Mathematical techniques in finance: tools for incomplete markets
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J. [u.a.]
Princeton Univ. Press
2004
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 378 S. graph. Darst. |
| ISBN: | 9780691088075 0691088063 0691088071 |
Internformat
MARC
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| 100 | 1 | |a Černý, Aleš |d 1971- |e Verfasser |0 (DE-588)130444898 |4 aut | |
| 245 | 1 | 0 | |a Mathematical techniques in finance |b tools for incomplete markets |c Aleš Černý |
| 264 | 1 | |a Princeton, N.J. [u.a.] |b Princeton Univ. Press |c 2004 | |
| 300 | |a XVIII, 378 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Actif financier |2 rasuqam | |
| 650 | 7 | |a Administração de risco |2 larpcal | |
| 650 | 7 | |a Finances |2 rasuqam | |
| 650 | 7 | |a Finanças (modelos matemáticos) |2 larpcal | |
| 650 | 7 | |a Fixation des prix |2 rasuqam | |
| 650 | 7 | |a Gestion des risques |2 rasuqam | |
| 650 | 7 | |a Instrument dérivé (Finances) |2 rasuqam | |
| 650 | 4 | |a Instruments dérivés (Finances) - Mathématiques | |
| 650 | 7 | |a Marché financier |2 rasuqam | |
| 650 | 7 | |a Modèle mathématique |2 rasuqam | |
| 650 | 7 | |a Onvolledige concurrentie |2 gtt | |
| 650 | 7 | |a Portfolio-theorie |2 gtt | |
| 650 | 4 | |a Prix - Fixation - Modèles mathématiques | |
| 650 | 7 | |a Risque financier |2 rasuqam | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 7 | |a Wiskundige methoden |2 gtt | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Derivative securities |x Mathematics | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Pricing |x Mathematical models | |
| 650 | 4 | |a Risk management |x Mathematical models | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface xiii
1 The Simplest Model of Financial Markets 1
1.1 One Period Finite State Model 1
1.2 Securities and Their Pay Offs 3
1.3 Securities as Vectors 3
1.4 Operations on Securities 4
1.5 The Matrix as a Collection of Securities 6
1.6 Transposition 6
1.7 Matrix Multiplication and Portfolios 8
1.8 Systems of Equations and Hedging 10
1.9 Linear Independence and Redundant Securities 12
1.10 The Structure of the Marketed Subspace 14
1.11 The Identity Matrix and Arrow Debreu Securities 16
1.12 Matrix Inverse 17
1.13 Inverse Matrix and Replicating Portfolios 17
1.14 Complete Market Hedging Formula 1 g
1.15 Summary 20
1.16 Notes 21
1.17 Exercises 21
2 Arbitrage and Pricing in the One Period Model 25
2.1 Hedging with Redundant Securities and Incomplete Market 25
2.2 Finding the Best Approximate Hedge 29
2.3 Minimizing the Expected Squared Replication Error 32
2.4 Numerical Stability of Least Squares 34
2.5 Asset Prices, Returns and Portfolio Units 37
2.6 Arbitrage 38
2.7 No Arbitrage Pricing 40
2.8 State Prices and the Arbitrage Theorem 42
2.9 State Prices and Asset Returns 45
2.10 Risk Neutral Probabilities 45
2.11 State Prices and No Arbitrage Pricing 45
2.12 Summary 48
2.13 Notes 49
2.14 Appendix: Least Squares with QR Decomposition 49
2.15 Exercises 52
x Contents
3 Risk and Return in the One Period Model 55
3.1 Utility Functions 55
3.2 Expected Utility Maximization 59
3.3 Reporting Expected Utility in Terms of Money 60
3.4 Scale Free Formulation of the Optimal Investment Problem with
the HARA Utility 62
3.5 Quadratic Utility 66
3.6 Reporting Investment Potential in Terms of Sharpe Ratios 70
3.7 The Importance of Arbitrage Adjustment 77
3.8 Portfolio Choice with Near Arbitrage Opportunities 78
3.9 Generalization of the Sharpe Ratio 82
3.10 Summary 83
3.11 Notes 84
3.12 Exercises 85
4 Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets 87
4.1 Sensitivity Analysis of Portfolio Decisions with the CRRA Utility 87
4.2 Newton s Algorithm for Optimal Investment with CRRA Utility 91
4.3 Optimal CRRA Investment Using Empirical Return Distribution 93
4.4 HARA Portfolio Optimizer 99
4.5 HARA Portfolio Optimization with Several Risky Assets 100
4.6 Quadratic Utility Maximization with Multiple Assets 104
4.7 Summary 106
4.8 Notes 107
4.9 Exercises 107
5 Pricing in Dynamically Complete Markets 109
5.1 Options and Portfolio Insurance 109
5.2 Option Pricing 110
5.3 Dynamic Replicating Trading Strategy 113
5.4 Risk Neutral Probabilities in a Multi Period Model 121
5.5 The Law of Iterated Expectations 124
5.6 Summary 126
5.7 Notes 126
5.8 Exercises 126
6 Towards Continuous Time 131
6.1 IID Returns, and the Term Structure of Volatility 131
6.2 Towards Brownian Motion 133
6.3 Towards a Poisson Jump Process 142
6.4 Central Limit Theorem and Infinitely Divisible Distributions 148
6.5 Summary 149
6.6 Notes 151
6.7 Exercises 151
7 Fast Fourier Transform 153
7.1 Introduction to Complex Numbers and the Fourier Transform 153
7.2 Discrete Fourier Transform (DFT) 158
7.3 Fourier Transforms in Finance 159
7.4 Fast Pricing via the Fast Fourier Transform (FFT) 164
7.5 Further Applications of FFTs in Finance 167
7.6 Notes 171
7.7 Appendix 172
7.8 Exercises 174
Contents xj
8 Information Management 175
8.1 Information: Too Much of a Good Thing? 175
8.2 Model Independent Properties of Conditional Expectation 179
8.3 Summary 183
8.4 Notes 184
8.5 Appendix: Probability Space 184
8.6 Exercises 188
9 Martingales and Change of Measure in Finance 193
9.1 Discounted Asset Prices Are Martingales 193
9.2 Dynamic Arbitrage Theorem 198
9.3 Change of Measure 199
9.4 Dynamic Optimal Portfolio Selection in a Complete Market 204
9.5 Summary 212
9.6 Notes 214
9.7 Exercises 214
10 Brownian Motion and ltd Formulae 219
10.1 Continuous Time Brownian Motion 219
10.2 Stochastic Integration and Ito Processes 224
10.3 Important Ito Processes 226
10.4 Function of a Stochastic Process: the Ito Formula 228
10.5 Applications of the Ito Formula 229
10.6 Multivariate Ito Formula 231
10.7 Ito Processes as Martingales 234
10.8 Appendix: Proof of the Ito Formula 235
10.9 Summary 235
10.10 Notes 236
10.11 Exercises 237
11 Continuous Time Finance 239
11.1 Summary of Useful Results 239
11.2 Risk Neutral Pricing 240
11.3 The Girsanov Theorem 243
11.4 Risk Neutral Pricing and Absence of Arbitrage 247
11.5 Automatic Generation of PDEs and the Feynman Kac Formula 252
11.6 Overview of Numerical Methods 256
11.7 Summary 257
11.8 Notes 258
11.9 Appendix: Decomposition of Asset Returns into Uncorrelated Components 258
11.10 Exercises 261
12 Dynamic Option Hedging and Pricing in Incomplete Markets 267
12.1 The Risk in Option Hedging Strategies 167
12.2 Incomplete Market Option Price Bounds 283
12.3 Towards Continuous Time 291
12.4 Derivation of Optimal Hedging Strategy 297
12.5 Summary 306
12.6 Notes 307
12.7 Appendix: Expected Squared Hedging Error in the Black Scholes Model 307
12.8 Exercises 309
Appendix A Calculus 313
A.I Notation 313
xii Contents
A.2 Differentiation 316
A.3 Real Function of Several Real Variables 319
A.4 Power Series Approximations 321
A.5 Optimization 324
A.6 Integration 326
A.7 Exercises 332
Appendix B Probability 337
B.I Probability Space 337
B.2 Conditional Probability 337
B.3 Marginal and Joint Distribution 340
B.4 Stochastic Independence 341
B.5 Expectation Operator 343
B.6 Properties of Expectation 344
B.7 Mean and Variance 345
B.8 Covariance and Correlation 346
B.9 Continuous Random Variables 349
B.10 Normal Distribution 354
B.ll Quantiles 359
B.12 Relationships among Standard Statistical Distributions 360
B.13 Notes 361
B.14 Exercises 361
References 369
Index 373
|
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| dewey-ones | 332 - Financial economics |
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| dewey-search | 332.0151 332/.01/51 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| language | English |
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| spelling | Černý, Aleš 1971- Verfasser (DE-588)130444898 aut Mathematical techniques in finance tools for incomplete markets Aleš Černý Princeton, N.J. [u.a.] Princeton Univ. Press 2004 XVIII, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Actif financier rasuqam Administração de risco larpcal Finances rasuqam Finanças (modelos matemáticos) larpcal Fixation des prix rasuqam Gestion des risques rasuqam Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Modèle mathématique rasuqam Onvolledige concurrentie gtt Portfolio-theorie gtt Prix - Fixation - Modèles mathématiques Risque financier rasuqam Stochastische processen gtt Wiskundige methoden gtt Mathematik Mathematisches Modell Derivative securities Mathematics Finance Mathematical models Pricing Mathematical models Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010352055&sequence=000008&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Černý, Aleš 1971- Mathematical techniques in finance tools for incomplete markets Actif financier rasuqam Administração de risco larpcal Finances rasuqam Finanças (modelos matemáticos) larpcal Fixation des prix rasuqam Gestion des risques rasuqam Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Modèle mathématique rasuqam Onvolledige concurrentie gtt Portfolio-theorie gtt Prix - Fixation - Modèles mathématiques Risque financier rasuqam Stochastische processen gtt Wiskundige methoden gtt Mathematik Mathematisches Modell Derivative securities Mathematics Finance Mathematical models Pricing Mathematical models Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4017195-4 |
| title | Mathematical techniques in finance tools for incomplete markets |
| title_auth | Mathematical techniques in finance tools for incomplete markets |
| title_exact_search | Mathematical techniques in finance tools for incomplete markets |
| title_full | Mathematical techniques in finance tools for incomplete markets Aleš Černý |
| title_fullStr | Mathematical techniques in finance tools for incomplete markets Aleš Černý |
| title_full_unstemmed | Mathematical techniques in finance tools for incomplete markets Aleš Černý |
| title_short | Mathematical techniques in finance |
| title_sort | mathematical techniques in finance tools for incomplete markets |
| title_sub | tools for incomplete markets |
| topic | Actif financier rasuqam Administração de risco larpcal Finances rasuqam Finanças (modelos matemáticos) larpcal Fixation des prix rasuqam Gestion des risques rasuqam Instrument dérivé (Finances) rasuqam Instruments dérivés (Finances) - Mathématiques Marché financier rasuqam Modèle mathématique rasuqam Onvolledige concurrentie gtt Portfolio-theorie gtt Prix - Fixation - Modèles mathématiques Risque financier rasuqam Stochastische processen gtt Wiskundige methoden gtt Mathematik Mathematisches Modell Derivative securities Mathematics Finance Mathematical models Pricing Mathematical models Risk management Mathematical models Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Actif financier Administração de risco Finances Finanças (modelos matemáticos) Fixation des prix Gestion des risques Instrument dérivé (Finances) Instruments dérivés (Finances) - Mathématiques Marché financier Modèle mathématique Onvolledige concurrentie Portfolio-theorie Prix - Fixation - Modèles mathématiques Risque financier Stochastische processen Wiskundige methoden Mathematik Mathematisches Modell Derivative securities Mathematics Finance Mathematical models Pricing Mathematical models Risk management Mathematical models Finanzmathematik |
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