Methods of Mathematical Finance:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York
Springer New York
[2016]
|
| Ausgabe: | Corrected 4th printing |
| Schriftenreihe: | Probability Theory and Stochastic Modelling
39 |
| Schlagworte: | |
| Online-Zugang: | http://www.springer.com/ Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | xv, 415 Seiten Illustrationen 23.5 cm x 15.5 cm, 0 g |
| ISBN: | 9781493968145 1493968149 |
Internformat
MARC
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| 653 | |a KF | ||
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| 653 | |a incomplete markets | ||
| 653 | |a mathematical finance | ||
| 653 | |a mathematics | ||
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Datensatz im Suchindex
| _version_ | 1806413620870905856 |
|---|---|
| adam_text |
Contents
Preface vii
1 A Brownian Model of Financial Markets 1
1.1 Stocks and a Money Market. 1
1.2 Portfolio and Gains Processes . 6
1.3 Income and Wealth Processes . 10
1.4 Arbitrage and Market Viability . . 11
1.5 Standard Financial Markets . 16
1.6 Completeness of Financial Markets. 21
1.7 Financial Markets with an Infinite Planning Horizon . 27
1.8 Notes . 31
2 Contingent Claim Valuation in a Complete Market 36
2.1 Introduction . 36
2.2 European Contingent Claims. 39
2.3 Forward and Futures Contracts . 43
2.4 European Options in a Constant-Coefficient Market . . . 47
2.5 American Contingent Claims . . 54
2.6 The American Call Option. 60
2.7 The American Put Option. 67
2.8 Notes .- . . 80
3 Single-Agent Consumption and Investment 88
3.1 Introduction . 88
3.2 The Financial Market. 90
XIV
Contents
3.3 Consumption and Portfolio Processes . 91
3.4 Utility Functions . . . . 94
3.5 The Optimization Problems . 97
3.6 Utility from Consumption and Terminal Wealth. 101
3.7 Utility from Consumption or Terminal Wealth . Ill
3.8 Deterministic Coefficients. 118
3.9 Consumption and Investment on an Infinite Horizon . 136
3.10 Maximization of the Growth Rate of Wealth. 150
3.11 Notes . 153
4 Equilibrium in a Complete Market 159
4.1 Introduction . 159
4.2 Agents, Endowments, and Utility Functions . 161
4.3 The Financial Market: Consumption and Portfolio
Processes . 163
4.4 The Individual Optimization Problems . . . 167
4.5 Equilibrium and the Representative Agent. 170
4.6 Existence and Uniqueness of Equilibrium. 178
4.7 Examples. 189
4.8 Notes . 196
5 Contingent Claims in Incomplete Markets 199
5.1 Introduction . 199
5.2 The Model . 201
5.3 Upper Hedging Price . 204
5.4 Convex Sets and Support Functions. 205
5.5 A Family of Auxiliary Markets. 208
5.6 The Main Hedging Result.· - ■ . 211
5.7 Upper Hedging with Constant Coefficients. 220
5.8 Optimal Dual Processes . 225
5.9 Lower Hedging Price. 238
5.10 Lower Hedging with Constant Coefficients . 254
5.11 Notes . 257 6
6 Constrained Consumption and Investment 260
6.1 Introduction . 260
6.2 Utility Maximization with Constraints. 261
6.3 A Family of Unconstrained Problems. 266
6.4 Equivalent Optimality Conditions. 275
6.5 Duality and Existence . 284
6.6 Deterministic Coefficients, Cone Constraints. 291
6.7 Incomplete Markets. 302
6.8 Higher Interest Rate for Borrowing Than for Investing . . 310
6.9 Notes . 318
Contents
XV
Appendix A. Essential Supremum of a Family of Random Variables 323
Appendix B. On the Model of Section 1.1 327
Appendix C· On Theorem 6.4.1 335
Appendix D- Optimal Stopping for Continuous-Parameter Processes 349
Appendix E. The Clark Formula 363
References 3T1
Symbol Index 403
Index 411 |
| any_adam_object | 1 |
| author | Karatzas, Ioannis 1952- Shreve, Steven E. |
| author_GND | (DE-588)140840346 (DE-588)140840451 |
| author_facet | Karatzas, Ioannis 1952- Shreve, Steven E. |
| author_role | aut aut |
| author_sort | Karatzas, Ioannis 1952- |
| author_variant | i k ik s e s se ses |
| building | Verbundindex |
| bvnumber | BV044321843 |
| ctrlnum | (OCoLC)1002244207 (DE-599)DNB1116623625 |
| dewey-full | 330 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 330 - Economics |
| dewey-raw | 330 |
| dewey-search | 330 |
| dewey-sort | 3330 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | Corrected 4th printing |
| format | Book |
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| id | DE-604.BV044321843 |
| illustrated | Illustrated |
| indexdate | 2024-08-04T00:11:14Z |
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| isbn | 9781493968145 1493968149 |
| language | English |
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| physical | xv, 415 Seiten Illustrationen 23.5 cm x 15.5 cm, 0 g |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Springer New York |
| record_format | marc |
| series | Probability Theory and Stochastic Modelling |
| series2 | Probability Theory and Stochastic Modelling |
| spelling | Karatzas, Ioannis 1952- Verfasser (DE-588)140840346 aut Methods of Mathematical Finance Ioannis Karatzas, Steven Shreve Corrected 4th printing New York Springer New York [2016] xv, 415 Seiten Illustrationen 23.5 cm x 15.5 cm, 0 g txt rdacontent n rdamedia nc rdacarrier Probability Theory and Stochastic Modelling 39 Kontingenztheorie (DE-588)4247907-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf KF Brownian motion Stochastic calculus agents equilibrium finance incomplete markets mathematical finance mathematics valuation Finanzmathematik (DE-588)4017195-4 s Stochastischer Prozess (DE-588)4057630-9 s 1\p DE-604 Kontingenztheorie (DE-588)4247907-1 s Mathematisches Modell (DE-588)4114528-8 s 2\p DE-604 3\p DE-604 Shreve, Steven E. Verfasser (DE-588)140840451 aut Erscheint auch als Online-Ausgabe 978-1-4939-6845-9 Erscheint auch als Druck-Ausgabe 9781441928528 Erscheint auch als Online-Ausgabe Karatzas, Ioannis Methods of Mathematical Finance New York, NY : Springer New York, 1998 Online-Ressource Probability Theory and Stochastic Modelling 39 (DE-604)BV042008213 39 http://www.springer.com/ Verlag X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=e53c102abbff469bbdcbbf04f1544a6f&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029725292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Karatzas, Ioannis 1952- Shreve, Steven E. Methods of Mathematical Finance Probability Theory and Stochastic Modelling Kontingenztheorie (DE-588)4247907-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4247907-1 (DE-588)4114528-8 (DE-588)4057630-9 (DE-588)4017195-4 |
| title | Methods of Mathematical Finance |
| title_auth | Methods of Mathematical Finance |
| title_exact_search | Methods of Mathematical Finance |
| title_full | Methods of Mathematical Finance Ioannis Karatzas, Steven Shreve |
| title_fullStr | Methods of Mathematical Finance Ioannis Karatzas, Steven Shreve |
| title_full_unstemmed | Methods of Mathematical Finance Ioannis Karatzas, Steven Shreve |
| title_short | Methods of Mathematical Finance |
| title_sort | methods of mathematical finance |
| topic | Kontingenztheorie (DE-588)4247907-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Kontingenztheorie Mathematisches Modell Stochastischer Prozess Finanzmathematik |
| url | http://www.springer.com/ http://deposit.dnb.de/cgi-bin/dokserv?id=e53c102abbff469bbdcbbf04f1544a6f&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029725292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042008213 |
| work_keys_str_mv | AT karatzasioannis methodsofmathematicalfinance AT shrevestevene methodsofmathematicalfinance |