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Mathematical Techniques in Finance: Tools for Incomplete Markets - Second Edition Second Edition [Pehme köide]

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  • Formaat: Paperback / softback, 412 pages, kõrgus x laius: 235x152 mm, kaal: 567 g
  • Ilmumisaeg: 26-Jul-2009
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691141215
  • ISBN-13: 9780691141213
Teised raamatud teemal:
Mathematical Techniques in Finance: Tools for Incomplete Markets - Second Edition Second EditionSuurem pilt
  • Formaat: Paperback / softback, 412 pages, kõrgus x laius: 235x152 mm, kaal: 567 g
  • Ilmumisaeg: 26-Jul-2009
  • Kirjastus: Princeton University Press
  • ISBN-10: 0691141215
  • ISBN-13: 9780691141213
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780691141213.html
Märksõnad:

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 Cern 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

Arvustused

"Ales erny's new edition of Mathematical Techniques in Finance is an excellent master's-level treatment of mathematical methods used in financial asset pricing. By updating the original edition with methods used in recent research, erny has once again given us an up-to-date first-class textbook treatment of the subject."Darrell Duffie, Stanford University

Muu info

Ales Cerny's new edition of Mathematical Techniques in Finance is an excellent master's-level treatment of mathematical methods used in financial asset pricing. By updating the original edition with methods used in recent research, Cerny has once again given us an up-to-date first-class textbook treatment of the subject. -- Darrell Duffie, Stanford University
Preface to the Second Edition xiii
From the Preface to the First Edition xix
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
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
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 Shame 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
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
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
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
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
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
9 Martingales and Change of Measure in Finance 187
9.1 Discounted Asset Prices Are Martingales
187
9.2 Dynamic Arbitrage Theorem
192
9.3 Change of Measure
193
9.4 Dynamic Optimal Portfolio Selection in a Complete Market
198
9.5 Summary
206
9.6 Notes
208
9.7 Exercises
208
10 Brownian Motion and Ito Formulae 213
10.1 Continuous-Time Brownian Motion
213
10.2 Stochastic Integration and Ito Processes
218
10.3 Important BO Processes
220
10.4 Function of a Stochastic Process: the Ito Formula
222
10.5 Applications of the Ito Formula
223
10.6 Multivariate IV) Formula
225
10.7 Ito Processes as Martingales
228
10.8 Appendix: Proof of the BO Formula
229
10.9 Summary
229
10.10 Notes
230
10.11 Exercises
231
11 Continuous-Time Finance 233
11.1 Summary of Useful Results
233
11.2 Risk-Neutral Pricing
234
11.3 The Girsanov Theorem
237
11.4 Risk-Neutral Pricing and Absence of Arbitrage
241
11.5 Automatic Generation of PDEs and the Feynman-Kac Formula
246
11.6 Overview of Numerical Methods
250
11.7 Summary
251
11.8 Notes
252
11.9 Appendix: Decomposition of Asset Returns into Uncon-elated Components
252
11.10 Exercises
255
12 Finite-Difference Methods 261
12.1 Interpretation of PDEs
261
12.2 The Explicit Method
263
12.3 Instability
264
12.4 Markov Chains and Local Consistency
266
12.5 Improving Convergence by Richardson's Extrapolation
268
12.6 Oscillatory Convergence Due to Grid Positioning
269
12.7 Fully Implicit Scheme
270
12.8 Crank-Nicolson Scheme
273
12.9 Summary
274
12.10 Notes
276
12.11 Appendix: Efficient Gaussian Elimination for Tridiagonal Matrices
276
12.12 Appendix: Richardson's Extrapolation
277
12.13 Exercises
277
13 Dynamic Option Hedging and Pricing in Incomplete Markets 280
13.1 The Risk in Option Hedging Strategies
280
13.2 Incomplete Market Option Price Bounds
299
13.3 Towards Continuous Time
304
13.4 Derivation of Optimal Hedging Strategy
309
13.5 Summary
318
13.6 Notes
319
13.7 Appendix: Expected Squared Hedging Error in the Black-Scholes Model
320
13.8 Exercises
322
Appendix A Calculus 326
A.1 Notation
326
A.2 Differentiation
329
A.3 Real Function of Several Real Variables
332
A.4 Power Series Approximations
334
A.5 Optimization
336
A.6 Integration
338
A.7 Exercises
344
Appendix B Probability 348
B.1 Probability Space
348
B.2 Conditional Probability
348
B.3 Marginal and Joint Distribution
351
B.4 Stochastic Independence
352
B.5 Expectation Operator
354
B.6 Properties of Expectation
355
B.7 Mean and Variance
356
B.8 Covariance and Correlation
357
B.9 Continuous Random Variables
360
B.10 Normal Distribution
364
B.11 Quanti les
370
B.12 Relationships among Standard Statistical Distributions
371
B.13 Notes
372
B.14 Exercises
372
References 381
Index 385
Ales Cerny is professor of finance at the Cass Business School, City University London.