March 2010
Intermediate to advanced
238 pages
5h 59m
English
Content preview from Portfolio Optimization
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Sec. 8.1 The Entire Efficient Frontier 175
Go to Step 2.
Step 2:
There is no i with (g
11
)
i
< 0 and 1 ≤ k
i
≤ m. Set
˜
t
2
= ∞.
ˆ
t
2
= min
−,
0.6
0.4
, −
= 1.50,
=
b
2
− a
′
2
h
01
a
′
2
h
11
, l
2
= 2.
Set t
2
= min{∞, 1.5} = 1.5 and go to Step 3.
Step 3:
The optimal solution is
0.0
0.6
0.4
+ t
0.0
−0.4
0.4
,
with full multiplier vector (−0.012 + t 0.038, 0, 0, −0.012 + t 1.088)
′
, for
all t ∈ [0.3158, 1.5].
Since t
2
=
ˆ
t
2
, set K
2
= {1, 2 , 4 }, n
2
= 3
Set j = 2 and go to Step 1.
Iteration
2
Step 1:
H
2
=
1 × 10
−2
0 0 −1 0 1
0 2 × 10
−2
0 0 −1 1
0 0 3 × 10
−2
0 0 1
−1 0 0 0 0 0
0 −1 0 0 0 0
1 1 1 0 0 0
,
ˆ
b
2
=
0.0
0.0
1.0
,
K
2
= {1, 2 , 4 }.
176 Determination of the Entire Efficient Frontier Chap. ...
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