LINEBURG


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0.1380
0.1380
0.3515
0.3515
project1_1(8)
um =
0.0108
0.3063
0.0801
0.1569
0.1200
0.0971
0.1539
0.0749
f=
0.0134
g=
-7.3581e-12
xm =
0
0.0108
0.0108
0.0908
0.0908
0.2109
0.2109
0.3647
0.3647
APPENDIX B: Some Computation Results 163

2. Results for Program B
project2_1(2,1)
um =
0.4167
0.5833
f=
1.8227
g=
-6.1625e-11
xm =
3.0000 5.0000
5.8281 -2.5048
0.6973 -11.1396
s=
0
0.4167
1.0000
project2_1(2,2)
um =
0.6512
0.3488
f=
0.9394
g=
-2.5978e-12
xm =
3.0000 5.0000
5.3714 -1.6031
2.3736 -1.6846
0.3249 -2.6175
-1.6526 -1.7606
s=
0
0.3256
0.6512
0.8256
1.0000
project2_1(4,1)
um =
0.0584
0.1610
0.5106
0.2700
f=
0.6311
g=
-2.8808e-11
xm =
3.0000 5.0000
164 OPTIMAL CONTROL MODELS IN FINANCE

4.2091 3.3108
4.3875 -2.2196
0.8660 -1.3209
-1.3328 -1.5506
s=
0
0.0584
0.2194
0.7300
1.0000
project2_1(4,2)
um =
0.0123
0.1431
0.5868
0.2578
f=
0.3388
g=
7.0286e-11
xm =
3.0000 5.0000
3.1513 4.8156
3.2968 4.6323
4.3621 1.4484
4.4301 -0.9324
2.5494 -1.2942
1.4915 -0.1476
0.8567 -1.6082
-0.3231 -1.9003
s=
0
0.0062
0.0123
0.0839
0.1554
0.4488
0.7422
0.8711
1.0000

project2_1(4,4)
um =
0.0024
0.1349
0.5626
0.3001
f=
0.2786
g=
APPENDIX B: Some Computation Results 165

-5.7630e-11
xm =
3.0000 5.0000
3.0147 4.9824
3.0293 4.9648
3.0438 4.9472
3.0583 4.9296
3.7520 3.3204
4.1877 1.8743
4.3942 0.6038
4.4016 -0.4854
3.7206 -1.2868
-1.2454
2.7950
2.0640 -0.7997
1.6791 -0.3053
1.3593 -1.3175
0.7498 -1.8604
0.0120 -2.0176
-0.7284 -1.8917
s=
0
0.0006
0.0012
0.0018
0.0024
0.0361
0.0698
0.1036
0.1373
027
.79
0.4186
0.5592
0.6999
0.7749
0.8499
0.9250
1.0000
project2_1(6,1)
um =
0.3257
0.1238
0.1980
-0.0000
0.3526
-0.0000
f=
0.5290
g=
-1.4863e-10
xm =
166 OPTIMAL CONTROL MODELS IN FINANCE

3.0000 5.0000
5.3715 -1.6041
3.5555 -3.8604
0.9604 -1.3485
0.9604 -1.3485
0.8020 0.9757
0.8020 0.9757
s=
0
0.3257
0.4495
0.6474
0.6474
1.0000
1.0000
project2_1(6,2)
um =
-0.0000
0.1329
0.5063
0.0741
0.1196
0.1671
f=
0.2615
g=
-4.3578e-11
xm =
3.0000 5.0000
3.0000 5.0000
3.0000 5.0000
4.1425 1.9787
4.3902 -0.3727
3.0702 -1.3534
1.8010 -0.5648
1.6448 -1.0998
1.4012 -1.5101
1.0408 -0.9124
0.8471 -0.3992
0.5008 -1.1814
-0.0789 -1.5304
s=
0
-0.0000
-0.0000
0.0665
0.1329
0.3861
0.6392
0.6763
APPENDIX B: Some Computation Results 167

0.7133
0.7731
0.8329
0.9165
1.0000



3. Results for Program C
Diferent controls in model1_1

p=0.1, k=0.15, r=0.2, d=0.1, c=1, T=10,

x0=(5,3)

control: [ ] [ ] [A]
C B

results:

model1_1(3,3,parameters)
um =
0.94900897415069
-0.00000000000000
0.05099102586178
f=
-6.98762419479152
g=
1.247046910179961e-11
xm =
5.00000000000000 3.00000000000000
5.40600401539454 3.47094537715380
5.95896569319826 3.95174665662712
6.63077320213855 4.46391793267020
44319272
.6973600
6.63077320213855
6.63077320213855 4.46391793267020
6.63077320213855 4.46391793267020
6.66948645920598 4.46391793267020
6.70754726725807 4.46391793267020
6.74496662226235 4.46391793267020
s=
0
0.31633632471690
0.63267264943379
0.94900897415069
0.94900897415069
0.94900897415069
0.94900897415069
0.96600598277128
0.98300299139188
0.99999999999990
168 OPTIMAL CONTROL MODELS IN FINANCE

control: [A] [B] [ ]
C

results:

model1_1(3,3,parameters)
um =
0
0
1.00000000000000
f=
-6.98439125301710
g=
-2.220446049250313e-16
xm =
5.00000000000000 3.00000000000000
50000000
.0000000 30000000
.0000000
3.00000000000000
5.00000000000000
5.00000000000000 3.00000000000000
5.00000000000000 3.00000000000000
5.00000000000000 3.00000000000000
5.00000000000000 3.00000000000000
5.43239375551053 3.49626657386023
6.02582277381470 4.00489471104744
6.74935621984978 4.55053034609536
s=
0
0
0
0
0
0
0
0.33333333333333
0.66666666666667
0.99999999999990



p=0.1, k=0.15, r=0.2, d=0.1, c=1, T=10,

x0=(3,2)

control: [ ] [ ] [A]
C B

model1_1(3,3,parameters)
um =
-.0000000
00000000
0.43627214331862
0.56372785682345
f=
APPENDIX B: Some Computation Results 169

-4.34971604717521
g=
1.420692452569483e-10
xm =
2.00000000000000
3.00000000000000
3.00000000000000 2.00000000000000
2.00000000000000
3.00000000000000
3.00000000000000 2.00000000000000
2.74560664232866 2.48750405168379
2.56260603757432 3.09383820357164
2.45034521298337 3.84796753331929
3.34895792223138 3.84796753331929
4.09363087946859 3.84796753331929
4.71073523102452 3.84796753331929
s=
0
-0.00000000000000
-0.00000000000000
-0.00000000000000
0.14542404777287
0.29084809554574
0.43627214331862
0.62418142892643
0.81209071453425
0.99999999999990

x0=(5,3)

model1_1(3,3,parameters)
um =
0.94900897415069
-0.00000000000000
0.05099102586178
f=
-6.98762419479152
g=
1.247046910179961e-11
xm =
5.00000000000000 3.00000000000000
5.40600401539454 3.47094537715380
3.95174665662712
5.95896569319826
6.63077320213855 4.46391793267020
6.63077320213855 4.46391793267020
6.63077320213855 4.46391793267020
6.63077320213855 4.46391793267020

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