LINEBURG


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6.66948645920598 4.46391793267020
6.70754726725807 4.46391793267020
6.74496662226235 4.46391793267020
s=
0
170 OPTIMAL CONTROL MODELS IN FINANCE

0.31633632471690
0.63267264943379
0.94900897415069
0.94900897415069
0.94900897415069
0.94900897415069
0.96600598277128
0.98300299139188
0.99999999999990



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

x0=(3,2)

control: [A] [ ] [ ]
B C

model1_1(3,3,parameters)
um =
0
0
1.00000000000000
f=
-4.49775108882148
g=
-2.220446049250313e-16
xm =
3.00000000000000 2.00000000000000
3.00000000000000 2.00000000000000
3.00000000000000 2.00000000000000
3.00000000000000 2.00000000000000
3.00000000000000 2.00000000000000
2.00000000000000
3.00000000000000
3.00000000000000 2.00000000000000
3.36336204900022 2.27071366163561
3.78530547911419 2.56979963470193
4.26744142249872 2.90415715247832
s=
0
0
0
0
0
0
0
0.33333333333333
0.66666666666667
0.99999999999990

x0=(5, 3)
APPENDIX B: Some Computation Results 171

model1_1(3,3,parameters)
um =
0
0
1.00000000000000
f=
-6.98439125301710
g=
-2.220446049250313e-16
xm =
5.00000000000000 3.00000000000000
3.00000000000000
5.00000000000000
5.00000000000000 3.00000000000000
3.00000000000000
5.00000000000000
3.00000000000000
5.00000000000000
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=(0.5, 1)

control : [C] , [B] , [A]

results:

model1_1(3,3,parameters)
um =
-0.00000000000000
0.44198331380348
0.55801668619645
f=
-2.03958198064794
g=
172 OPTIMAL CONTROL MODELS IN FINANCE

-6.283862319378386e-14
xm =
0.50000000000000 1.00000000000000
0.50000000000000 1.00000000000000
0.50000000000000 1.00000000000000
0.50000000000000 1.00000000000000
0.50836518053403 1.24730846467207
0.53459240084601 1.55577840604261
0.58093560157541 1.94053557501097
1.14106504606018 1.94053557501097
1.60612415480481 1.94053557501097
1.99224914208392 1.94053557501097
s=
0
-0.00000000000000
-0.00000000000000
-0.00000000000000
0.14732777126783
0.29465554253566
0.44198331380348
0.62798887586897
0.81399443793445
0.99999999999990


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

x0=(0.5, 1)

control : [A] , [B] , [C]

results:

model1_1(3,3,parameters)
um =
0.52071677552328
-0.00000000000000
0.47928322447289
f=
-1.81807434266798
g=
-3.836042594684841e-12
xm =
0.50000000000000 1.00000000000000
0.73901347970328 1.00000000000000
0.93994199708665 1.00000000000000
1.10885409839574 1.00000000000000
1.10885409839574 1.00000000000000
1.10885409839574 1.00000000000000
1.10885409839574 1.00000000000000
173
APPENDIX B: Some Computation Results

1.24170396001051 1.01227203398012
1.36155842306688 1.04280425406198
1.47466384342158 1.08536853674905
s=
0
0.17357225850776
0.34714451701552
0.52071677552328
0.52071677552328
0.52071677552328
0.52071677552328
0.68047785034757
0.84023892517187
0.99999999999990

model1_1(6,6,parameters)
um =
0.39890660392318
-0.00000000000000
0.00000000000000
0.11928746513786
-0.00000000000000
0.48180593092858
f=
-1.82053330509933
g=
-1.038513719464618e-11
xm =
0.50000000000000 1.00000000000000
0.59648376317515 1.00000000000000
0.68676144864600 1.00000000000000
0.77123224690021 1.00000000000000
0.85026967149177 1.00000000000000
0.92422321064582 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
0.99341987262807 1.00000000000000
1.01323431734672 1.00000000000000
1.03265871639605 1.00000000000000
1.00000000000000
1.05170074779209
174 OPTIMAL CONTROL MODELS IN FINANCE

1.07036793840976 1.00000000000000
1.00000000000000
1.08866766695811
1.10660716689690 1.00000000000000
1.00000000000000
1.10660716689690
1.10660716689690 1.00000000000000
1.10660716689690 1.00000000000000
1.10660716689690 1.00000000000000
1.00000000000000
1.10660716689690
1.00000000000000
1.10660716689690
1.17569510221352 1.00307087089333
1.24040740530816 1.01202132418871
1.30187570955606 1.02549798919538
1.36097381645976 1.04259929524034
1.41839237440713 1.06270178723606
1.08536187030624
1.47468755717307
s=
0
0.06648443398720
0.13296886797439
0.19945330196159
0.26593773594879
0.33242216993598
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.39890660392318
0.41878784811282
0.43866909230247
0.45855033649211
0.47843158068175
0.49831282487140
0.51819406906104
0.51819406906104
0.51819406906104
0.51819406906104
0.51819406906104
0.51819406906104
0.51819406906104
0.59849505754914
0.67879604603723
0.75909703452533
APPENDIX B: Some Computation Results 175

0.83939802301342
0.91969901150152
0.99999999999990



4. Results for Program D
project3_1(3,1)
f=
1.0586
g=
-6.2238e-11
xm =
3.0000 5.0000
3.2515 -3.4665
3.2515 -3.4665
-9.1222 1.1345
s=
0
0.2840
0.2840
1.0000

project3_1(3,2)
f=
1.1967
g=
-1.4602e-10
xm =
3.0000 5.0000
3.2944 -3.4031
-1.4369 -2.7269
-2.4523 0.2524
-1.6076 1.3348
-1.3167 1.7035
-0.9671 1.9524
s=
0
0.2792
0.5584
0.7411
0.9239
0.9620
1.0000

project3_1(3,3)
f=
0.9367
g=
1.7265e-10
176 OPTIMAL CONTROL MODELS IN FINANCE
xm =
3.0000 5.0000
3.7672 -2.6588
-3.3194
-0.0810
-2.7291 -1.1775
-2.8827 0.4586
-2.3886 1.3429
-1.6078 1.5983
-1.6078 1.5983
-1.6078 1.5983
-1.6078 1.5983
s=
0
0.2302
0.4604
0.6906
0.7938
0.8969
1.0000
1.0000
1.0000
1.0000

project3_1(6,1)
f=
0.7708
g=
2.0042e-10
xm =
3.0000 5.0000
4.3970 -0.4306
4.3970 -0.4306
4.3970 -0.4306
2.5059 -3.3710
2.5059 -3.3710
-8.8124 3.4589
s=
0
0.1346
0.1346
0.1346
0.3056
0.3056
1.0000

project3_1(6,2)
f=
0.9828
g=
-1.9679e-10
APPENDIX B: Some Computation Results 177
xm =
3.0000 5.0000
3.6722 -2.8237
-0.3772 -3.2174
-0.6028 -2.9559
-0.8093 -2.6976
-0.8093 -2.6976
-2.6976
-0.8093
-2.8731 -0.6405
-2.8489 0.5052
0.5052
-2.8489
-2.8489 0.5052
-2.8489 0.5052
-2.8489 0.5052
s=
0

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