Markov decision processes with applications to finance:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XVI, 388 S. graph. Darst. |
| ISBN: | 9783642183232 3642183239 9783642183249 |
Internformat
MARC
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Datensatz im Suchindex
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IMAGE 1
CONTENTS
1 INTRODUCTION AND FIRST EXAMPLES 1
1.1 APPLICATIONS 4
1.2 ORGANIZATION OF THE BOOK G
1.3 NOTES AND REFERENCES 7
PART I FINITE HORIZON OPTIMIZATION PROBLEMS AND FINANCIAL MARKETS
2 THEORY OF FINITE HORIZON MARKOV DECISION PROCESSES 13 2.1 MARKOV
DECISION MODELS 14
2.2 FINITE HORIZON MARKOV DECISION MODELS 17.
2.3 THE BELLMAN EQUATION 19
2.4 STRUCTURED MARKOV DECISION MODELS 28
2.4.1 SEMICONTINUOUS MARKOV DECISION MODELS 29 2.4.2 CONTINUOUS MARKOV
DECISION MODELS 32
2.4.3 MEASURABLE MARKOV DECISION MODELS 33
2.4.4 MONOTONE AND CONVEX MARKOV DECISION MODELS 34 2.4.5 COMPARISON OF
MARKOV DECISION MODELS 38
2.5 STATIONARY MARKOV DECISION MODELS 39
2.6 APPLICATIONS AND EXAMPLES 44
2.6.1 RED-AND-BLACK CARD GAME 44
2.6.2 A CASH BALANCE PROBLEM 46
2.6.3 STOCHASTIC LINEAR-QUADRATIC PROBLEMS 50
2.7 EXERCISES 53
2.8 REMARKS AND REFERENCES 56
3 THE FINANCIAL MARKETS 59
3.1 ASSET DYNAMICS AND PORTFOLIO STRATEGIES 59
3.2 JUMP MARKETS IN CONTINUOUS TIME 66
3.3 WEAK CONVERGENCE OF FINANCIAL MARKETS 69
3.4 UTILITY FUNCTIONS AND EXPECTED UTILITY 70
IX
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1009117661
DIGITALISIERT DURCH
IMAGE 2
X CONTENTS
3.5 EXERCISES 72
3.6 REMARKS AND REFERENCES 73
4 FINANCIAL OPTIMIZATION PROBLEMS 75
4.1 THE ONE-PERIOD OPTIMIZATION PROBLEM 76
4.2 TERMINAL WEALTH PROBLEMS 79
4.3 CONSUMPTION AND INVESTMENT PROBLEMS 93
4.4 OPTIMIZATION PROBLEMS WITH REGIME SWITCHING 100
4.5 PORTFOLIO SELECTION WITH TRANSACTION COSTS 106
4.6 DYNAMIC MEAN-VARIANCE PROBLEMS 117
4.7 DYNAMIC MEAN-RISK PROBLEMS 124
4.8 INDEX-TRACKING 132
4.9 INDIFFERENCE PRICING 134
4.10 APPROXIMATION OF CONTINUOUS-TIME MODELS 140
4.11 REMARKS AND REFERENCES 142
PART II PARTIALLY OBSERVABLE MARKOV DECISION PROBLEMS
5 PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES 147
5.1 PARTIALLY OBSERVABLE MARKOV DECISION PROCESSES 148
5.2 FILTER EQUATIONS 151
5.3 REFORMULATION AS A STANDARD MARKOV DECISION MODEL 157 5.4 BAYESIAN
DECISION MODELS 159
5.5 BANDIT PROBLEMS WITH FINITE HORIZON 166
5.6 EXERCISES 171
5.7 REMARKS AND REFERENCES 173
6 PARTIALLY OBSERVABLE MARKOV DECISION PROBLEMS IN FINANCEL75 6.1
TERMINAL WEALTH PROBLEMS 176
6.2 DYNAMIC MEAN-VARIANCE PROBLEMS 183
6.3 REMARKS AND REFERENCES 188
PART III INFINITE HORIZON OPTIMIZATION PROBLEMS
7 THEORY OF INFINITE HORIZON MARKOV DECISION PROCESSES . . . 193 7.1
MARKOV DECISION MODELS WITH INFINITE HORIZON 194
7.2 SEMICONTINUOUS MARKOV DECISION MODELS 201
7.3 CONTRACTING MARKOV DECISION MODELS 205
7.4 POSITIVE MARKOV DECISION MODELS 208
7.5 COMPUTATIONAL ASPECTS 211
7.5.1 HOWARD'S POLICY IMPROVEMENT ALGORITHM 212
7.5.2 LINEAR PROGRAMMING 214
7.5.3 STATE SPACE DISCRETIZATION 220
7.6 APPLICATIONS AND EXAMPLES 223
7.6.1 MARKOV DECISION MODELS WITH RANDOM HORIZON 223 7.6.2 A CASH
BALANCE PROBLEM WITH INFINITE HORIZON 224
IMAGE 3
CONTENTS XI
7.6.3 CASINO GAMES 226
7.6.4 BANDIT PROBLEMS WITH INFINITE HORIZON 230
7.7 EXERCISES 236
7.8 REMARKS AND REFERENCES 240
8 PIECEWISE DETERMINISTIC MARKOV DECISION PROCESSES 243 8.1 PIECEWISE
DETERMINISTIC MARKOV DECISION MODELS 243 8.2 SOLUTION VIA A
DISCRETE-TIME MARKOV DECISION PROCESS 247 8.3 CONTINUOUS-TIME MARKOV
DECISION CHAINS 256
8.4 EXERCISES 262
8.5 REMARKS AND REFERENCES 264
9 OPTIMIZATION PROBLEMS IN FINANCE AND INSURANCE 267
9.1 CONSUMPTION-INVESTMENT PROBLEMS WITH RANDOM HORIZON . . 267 9.2 A
DIVIDEND PROBLEM IN RISK THEORY 271
9.3 TERMINAL WEALTH PROBLEMS IN A PURE JUMP MARKET 280
9.4 TRADE EXECUTION IN ILLIQUID MARKETS 293
9.5 REMARKS AND REFERENCES 298
PART IV STOPPING PROBLEMS
10 THEORY OF OPTIMAL STOPPING PROBLEMS 303
10.1 STOPPING PROBLEMS WITH FINITE HORIZON 303
10.2 STOPPING PROBLEMS WITH UNBOUNDED HORIZON 309
10.3 APPLICATIONS AND EXAMPLES 316
10.3.1 A HOUSE SELLING PROBLEM 316
10.3.2 QUIZ SHOW 318
10.3.3 THE SECRETARY PROBLEM 319
10.3.4 A BAYESIAN STOPPING PROBLEM 323
10.4 EXERCISES 329
10.5 REMARKS AND REFERENCES 330
11 STOPPING PROBLEMS IN FINANCE 331
11.1 PRICING OF AMERICAN OPTIONS 331
11.2 CREDIT GRANTING 340
11.3 REMARKS AND REFERENCES 343
PART V APPENDIX
A TOOLS FROM ANALYSIS 347
A.I SEMICONTINUOUS FUNCTIONS 347
A.2 SET-VALUED MAPPINGS AND A SELECTION THEOREM 351
A.3 MISCELLANEOUS 352
IMAGE 4
XII CONTENTS
B TOOLS FROM PROBABILITY 355
B.I PROBABILITY THEORY 355
B.2 STOCHASTIC PROCESSES 356
B.3 STOCHASTIC ORDERS 358
C TOOLS FROM MATHEMATICAL FINANCE 365
C.I NO ARBITRAGE PRICING THEORY 365
C.2 RISK MEASURES 367
REFERENCES 369
INDEX 385 |
| any_adam_object | 1 |
| author | Bäuerle, Nicole Rieder, Ulrich |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 9783642183232 3642183239 9783642183249 |
| language | English |
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| spelling | Bäuerle, Nicole Verfasser aut Markov decision processes with applications to finance Nicole Bäuerle ; Ulrich Rieder Berlin [u.a.] Springer 2011 XVI, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Markov-Entscheidungsprozess (DE-588)4168927-6 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Markov-Entscheidungsprozess (DE-588)4168927-6 s Finanzmathematik (DE-588)4017195-4 s DE-604 Rieder, Ulrich Verfasser (DE-588)171034708 aut Erscheint auch als Online-Ausgabe Markov Decision Processes with Applications to Finance X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3639510&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022635402&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4168927-6 (DE-588)4017195-4 |
| title | Markov decision processes with applications to finance |
| title_auth | Markov decision processes with applications to finance |
| title_exact_search | Markov decision processes with applications to finance |
| title_full | Markov decision processes with applications to finance Nicole Bäuerle ; Ulrich Rieder |
| title_fullStr | Markov decision processes with applications to finance Nicole Bäuerle ; Ulrich Rieder |
| title_full_unstemmed | Markov decision processes with applications to finance Nicole Bäuerle ; Ulrich Rieder |
| title_short | Markov decision processes with applications to finance |
| title_sort | markov decision processes with applications to finance |
| topic | Markov-Entscheidungsprozess (DE-588)4168927-6 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Markov-Entscheidungsprozess Finanzmathematik |
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