Tools for Incomplete Markets - Second Edition
Buch, Englisch, 416 Seiten, Format (B × H): 155 mm x 234 mm, Gewicht: 580 g
ISBN: 978-0-691-14121-3
Verlag: Princeton University Press
Originally published in 2003, Mathematical Techniques in Finance has become a standard textbook for master's-level finance courses containing a significant quantitative element while also being suitable for finance PhD students. This fully revised second edition continues to offer a carefully crafted blend of numerical applications and theoretical grounding in economics, finance, and mathematics, and provides plenty of opportunities for students to practice applied mathematics and cutting-edge finance. Ales Cerný mixes tools from calculus, linear algebra, probability theory, numerical mathematics, and programming to analyze in an accessible way some of the most intriguing problems in financial economics. The textbook is the perfect hands-on introduction to asset pricing, optimal portfolio selection, risk measurement, and investment evaluation.The new edition includes the most recent research in the area of incomplete markets and unhedgeable risks, adds a chapter on finite difference methods, and thoroughly updates all bibliographic references. Eighty figures, over seventy examples, twenty-five simple ready-to-run computer programs, and several spreadsheets enhance the learning experience. All computer codes have been rewritten using MATLAB and online supplementary materials have been completely updated. A standard textbook for graduate finance courses Introduction to asset pricing, portfolio selection, risk measurement, and investment evaluation Detailed examples and MATLAB codes integrated throughout the text Exercises and summaries of main points conclude each chapter
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik EDV | Informatik Angewandte Informatik Wirtschaftsinformatik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik
Weitere Infos & Material
Preface to the Second Edition xiii
From the Preface to the First Edition xix
Chapter 1: The Simplest Model of Financial Markets 1
1.1 One-Period Finite State Model 1
1.2 Securities and Their Payoffs 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 19
1.15 Summary 20
1.16 Notes 21
1.17 Exercises 22
Chapter 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 36
2.6 Arbitrage 38
2.7 No-Arbitrage Pricing 40
2.8 State Prices and the Arbitrage Theorem 41
2.9 State Prices and Asset Returns 44
2.10 Risk-Neutral Probabilities 45
2.11 State Prices and No-Arbitrage Pricing 46
2.12 Asset Pricing Duality 47
2.13 Summary 48
2.14 Notes 49
2.15 Appendix: Least Squares with QR Decomposition 49
2.16 Exercises 52
Chapter 3: Risk and Return in the One-Period Model 55
3.1 Utility Functions 56
3.2 Expected Utility Maximization 59
3.3 The Existence of Optimal Portfolios 61
3.4 Reporting Expected Utility in Terms of Money 62
3.5 Normalized Utility and Investment Potential 63
3.6 Quadratic Utility 67
3.7 The Sharpe Ratio 69
3.8 Arbitrage-Adjusted Sharpe Ratio 71
3.9 The Importance of Arbitrage Adjustment 75
3.10 Portfolio Choice with Near-Arbitrage Opportunities 77
3.11 Summary 79
3.12 Notes 81
3.13 Exercises 82
Chapter 4: Numerical Techniques for Optimal Portfolio Selection in Incomplete Markets 84
4.1 Sensitivity Analysis of Portfolio Decisions with the CRRA Utility 84
4.2 Newton's Algorithm for Optimal Investment with CRRA Utility 88
4.3 Optimal CRRA Investment Using Empirical Return Distribution 90
4.4 HARA Portfolio Optimizer 94
4.5 HARA Portfolio Optimization with Several Risky Assets 96
4.6 Quadratic Utility Maximization with Multiple Assets 99
4.7 Summary 102
4.8 Notes 102
4.9 Exercises 102
Chapter 5: Pricing in Dynamically Complete Markets 104
5.1 Options and Portfolio Insurance 104
5.2 Option Pricing 105
5.3 Dynamic Replicating Trading Strategy 108
5.4 Risk-Neutral Probabilities in a Multi-Period Model 116
5.5 The Law of Iterated Expectations 119
5.6 Summary 121
5.7 Notes 121
5.8 Exercises 121
Chapter 6: Towards Continuous Time 125
6.1 IID Returns, and the Term Structure of Volatility 125
6.2 Towards Brownian Motion 127
6.3 Towards a Poisson Jump Process 136
6.4 Central Limit Theorem and Infinitely Divisible Distributions 142
6.5 Summary 143
6.6 Notes 145
6.7 Exercises 145
Chapter 7: Fast Fourier Transform 147
7.1 Introduction to Complex Numbers and the Fourier Transform 147
7.2 Discrete Fourier Transform (DFT) 152
7.3 Fourier Transforms in Finance 153
7.4 Fast Pricing via the Fast Fourier Transform (FFT) 158
7.5 Further Applications of FFTs in Finance 162
7.6 Notes 166
7.7 Appendix 167
7.8 Exercises 169
Chapter 8: Information Management 170
8.1 Information: Too Much of a Good Thing? 170
8.2 Model-Independent Properties of Conditional Expectation 174
8.3 Summary 178
8.4 Notes 179
8.5 Appendix: Probability Space 179
8.6 Exercises 183
Chapter 9: Martingales and Change of Measure in Finance 187
9.1 Discounted Asset Prices Are Martingales 187
9.2 Dynamic Arbitrage Theor
