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[IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - On Portfolio Investment Model Using Ant Colony Optimization Algorithm

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Page 1: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - On Portfolio Investment Model Using Ant Colony Optimization Algorithm

494

Proceedings of the 26th Chinese Control ConferenceJuly 26-31, 2007, Zhangjiajie, Hunan, China

��������� ��������1�� �1,2��1

1. ���������� �� 071003E-mail: [email protected]

2. ������� ���� 830002E-mail: [email protected]

� ���� Markowitz ������ ���� !"�#$%&'( )*+ !��"�#,-./012

3456789:+12#;< =>+?4 Lingo 12;<@A#BCD

���� !��"� ,-./0 5678 Lingo

On Portfolio Investment Model Using Ant Colony OptimizationAlgorithm

Zhou Jianguo 1�Zhang Hui 1�2�Tian Jiming 1

1. School of Business and Administration North China Electric Power University Baoding 071003 P. R. ChinaE-mail: [email protected]

2. Urumchi Electric Power Bureau Urumchi 830002 P. R. ChinaE-mail: [email protected]

Abstract: Based on Markowitz' theory of asset portfolio a multiple-goal optimization model of portfolio investment was setup considering both risk and return. Then applying ant colony optimization algorithm to solve the model we got a better resultthan that of using Lingo.Key Words: Portfolio investment Multi-objective programming Ant colony algorithm Lingo

1 �(Introduction)

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2 �� ���������(Multi- ob-jective Decision Model of Portfolio Investment)

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Page 2: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - On Portfolio Investment Model Using Ant Colony Optimization Algorithm

495

"# [ ]T

1 21

min ( ) ( ), ( ) 1n

ii

F x f x f x x=

⎧ ⎫= ⎪ =⎨ ⎬⎭⎩

∑ (4)

T T1 2( ) , ( )f x R X f x X CX= − =

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σ μσ μ2− = − −

⎧ = ⎨⎩ (

(5)

*+A� μ #,-./[ 0 1μ0 0 D�-1�2B

"�a13)45$% 1μ = 6"�a_7/�$

%D

3 ����(Ant Colony Optimization Algo-rithm)

�����#��T\E �� ���[

����R�-.�� �������[2 2 Tmin ( , ) (1 ) 1F R R M E Xσ μσ μ− = − − + − (6)

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0j ij ij

ijpα βτ η η⎧ <⎪= ⎨

⎪⎩ � ��, 1,2, ,i j l= � (7)

�E jτ �< j �#����� i jη �=[

min mini j j iF Fη = − �56T�X j &�X i -.�>���#���� #? �!�"# , 0α β > [$

]��% �/�<�5T&'()E,�X��

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56 �T�X iE#�5 k#��0���/7[

{ }arg max ,

,ijp j

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⎧ ⎪= ⎨ ⎪⎩

���X7564L��

T8�X7564L��(8)

, 1,2, ,i j l= ��X j9:B#@;<)[

1( 1) ( )

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j j jk

t tτ ρτ τ=

+ = + Δ∑ 1,2, ,j l= � (9)

, 01,2, ,

0, 0

k kj jk

j kj

QL Lj l

⎧ >⎪Δ = =⎨⎪⎩

�=

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X j#�3��E-.B##CD �=[

0( ) ( )k k kj j jL f x f x= − (10)

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(�)*#�� �+,-.E\/ n0(�)*F1#;<()E 5 kTX j2# ���

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01( 1 )k

i j i jx x jl

= + − + γ (11)

0 0 01( 1 )k

ij i jx x jl

= + − + γ (12)

1,2, ,i n= � 1,2, ,j l= ��E k

jγ 0kjγ [ [ ]0,1 l G58E6-�.#�L�7

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L� 1 2[ , , , ]k k k kj j j njX x x x= … M 0 1 0 2 0 0[ , , , ]k k k k

j j j njX x x x= �[ n0*5# �9#��:;D

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l n× ���X56�� �:?@#����A

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l

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X X XX X X

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⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

��

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(13)

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2 2 21 2

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��

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(15)

Page 3: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - On Portfolio Investment Model Using Ant Colony Optimization Algorithm

496

1 1 11 2

2 2 21 2

1 2

( )

l

l

m m ml

F F FF F F

F X

F F F

⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

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#�� �HE8=#���� -.(� #C

*;FE[-

0( ) ( )L F X F X= − (18)56T56G>#>��� �H KK�(18)

D=#?@ �BC L?LM4AF7M@C�

X#���� T9�MGL@N�TJ>O#�

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Begin��*()�

Ncycle=1 Uncycle [?/Y�+ ���V

�� , , , , (0) , , , ;jQ c n lα β ρ τ δ=

�K�L�EW# 0kjγ KI 0X O 0X X= �

F7 0( )F X 'F N���12FE�

WhileUnot termination coditionV{for(k=1�k<=m�k++)

{ Pm�5�L����XG�}for (index=0�index<n�index++)

{�K�L�FE kjγ M 0

kjγ �

for(k=1�k<=m�k++){if( ηij >=0){5 kH��/7�Q�

else.X2# ��}}

F73�JX���< �#-.(�#

�F :;�

H@���)< min minx F� �

@CX#���� jτ �}Ncycle=ncycle+1�If( min 2 min1x x− < δ )

Break�}X>�)BC�End

4 ����(Computational Experiment)

\/�>+>�A� !#��AB \12

� !#'(�:;[- (0.151,0.137)R = DA�

!#'(�DT 1D<D

� 1 �� !"

?@#'(�<Y

�Z ! 1 ! 2��

1 -0.188 0.188 0.22 0.26 -0.248 0.13 0.221 0.238 0.44 0.246 0.27 0.25 0.253 -0.246 0.16 0.151 0.137 -

�BE78��#' �/[-5TX

�E� #!"#$� 1Q = X�����

��Q� 0.7ρ = ����$]��% 1α = 12

$]��% 1.5β = &7#0R��[5678;

=#�) &)*F1I8#���) #?/F

� 0.001 �- 0.001δ = �(�<*5�� 10l =

3O5��[ 9m = D\/1KK$%[A4-

�/=

� 2 #$��%&'()*+,-.��

\/78$%[A

! 1 ! 2 2σ R -.(�

0.3 0.834 0.1659 0.023 0.149 -0.10090.4 0.754 0.2458 0.0187 0.1479 -0.0850.5 0.706 0.2938 0.017 0.1472 -0.06930.6 0.674 0.3257 0.0163 0.1468 -0.05380.7 0.651 0.3486 0.016 0.1465 -0.03480.8 0.634 0.3657 0.0158 0.1462 -0.0229

Lingo$%[A

! 1 ! 2 2σ R -.(�

0.3 0.723 0.277 0.0175 0.1474 -0.09770.4 0.683 0.3172 0.0165 0.1469 -0.08140.5 0.659 0.3414 0.016 0.1464 -0.06510.6 0.643 0.3575 0.0159 0.1463 -0.04890.7 0.631 0.369 0.0158 0.1462 -0.03270.8 0.622 0.3776 0.0157 0.1461 -0.0166

B+ 0.3μ = 0.4μ = 0.5μ = 0.6μ = 0.7μ =

0.8μ = :#4-��D

BCC< T;>�$%[A��J G\/7

8D=#-.(� 6F�G lingo D=-.(�

T\\/78T;<,-./0F1E)�

lingoDPG\/78MLingo�/;=#��"�#$

%&'(D��L$%[]G. L'([SG.#

^��.�E =� 1�$%&'(���D

� 1�\/78�=#� �� Lingo�=

� #��D2��T��#$%J G\/78�

="���#'(�?G Lingo �=#��"�#

'(�����T��#'(�JG\/78�=�

�#$%?G Lingo�=��#$%��D

G����?� \/78T;<,-./0�

��* !��"�E�� LingoD

Page 4: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - On Portfolio Investment Model Using Ant Colony Optimization Algorithm

497

0.1455

0.146

0.1465

0.147

0.1475

0.148

0.1485

0.149

0.1495

0.015 0.017 0.019 0.021 0.023 0.025

/ 1 ()0 !�1/

5 23(Conclusion)

\/��JF- !"�GH��(!"#K* !) $>+%&"�?'()*�J !"�

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�78T;<,-./0���� !��"�#

4E��#D 5678&���7L��#�

7���B� �="�aT345��@[��D

45678References9

[1] 6��. ����78#,�� !��"�� 12

[J]. !�#3"&#$, 2004, 34(6): 32-37.[2] U%7, ���. ����78#����"���

#1 ��[J]. �E������(�����), 2004,38(4): 37-39.

[3] ��, ���, ���. ����678# !��[J]."�12#9:, 2006, 16: 49-51.

[4] ���. !"#$%&A& 2!4� 12[J]. "#&$%9:, 2006, 21(5): 77-81.

[5] '&, '(). 4��78*+,- !��"�#�!

./[J]. 01�2��, 2002, 17(4): 364-367.[6] 345, 6(J. )*#K+#,�� !��"��

12[J]. 01�2��&3", 2000, 20(22): 37-43.[7] 789. 5678�:T;0,+<��E#=4

[D]. ->��, ?8����, 2002.[8] @A�, 8.�. !��"�129:[J]. /BC�

����, 2002, 15(3): 56-58.[9] Song Xuemei, Li Bing, Li Xiaoying. An improved ant col-

ony optimization solving continuous optimization problem.2006, 23(10): 173-175, 180.

[10] Shelokar P S, et al., Particle swarm and ant colony algo-rithms hybridized[J]. Appl.Math. Comput.2006, 10.

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