Bartholomew-Biggs Nonlinear Optimization with Financial Applications

1. Auflage 2006
ISBN: 978-0-387-24149-4
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 276 Seiten

This instructive book introduces the key ideas behind practical nonlinear optimization, accompanied by computational examples and supporting software. It combines computational finance with an important class of numerical techniques.

Autoren/Hrsg.

Bartholomew-Biggs, Michael

Inhaltsverzeichnis

1;output\0983.tif;2
2;output\0985.tif;3
3;output\0986.tif;4
4;output\0987.tif;5
5;output\0988.tif;6
6;output\0989.tif;7
7;output\0990.tif;8
8;output\0991.tif;9
9;output\0993.tif;10
10;output\0995.tif;11
11;output\0996.tif;12
12;output\0997.tif;13
13;output\0998.tif;14
14;output\0999.tif;15
15;output\1001.tif;16
16;output\1002.tif;17
17;output\1003.tif;18
18;output\1004.tif;19
19;output\1005.tif;20
20;output\1006.tif;21
21;output\1007.tif;22
22;output\1008.tif;23
23;output\1009.tif;24
24;output\1010.tif;25
25;output\1011.tif;26
26;output\1012.tif;27
27;output\1013.tif;28
28;output\1014.tif;29
29;output\1015.tif;30
30;output\1016.tif;31
31;output\1017.tif;32
32;output\1018.tif;33
33;output\1019.tif;34
34;output\1020.tif;35
35;output\1021.tif;36
36;output\1022.tif;37
37;output\1023.tif;38
38;output\1024.tif;39
39;output\1025.tif;40
40;output\1026.tif;41
41;output\1027.tif;42
42;output\1028.tif;43
43;output\1029.tif;44
44;output\1030.tif;45
45;output\1031.tif;46
46;output\1032.tif;47
47;output\1033.tif;48
48;output\1034.tif;49
49;output\1035.tif;50
50;output\1036.tif;51
51;output\1037.tif;52
52;output\1038.tif;53
53;output\1039.tif;54
54;output\1040.tif;55
55;output\1041.tif;56
56;output\1042.tif;57
57;output\1043.tif;58
58;output\1044.tif;59
59;output\1045.tif;60
60;output\1046.tif;61
61;output\1047.tif;62
62;output\1048.tif;63
63;output\1049.tif;64
64;output\1050.tif;65
65;output\1051.tif;66
66;output\1052.tif;67
67;output\1053.tif;68
68;output\1054.tif;69
69;output\1055.tif;70
70;output\1056.tif;71
71;output\1057.tif;72
72;output\1058.tif;73
73;output\1059.tif;74
74;output\1060.tif;75
75;output\1061.tif;76
76;output\1062.tif;77
77;output\1063.tif;78
78;output\1064.tif;79
79;output\1065.tif;80
80;output\1066.tif;81
81;output\1067.tif;82
82;output\1068.tif;83
83;output\1069.tif;84
84;output\1070.tif;85
85;output\1071.tif;86
86;output\1072.tif;87
87;output\1073.tif;88
88;output\1074.tif;89
89;output\1075.tif;90
90;output\1076.tif;91
91;output\1077.tif;92
92;output\1078.tif;93
93;output\1079.tif;94
94;output\1080.tif;95
95;output\1081.tif;96
96;output\1082.tif;97
97;output\1083.tif;98
98;output\1084.tif;99
99;output\1085.tif;100
100;output\1086.tif;101
101;output\1087.tif;102
102;output\1088.tif;103
103;output\1089.tif;104
104;output\1090.tif;105
105;output\1091.tif;106
106;output\1092.tif;107
107;output\1093.tif;108
108;output\1094.tif;109
109;output\1095.tif;110
110;output\1096.tif;111
111;output\1097.tif;112
112;output\1098.tif;113
113;output\1099.tif;114
114;output\1100.tif;115
115;output\1101.tif;116
116;output\1102.tif;117
117;output\1103.tif;118
118;output\1104.tif;119
119;output\1105.tif;120
120;output\1106.tif;121
121;output\1107.tif;122
122;output\1108.tif;123
123;output\1109.tif;124
124;output\1110.tif;125
125;output\1111.tif;126
126;output\1112.tif;127
127;output\1113.tif;128
128;output\1114.tif;129
129;output\1115.tif;130
130;output\1116.tif;131
131;output\1117.tif;132
132;output\1118.tif;133
133;output\1119.tif;134
134;output\1120.tif;135
135;output\1121.tif;136
136;output\1122.tif;137
137;output\1123.tif;138
138;output\1124.tif;139
139;output\1125.tif;140
140;output\1126.tif;141
141;output\1127.tif;142
142;output\1128.tif;143
143;output\1129.tif;144
144;output\1130.tif;145
145;output\1131.tif;146
146;output\1132.tif;147
147;output\1133.tif;148
148;output\1134.tif;149
149;output\1135.tif;150
150;output\1136.tif;151
151;output\1137.tif;152
152;output\1138.tif;153
153;output\1139.tif;154
154;output\1140.tif;155
155;output\1141.tif;156
156;output\1142.tif;157
157;output\1143.tif;158
158;output\1144.tif;159
159;output\1145.tif;160
160;output\1146.tif;161
161;output\1147.tif;162
162;output\1148.tif;163
163;output\1149.tif;164
164;output\1150.tif;165
165;output\1151.tif;166
166;output\1152.tif;167
167;output\1153.tif;168
168;output\1154.tif;169
169;output\1155.tif;170
170;output\1156.tif;171
171;output\1157.tif;172
172;output\1158.tif;173
173;output\1159.tif;174
174;output\1160.tif;175
175;output\1161.tif;176
176;output\1162.tif;177
177;output\1163.tif;178
178;output\1164.tif;179
179;output\1165.tif;180
180;output\1166.tif;181
181;output\1167.tif;182
182;output\1168.tif;183
183;output\1169.tif;184
184;output\1170.tif;185
185;output\1171.tif;186
186;output\1172.tif;187
187;output\1173.tif;188
188;output\1174.tif;189
189;output\1175.tif;190
190;output\1176.tif;191
191;output\1177.tif;192
192;output\1178.tif;193
193;output\1179.tif;194
194;output\1180.tif;195
195;output\1181.tif;196
196;output\1182.tif;197
197;output\1183.tif;198
198;output\1184.tif;199
199;output\1185.tif;200
200;output\1186.tif;201
201;output\1187.tif;202
202;output\1188.tif;203
203;output\1189.tif;204
204;output\1190.tif;205
205;output\1191.tif;206
206;output\1192.tif;207
207;output\1193.tif;208
208;output\1194.tif;209
209;output\1195.tif;210
210;output\1196.tif;211
211;output\1197.tif;212
212;output\1198.tif;213
213;output\1199.tif;214
214;output\1200.tif;215
215;output\1201.tif;216
216;output\1202.tif;217
217;output\1203.tif;218
218;output\1204.tif;219
219;output\1205.tif;220
220;output\1206.tif;221
221;output\1207.tif;222
222;output\1208.tif;223
223;output\1209.tif;224
224;output\1210.tif;225
225;output\1211.tif;226
226;output\1212.tif;227
227;output\1213.tif;228
228;output\1214.tif;229
229;output\1215.tif;230
230;output\1216.tif;231
231;output\1217.tif;232
232;output\1218.tif;233
233;output\1219.tif;234
234;output\1220.tif;235
235;output\1221.tif;236
236;output\1222.tif;237
237;output\1223.tif;238
238;output\1224.tif;239
239;output\1225.tif;240
240;output\1226.tif;241
241;output\1227.tif;242
242;output\1228.tif;243
243;output\1229.tif;244
244;output\1230.tif;245
245;output\1231.tif;246
246;output\1232.tif;247
247;output\1233.tif;248
248;output\1234.tif;249
249;output\1235.tif;250
250;output\1236.tif;251
251;output\1237.tif;252
252;output\1238.tif;253
253;output\1239.tif;254
254;output\1240.tif;255
255;output\1241.tif;256
256;output\1242.tif;257
257;output\1243.tif;258
258;output\1244.tif;259
259;output\1245.tif;260
260;output\1246.tif;261
261;output\1247.tif;262
262;output\1248.tif;263
263;output\1249.tif;264
264;output\1250.tif;265
265;output\1251.tif;266
266;output\1252.tif;267
267;output\1253.tif;268
268;output\1254.tif;269
269;output\1255.tif;270
270;output\1256.tif;271
271;output\1257.tif;272
272;output\1258.tif;273
273;output\1259.tif;274
274;output\1260.tif;275
275;output\1261.tif;276

Leseproben

Preface (p. XVI)

This book has grown out of undergraduate and postgraduate lecture courses given at the University of Hertfordshire and the University of Bergamo. Its pri- mary focus is on numerical methods for nonlinear optimization. Such methods can be applied to many practical problems in science, engineering and manage- ment: but, to provide a coherent secondary theme, the applications considered here are all drawn from financial mathematics. (This puts the book in good company since many classical texts in mathematics also dealt with commer- cial arithmetic.) In particular, the examples and case studies are concerned with portfolio selection and with time-series problems such as fitting trend- lines and trend-channels to market data.

The content is intended to be suitable for final-year undergraduate students in mathematics (or other subjects with a high mathematical or computational content) and exercises are provided at the end of most sections. However the book should also be useful for postgraduate students and for other researchers and practitioners who need a foundation for work involving development or application of optimization algorithms.

It is assumed that readers have an un- derstanding of the algebra of matrices and vectors and of the Taylor and Mean Value Theorems in several variables. Prior experience of using computational methods for problems such as solving systems of linear equations is also de- sirable, as is familiarity with iterative algorithms (e.g., Newton's method for nonlinear equations in one variable).

The approach adopted in this book is a blend of the practical and theoretical. A description and derivation is given for most of the currently popular methods for continuous nonlinear optimization. For each method, important conver- gence results are outlined (and we provide proofs when it seems instructive to do so). This theoretical material is complemented by numerical illustrations which give a flavour of how the methods perform in practice.

It is not always obvious where to draw the line between general descriptions of algorithms and the more subtle and detailed considerations relating to re- search issues. The particular themes and emphases in this book have grown out of the author's experience at the Numerical Optimization Centre (NOC). This was established in 1968 at the Hatfield College of Technology (predeces- sor of the University of Hertfordshire) as a centre for research in optimization techniques.

Since its foundation, the NOC has been engaged in algorithm de- velopment and consultancy work (mostly in the aerospace industry). The NOC staff has included, at various times, Laurence Dixon, Ed Hersom, Joanna Go- mulka, Sean McKeown and Zohair Maany who have all made contributions to the state-of-the-art in fields as diverse as quasi-Newton methods, sequential quadratic programming, nonlinear least-squares, global optimization, optimal control and automatic differentiation.

The computational results quoted in this book have been obtained using a Fortran90 module called SAMPO. This is based on the NOC's OPTIMA library - a suite of subroutines for different types of minimization problem. The name SAMPO serves as an acronym for Software And Methods for Portfolio Optimization. (However, it is also worth mentioning that The Sampo appears in Finnish mythology as a magical machine which grinds out endless supplies of corn, salt and gold.