversification of Investment, Basil Blackwell, Cambridge (x51x2cx3ax6fx2a
x6x4ex75x1dx48 H.x48 1999x48x1ex37x14x25x7x8x4x1ex6fx42x43x54x72x6x64x69x7dx33
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? x3x66x6ex66x69xax54Modigliani(1918–)–Miller(1923–2000)x62x69(Modigliani–
Miller Theorem, MMT)
Modigliani, F., and M. Miller, 1958, The cost of capital, corporation
finance, and the theory of investment, American Economic Review, 48:
261–297.
? Sharpe(1934–), Lintner(1918–), Mossinx9x54x1ex6fx1ex37x62x4ax55x56(Cap-
ital Asset Pricing Model, CAPM)
Sharpe, W., 1964, Capital asset prices: a theory of market equilibrium
under conditions of risk, Journal of Finance, 19: 425–442.
Lintner, J., 1965, The valuation of risk assets and the selection of risky
investments in stock portfolios and capital budgets, Review of Eco-
nomics and Statistics, 47: 13–37.
Mossin, J., 1966, Equilibrium in a capital asset market, Econometrica,
34: 768–783.
? Fama (1939–)x42x43x51x3ax1dx69x63
Fama, E. F., 1965, Random walks in stock market prices, Financial
Analysts Journal,. September/October.
Fama, E. F., 1970, Efficient Capital Markets: A review of theory and
empirical work, Journal of Finance, 25: 383–417.
? Black (1938–1995)–Scholes (1941–)–Merton (1944–)x3exbx62x4ax69x63
Black, F., and M. Scholes, 1973, The pricing of options and corporate
liabilities, Journal of Political Economy, 81: 637–654.
Merton, R., 1973, The theory of rational option pricing, Bell Journal
of Economics and Management Science, 4: 141–183.
Merton, R. C., 1992, Continuous-Time Finance, Rev. ed., Blackwell,
Oxford.
13
? Ross (1944–)x6dx3cx62x4ax69x63(Arbitrage Pricing Theory, APT)
Ross, S. A., 1976, The arbitrage theory of capital asset pricing, Journal
of Economic Theory, 13: 341–360.
Ross, S. A., 1978, A simple approach to the valuation of risky streams,
Journal of Business, 51: 453–475.
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x2bx48x26x7x59x5bx57x58x5ax68x74 Merton, Scholes x9x7dx5fx14x54x3dx3ex1ex6fx23x69x6e
x66(Long-Term Capital Management)x49x25x78x6ex5bx68x7x59x5bx5ax13x54x65x8x46
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x1x15x6bx54x7dx78x10x67x2x70x2bx71x7bx36x37x76x69x5fx60x78x52x53x54Grossman–Stiglitz
x67x63 (1976) x54x60x61x70x55x2x2ax31x32x42x43x4ax4bx19x57x7ax7bx61x21x51x7cx6ax48x33x34
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x6ax4a S0 x2x19x1bx54x48x58xdx50x27xfx54x6ax4ax23x25x51x78x64x74x75x48x6fx2x2ax41 aS0,
x6fx2x2ax41bS0,x17x2ca 6= b,x35xex50x27x54x6ax4ax67x3cx62x61x78x1x28x6dx14x4fx48x3a
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x1ax49x61x62x3exbx54x7ax4fx4ax4bx1K. x33x34x3exbx49xdx50x27xfx23x25x51x54x78x64
x4ax4bx1Ca = max(aS0 ?K;0)x4Cb = max(bS0 ?K;0),x17x2cmaxx60x27x46
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1. x26x66x3cx8x6ax73x57x70x1x3exbx2x78x64x69x6ax69x24x7bx7ax54x4fx1ex4fx1x48x24
x17x14x25x25x78x64x4fx1ex4fx1x48x67x23x54x19x7ex7fx7cx6x54x2ex3bx78x25x26x48xd C0 x1
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x6ax2a
?S0 +xC0 = ?aS0 +xCa; ?S0 +xC0 = ?bS0 +xCb:
x26x7ex23x1ex68x3exbx54xdx17xbxfx4ax4bx1x2a
C0 = Ca ?Cb +aCb ?bCaa?b :
2. x3exbx54xdx50x27xfx4ax6x79x7ax2x2ex3cx62x54x48xfx2x10x7ex7fx49x45x66x6ax73x54
x2ex3cx62x54x4ax4bx48x24x5ex3exbx6fx50x23x24x7ex1fx6ax73x66x16x4x22x4fx66x3(x3ax3ex61x62
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x3exbx7bx17x66 y x38x22x4fx66x3x57 z x49x6ax73x54x14x25x78x66x2x26x25x64x14x25x54xdx50
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y +zaS0 = Ca; y +zbS0 = Cb:
x26x7ex23x1ex68
z = Ca ?CbS
0(a?b)
; y = aCb ?bCaa?b ; C0 = y +zS0 = Ca ?Cb +aCb ?bCaa?b :
3. x3ax3ex73x61x62xdx50x27xfx23x25x51x78x64x74x75x48xfx51x50x33x62x25x78x64x74x75x54
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23
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x33x6dx3cx61xdx2x5dx2ax17x61x62xdx17xbxfx57xdx50x27xfx54x50x51x4ax6x70x26x18x48x2ex66
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x49x25x64x61x62x56x48x67x66x49x51x70x64x10x50x27x54x23x25x1dx4x6bx48x53x68xdx50x27xf
x54x6ax4ax54x36x72x6x68x28x67x9x66xdx17xbxfx54x6ax4ax78x25x2x7bx1ax4bx2cxcx7ax51
x70x2bx4ex661,x4dx70x2bx16x661,x39x58x66x490x571x75x76x54x68q (x25x27)x53x68
aq +(1?q)b = 1; x4 q = 1?ba?b:
x58xdx17xbxfx54x3exbx4ax4bx7x8x67x2x49x25x64x23x25x1dx4x6bx56x54xdx50x27xfx54x3exb
x4ax4bx54x36x72x6x48x4
C0 = qCa +(1?q)Cb = Ca ?Cb +aCb ?bCaa?b :
Black–Scholes x55x56x17x7ax36x51x33x34x28x6dx48x17x2cx15x74x75x54x70x77x49x66x62
x3ex61xdx18x76x54x2ax5cx2x7fx0x54x48x6ax4ax54x2ax5cx5ax2x7fx0x54x78x25x10x66x3bx2dx4f
x1ex31x59x17x5bx23x56x15x79x2ex6dx66x16x54x6bx56x6ax42x27x70x48x2x70x2bxfx28x54x23x37x78
x25x18x6ax4ax2ax5cx11x61x62x1x49x68x4fx44x3bx21x22x3x1fBrownx5x30x27x60x27x57x10x18x48
x58x61x62x51x70x64x17x4ax6x2ex5dx68x54x3dx54x33x69x6ax2cx68 (x69x68x6fx22x4fx66x3)x48x27
x2ex1x6ax4ax54x46x16x5x78 Black–Scholes x54x6ax7cx63x64x2cx3bx54x2x25x18x54x65x70x64
x76x77x48x4x6ax73x66x16x57x3exbx66x16x54x24x17x14x25x23x10x6x69x6ax48x39x58x41x1x70x64
x33x69x6ax2cx68x78x26x7ex1fx68x70x2bx7x1x33x69x6ax48x17x1ex67x2 Black–Scholes x3exb
x6ex26x78x13x27x54xcxdx48x16x17x2 Merton x9x54xcxdx48x7fx40x41x61x4dx78x64x76x77x48
x10x3ex49x10 Black–Scholes x69x63x54x22x5cx4x76x77x2cx48x14x61x3x1dx2ex3bx78x65x8x64
x76x77x7ax6ex42x70x64xdx7ex7fx42x43xfx54x25x22x78x49x7ex7fx42x43x2cx48x59x70x64x4ax6x47x44
x66x6ax4ax2ax5cx54x1ax36x2cx68(x69x63x44x7fxcxdx50x62xbx21 (contingent claim)xf)x5b
x23x24x7ex1fx11x64x6ax42x66x16xex0x27xdx1x10xfx48x39x58x10x3ex54x4ax4bx5ax67x26x6ax4ax4
x66x16xex0x16x5ex1cx1dx62x4ax55xex27x44x62x78x7ex7fx42x43x54x25x22x49x69x63x44x24x1x45
x75x78x31x32x79x19x74x75x43x7fx1ex1fx48x58x6ax73x75x72x54x2cx68x64x72x7fx2ex2xax63x2ex48x33
x34x7bx17x2ex54x1ax36x2cx68x2x2ex23x25xdx1x10xfx54x48x39x58x10x3ex67x2ex23x25x51x1dx70x54
x62x4ax78x1ax71x54x42x43x5x2x2ex7ex7fx54x48x7bx58x2dx2ex6fx60x44x2ex25x62x4ax54x1ax36x2c
x68x66x16xcx7ax45x6ex6fx60x54x2ex23x8x16x54x69x6ax78x65x60x64x76x77x60x54x1x67x4bx54x68
x4fx40x26x13x48xcx1xdx1ex37x62x4ax40x6fx62x69xfx78x3bx2ex7ex46x3cx54x12x7fx3bx11x48x10x23
x24x70x41x2a (x7ex1ex54)x33x6dx3cx61xdx9x4ax66x66x49x10x50x27x54x2ex3cx62x1dx54x70x64x4
24
x6b(x68x4fx44xcx1xdx9x4ax9x51x3bxf)x48x53x68x15x1fx18x23x54x6ax4ax5bx9x66x50x27x6ax4a
x54x36x72x6(x68x4fx44xcx1x6ax4ax40x41xdx9x1fx6axfx57x31x32x3cx27x2ex1x7dx48x25x18x58
x75x47x48x6ax4ax54x13x1ax6)x78x25x49x11x64x79x7ax44x23x24x70x48x17x42x43x1dx33x5fx3fx19x15
x1fx7dx5bx2ex25xax4ex17x41x18x48x50x27x54x2ex3cx62x1dx51x17x10x49x54x33x3x48x7dx3ex2ex7
xbxcx70x64xdx4bx21x69x12xex53xfx51x48x58x7x43x39x12x6dx6ex25x64x33x3x78x3bx2x49x25
x70x77x44x48 Black–Scholes x69x63x74x27x61x10x10x6ax42x71x72x24x5ex21x70x71x54x2ex3cx62
x70x71x56x54x44xex5fx60xcxdx44x54x45x75x1dx78
x2ex1fx48x3bx31x3ax3ex49x44x4bx19x57x1fx79x19x54x48x25x18x54xbx78x64x76x77x73x75x39
xdx1cx1dx62x4ax55xexfx48x58x65x60x64x76x77x47x75x7ex1ex54x33x6dx3cx61xdx48x35xepx23x25
x2ex80 x571 x75x76x48x58x2ex13x51x25x27x79x7ax78x22x23x3ax3ex68x19x54x15x13x31x32x49x40
x26x44x5bx2x70x26x54x48xfx49x76x1fx2cx48x65x60x64x76x77x25x7cx2cx17x3exbx54x50x27x4ax6
x43x50x18x48x17x17xbx4ax6x5ax70x62x43x50x78x10x17x71x5ax67x2x7ex1ex54x33x6dx3cx61xdx54
x75x39x78x58x49xbx78x64x76x77x56x48x51x2ex25x7cx2cx25x70x77x78x5ax67x2x70x48 xdx1cx1dx62x4a
x55xexfx51x2ex25x7cx2cx50x27x4ax6x43x50x54x3exbx48x17x17xbx4ax6x5ax43x50x78x2bx71x44x48
x3ax3exfx75x16x4dx48x25x64x7ax45x2ax45x31x48x47bx4a?bxax63x16x48 Ca = 0, Cb > 0,
x67x25x53C0x47x15x79x54x50x6x78x22x23x3dx3ex42x43x54x71x72x53x68x7ex7fx2ex4dx8x1ax25x26
x54x74x75x48xfx2x25x26x54x45x14x70x68x48 xdx1cx1dx62x4ax55xexfx57xdx66x49x6dx3cxfx2x2e
x5dx23x54x48x10x5ax23x25x24x3bx66x3dx3ex42x43x2cx54x2dx2exdx7ax7fx74x40xfx78
x39x25x70x45x14x2cx3ax3ex23x24x3cx8x1ax4ex3dx3ex57x58x4fx54x76x69x69x26x78x70x71x27
x70x48x17x2cx3bx19x54x68x4fx5bx77x25x18x21x70x54x75x1x2x68x2ex78xfx2x49x40x6fx5ex55x44
x4ex2ax67x2x31x7ex78x10x66x68x4fx40x41x77x28x54x26x31x48x23x24x3ax42x25x26x54x5ex7ex2ex68
xfx7fx78x58x10x66x68x4fx44x51x70x62xexfx54x26x31x27x70x48x7ex1fx25x26x54x28x6dx55x56x5a
x25x6dx6ex69x63x54x10x29x48x51x6cx26x7ex47x23x3cx19x69x63x54x10x43x48x5ax23x3cx19x69x63x54
x1bx2ax1dx78x17x7ax48x28x6dx54x55x56x36x51x71x3bx4ax6x78x3ax3ex2ex25x5dx2bx25x70x51x2cx20
x8x54x55x56x67x25x3bx27x4ex4fx3exbx62x4ax54x71x72x6bx12x78
1.7 x56x4bx3ax3ex13x10x33x6dx3cx61xdx4x1ex37x62x4ax40x6fx62x69x39x4dx19x70x2bx3a
x3bx27x4ex4fx65x63x78x3ax3ex19x57x3cx19x48x7ex1fx1cx1dx62x4ax55xex6fx33x6dx3cx61xdx48x23
x24x3bx40x6fx2cx68x27x1x1ax36x2cx68x62x4ax78x25x26x54x62x4ax69x55x4bx57x3dx3ex1x7dx3ex21
x2ex69x1ex78x6ax7bx49x66x11x12x54x62x4ax69x63x5bx2x16x5ex57x58x2fx30x31x54x47x39x4x48x49x48
x49x70x71x57x58x72x73xex4cx2cx40x41x54x78x58x49x44x4bx54x62x4ax69x55x2cx48x73x2ex1fx2x7e
x1fx6ax73x54x4ax4bx4x50x51x54x52x10x7cx6x27x1x3exbxdx7bx10x62x4axfx78x10x51x2ex3x21x6a
x73x4ax4bx6fx50x32x26x40x41x25x70x5fx60x78x25x18x3ax3ex7ex7fx3cx2ex19x42x43x2cx54x57x58x2f
x30x31x78x25x70x5dx23x49x13x0x54xcxdx2cx11x11x5ax12x7bx7cx61x78x49x25x70x16x51x2cx48x3a
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x1ex37x62x4ax40x6fx62x69x48x10x5ax2x25x69x54x78
x3ax3ex54x8x5fx77x1cx7ax57xbx4bx70x26x2ax61xdx73x51xdx17xbxfx57xdx50x27xfx78x2b
x18x23x78 xdx17xbxfx54x6ax4aS0x2x19x1bx54x48x58xdx50x27xfx54x6ax4ax23x25x51x78x64x74x75x48
25
x6fx2x2ax41 aS0, x6fx2x2ax41 bS0, x17x2c a 6= b. xdx17xbxfx57xdx50x27xfx54x50x51x4a
x6x2x70x26x54x48x47x33x7ex50x7fx0x48x5ax33x22x4fx3cx6ax78x61xdx51x70x53x4fx1ex64x34x35
x31 A. x62x21x38x39x54xax38x2x62x54x34x35x3ax3bx15x4ex78x1x7ex47x75x62x7ax62x54x3ax3b
x65x68x78x6cx79x2x51x25x26x70x2bx71x71x54x3ax3bx65x68u(c),x17x2ccx2x62x21x34x35x54x4a
x6x78x70x2bx25x69x54x61x62x1 u x2 c x54x49x54x65x68x48x4x10 A x27x70x48 xdx5bx13x68x4b
x2ex4bx28xfx78xfx2x3ax3exaxbx51xdx17xbxfx4xdx50x27xfx78x2bx18x23x48x10Ax27x70x48x58
x47x75x7ex1fx17xbx54x3cx62x34x35x4x53x27x54x2ex3cx62x34x35x48x27x4dx41x70x2bx18x25x54x3a
x3bx65x68x78
x49x3ax3exbx4bx54x65x63x2cx48x3ax3ex7cx52x36x51x20x58xdx50x27xfx23x25x5fx36x54x78x64
x70x71x54x25x27x78x2bx71x44x48x3ax3ex49x15x13x5ax3cx19x48x1ax36x2cx68x54x62x4ax57x6ax73x54x78
x64x70x71x54x5fx36x54x25x27x36x51x3x4cx78xfx2x49x25x18x48x17Ax75x10x36x57x54x4fx1ex34
x35x4fx1x4ex4fx44xex18x48x67x2ex68x2ex16x5ex62x21x6dx6ex54x7cx6ax48x10xdx50x27xfx51x70x2b
x4x6bx78x66x2x62x4x6bx6ax73x4ax6x1aS0 (x24x13x3ax3excx25x70x70x71x1x70x71a)x54x25
x27x1p,x58x1bS0 (x24x13x3ax3excx25x70x70x71x1x70x71b)x54x25x27x67x21?p. x25x2b
(p;1?p)x23x25x2x3cx71x75x5fx36x54xdx68x76x25x27xfx48x5ax23x25x2Ax16x5ex36x57x6dx6e
x54x7cx6ax27x72x73x54xdx74x76x25x27xfx78x16x5ex21x22 von Neumann–Morgenstein x54
x3ex2bx3ax3bx65x68x69x63(x4fx65x14x51)x48 Ax54x50x27x2ex3cx62x34x35x54x3ax3bx67x9x66x17x2e
x3cx62x3ax3bx54x68x4fx3ex2bx78x5ax67x2x70x48x31x32Ax49x70x71ax54x34x35x4ax6x1ca,x49
x70x71bx54x34x35x4ax6x1cb,x33x34x17x50x27x34x35x54x3ax3bx67x2pu(ca)+(1?p)u(cb),
x25x18x3ax3ex61x62x50x27x54x34x35x3ax3bx65x68x57x17xbx34x35x3ax3bx65x68x2x70x26x54x78x31
x32x3ax3ex13x61x62x48 Ax54x5x34x35x3ax3bx65x68x67x2x62x54x17xbx34x35x3ax3bx57x50x27x34
x35x3ax3bx75x4x48x33x34x62x54x5x3ax3bx65x68x67x2
U(c0;ca;cb) = u(c0)+pu(ca)+(1?p)u(cb);
x17x2cc0 x2x17xbx34x35x4ax6x48 ca x4cb x33x3fx2x78x64x50x27x34x35x4ax6x78x25x18x71x72
x44x58x61x62 A x10x17xbx4x50x27x54x45x15x6ax3bx70x26x78x31x32x62x45x17xbx48x16x50x27x48
x49x25x2bx3ax3bx65x68x54x13x78x66xbx16x70x2b0x571x75x76x54xdx13x1ax7bx14xfx78xfx25x51
x2ex13x14x56x4bx54x65x63x78
x1ax49x3ax3ex75x65x63x54x5fx60x2x2a A x32x26x7ex1fx62x10x22x4fx4x6ax42x54x4fx1ex48
x27x53x62x54x5x34x35x3ax3bx15x4ex78x25x18x58x47x61x62 A x49x17xbx51x1ex3d e0, x49x50x27
x51x1ex3dea x4eb. x66x2x31x32Ax49x17xbx24x22x4fx66x3xd (x31x32xd < 0x79x41x42
x1cx3),x49x6ax42x70x1x6ax73xs (x31x32xs < 0x79x41x42xdx3cx72xf)x48x49x50x27x39x22x4f
x47x3x48x24x6ax42x3cx8x6ax73x48x33x34x3ax3ex67x51
c0 = e0 ?xd ?S0xs; ca = ea +xd +aS0xs; cb = eb +xd +bS0xs:
x25x18x3ax3ex1cx7ax61xdx22x4fx2x33x3cx6ax54x78x25x26x48x10Ax27x70x54x15x6dx4fx1ex64x34
26
x35x44xex5fx60x67x28
>><
>>:
max U(c0;ca;cb) = u(c0)+pu(ca)+(1?p)u(cb)
s:t: c0 = e0 ?xd ?S0xs > 0
ca = ea +xd +aS0xs > 0
cb = eb +xd +bS0xs > 0
x25x70x2bx5fx60x2x2ex2x70x62x51x1ex7ex2ex70x62x78x2bx71x44x48x73x75x61xd u x2x49
x54x65x68x48x17 a x4 b x2ex49 1 x78x17x48x33x34x25x2bx5fx60x70x62x36x51x1ex78x25x2x7bx1
x25x18x67x4dx5fx36x3ax3ex44x4bx5fx19x54x6dx3cx29x4dx78 Ax73x47x75x7ex1fx17xbx24x22x4fxc
x3x48x6fx4ax70x1x6ax73x48x50x27x71x4ax3cx8x6ax73(x6fx31x17xbx71x4ax3cx72x6ax73x48x5dx5b
x66x1x22x4fx48x50x27x6fx4ax70x1x6ax73x27x66x7)x67x25x54x0x62x54x5x3ax3bx48x51x6cx25x26
x56x2x33x1bx71x54x78x3bx70x9x68x4fx54x3fx27x70x48x3ax3ex23x24x49x2ax6cx54x65x18x5ax1ax10
x53ux55x24x66x33x2ax4ex78x4dx70x69x4bx48x31x32x25x70x5fx60x51x1e ˉxd, ˉxsx48x33x34x2ex1x44
x29x31x63x54x19x35x4x60x48 (x7ex1ex54) x33x6dx3cx61xdx70x62x41x7dx78x25x67x2x70x48x31x32
x3ax3ex47x75x3bx70x71x72x73xex4cx27x65x63x3dx3ex5fx60x48x33x6dx3cx61xdx54x41x7dx17x71x5a
x2x79x44x38x3dx78x25x67x4ex70x57x1ax62x61x33x6dx3cx61xdx49x69x63x44x54x45x75x1dx78x2exf
x31x7ex48x31x32x49x68x4fx44x61x62x70x62x54x65x68x7ex1bx1dx38x3dx48x33x34x3ax3ex58x23x39x1e
x54x70x7bxcx75x38x3dx68x19
@U(e0 ?xd ?S0xs;ea +xd +aS0xs;eb +xd +bS0xs)
@xd
flfl
flfl
xd=ˉxd;xs=ˉxs
= 0;
@U(e0 ?xd ?S0xs;ea +xd +aS0xs;eb +xd +bS0xs)
@xs
flfl
flfl
xd=ˉxd;xs=ˉxs
= 0:
x4
u0(ˉc0) = pu0(ˉca)+(1?p)u0(ˉcb)
S0u0(ˉc0) = aS0pu0(ˉca)+bS0(1?p)u0(ˉcb)
x17x2c3
ˉc0 = e0 ? ˉxd ?S0ˉxs > 0
ˉca = ea + ˉxd +aS0ˉxs > 0
ˉcb = eb + ˉxd +bS0ˉxs > 0
x26x7ex23x24x68x19x48
1 = pu
0(ˉca)
u0(ˉc0) +(1?p)
u0(ˉcb)
u0(ˉc0)
1 = apu
0(ˉca)
u0(ˉc0) +b(1?p)
u0(ˉcb)
u0(ˉc0)
3x5dx17xex2dx5x3x5cx20>x60x0x12x37 >. xbx6x52x6fx4ax7ax32 u x36x2ax26x20x3cx43x12x47x25x2fx72
x20x29x27x44x24x25x5dx17x20x2bx33x67xax2ax5x3bx56x4dx2dx5x20x23x20x20x3bx12x74x2cx36x6cx2bx3bx43xax2ax29
27
x57x44x4bx54x65x60x64x76x77x7bx77x77x48x12 q = pu0(ˉca)u0(ˉc0), x33x34 1 ? q = (1 ? p)u0(ˉcb)u0(ˉc0).
x25x67x68x19x61xbx4bx54xdx9x4ax25x27x9x51x3bxf (x46x1fx79x48x26x66 u x2x49x54x65x68x48
x17x1fx68 (xdx17x72x3ax3bxf) x5x2x3bx54)x78x5ax67x2x70x48x25x17x71x67x2x4dx70x64xcx5a
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x54x5fx60x8x5fx48x49x68x19x6ax4ax62x4ax3x4cx54x10x2bx48x3ax3ex10x26x23x24x68x19x1ex37x62
x4ax40x6fx62x69x78x49x25x18x10x23x60x54x1x2a x1cx1dx24x1ex1fx20x21x22x23x24x25x10x26x27x28
x29x2ax2bx4x2cx2dx20x2ex2fx30x31x32x33x34x1dx35x36x28x37x38x36x3fx30x31x39x25x26x48x39x33
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x54x62x4ax55xex78xfx2x7fx1fx4fx1ex64x34x35x31x54x62x4ax55xex31x1fx49x42x43x44x12x70x48
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x5axfx54x57x58x4fx59x51x45x75x79x7ax48x58x10x73x55x1bx2axdx1x76x33x5axfx54x45(x23x69)x4f
x56x4fx36x27x70x48x23x25x51x2ex33x34x45x75x78
1.8 x3ax3ex54x51x7ax53x25x26x27x65x2bx2ax79x65x63x39x1cx1dx62x4ax55xex8x5fx54xdx6d
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29
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[1] x2cx65x55x48 A. S.x48 1990x48x57x58x4fx1x37x34x58x2ex2x70x23x4ex4fx48x48x7ex9x3ax48
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[2] x6cx74x4bx48 M.x48 1990x48x57x58x4fx69x55x63x48x33x68x30x9x3ax48x41x42x4ex4fx8x9x6x78
[3] x6cx74x4bx48 M. x9x52x48 R. E. x1x40x31x5dx49x48 2000x48x57x58x4fx69x55x63x54x20x55
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[4] x4bx73x48 L. A., x9x52x48 2000x48x6x72x54x57x58x4fx69x55x63x48x5x4bx36x9x3ax48x57
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[5] x8x4cx48 K. R.x48 1999x48x4ex4fx5fx1ax54x36x37x48x64x4dx25x3x4ex4fx50x3ax48x41x42x57
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[6] x43x1cx5dx48 J. M.x48 1988x48x67x3x3x3cx6ax4x50x51x7ex63x48x51x52(x53x6f)x3ax48x45x2
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[7] x0x3dx36x48 2002x48x7x28x3x7cx22x3x7cx6ax57x2cx68x4ax4bx48x44x31x7dx32x8x9x6x48x44
x31x78
[8] Cochrane, J. H., 2001, Asset Pricing, Princeton University Press, Prince-
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in Positive Economics, (University of Chicago Press, Chicago), 3–43
(x2cx3ax64x4fx2ax52x18x68x4ax64x54x48 2001x48xex55x22x3x49x56x57x3ax48x6cx5bx57x58
x58x16x4ex4fx8x9x6x48x41x42x48 118–165)x78
30
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[14] Hull, J. C., 1999, Options, Futures, and Other Derivatives, 4th ed.,
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x4x1ax36x2cx68x48x0x20x59x3ax48x1x56x8x9x6x48x41x42).
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N. J..
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[18] Paulos, J. A., 1998, Once upon a Number, Basic Books. L.A.. (x2cx3a
x6fx2ax7cx6ax5dx48 J. A., 2001x48x5ax4bx74x5bx48x63x33x2cx9x3ax48x44x31x4ex26x8x9
x6x78 )
[19] Pliska, S. R., Introduction to Mathematical Finance: Discrete Time
Models, Blackwell, Massachusetts.
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32
