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4 4
A=
16 3 2 135 10 11 89 6 7 124 15 14 1
1 1
=
[ ]
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Aij i j A
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3 3
1 2
%
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%%
20 1
aj+1 = aj+ 0.25 aj j
==,=, > , < , >=,
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y = min{e2x+2, 20}
PROGRAM
...
global x;
x=1:10;
y=2;
z=mult(y);
...
FUNCTION
function a=mult(b);
global x;
a=x*b;
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a b
/ /
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-30 -20 -10 0 10 20 30 40 500
0.05
0.1
0.15
0.2
0.25
0.3
0.35Frequency distribution of monthly excess returns, 1932-2005
Return
Frequency,
fraction
Y = KL1
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m n {}
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{ }
f(x) f(x)
f(x)f(x+) f(x )2
f(x)
f(x)f(x+) 2f(x) +f(x )2
.
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x
x
f(x)
x
f x0
x0 x
f(x)f(x0) +f
(x0)(x x0). f
f(x)f(x0) +f(x0)(x x0)
x x f(x) = 0 f(x0) +f
(x0)(x x0)0
x x0 f(x0)
f(x0).
x0 x
x1x0 f(x0)
f(x0).
x1=x x1 x x0
x1 x2
x2x1 f(x1)
f(x1)
(n+ 1)
xn+1xn f(xn)
f(xn)
x xn+1xn
|xn+1xn|<
= 1012
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x
f
(x) = 0
x
x
x
x
f(x) =y f(x) y = 0 x
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x1+x22x3 = 03x1x3 = 52x1x2 = 1
(x1, x2, x3)
1 1 23 0 12 1 0
x1x2x3
=
051
A=
1 1 23 0 12 1 0
, x=
x1x2x3
, b=
051
Ax= b
x x= A1b A1 A
maxs
U(c1, c2) = c111 +
c121
c1 = y s c2 = y + (1 +r)s ci i s y r
s
(y s) R(y+Rs) = 0.
s =
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a, b x x[a, b] x f(x) = 0 f(a) f(b) x0 = 0.5(a+ b) f(x0) f(a) x0 b x1 = 0.5(x0+b) f(b) x1 = 0.5(x0+a)
f(xn)0
f(x)
0
a
b
c s c0 c1
c0 (1 +r)c1 = 0c0+
c11 +r
y y1 +r
= 0
c0 c1
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a b
20 1 aj+1 = aj+ 0.25 aj j
y = x2 y = x3 y= ex y= log(x) y=
x
0< k
