Gan / Ma / Xie Measure, Probability, and Mathematical Finance

A Problem-Oriented Approach
1. Auflage 2014
ISBN: 978-1-118-83198-4
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: 0 - No protection

E-Book, Englisch, 744 Seiten, E-Book

An introduction to the mathematical theory and financialmodels developed and used on Wall Street
Providing both a theoretical and practical approach to theunderlying mathematical theory behind financial models, Measure,Probability, and Mathematical Finance: A Problem-OrientedApproach presents important concepts and results in measuretheory, probability theory, stochastic processes, and stochasticcalculus. Measure theory is indispensable to the rigorousdevelopment of probability theory and is also necessary to properlyaddress martingale measures, the change of numeraire theory, andLIBOR market models. In addition, probability theory is presentedto facilitate the development of stochastic processes, includingmartingales and Brownian motions, while stochastic processes andstochastic calculus are discussed to model asset prices and developderivative pricing models.
The authors promote a problem-solving approach when applyingmathematics in real-world situations, and readers are encouraged toaddress theorems and problems with mathematical rigor. In addition,Measure, Probability, and Mathematical Finance features:
* A comprehensive list of concepts and theorems from measuretheory, probability theory, stochastic processes, and stochasticcalculus
* Over 500 problems with hints and select solutions to reinforcebasic concepts and important theorems
* Classic derivative pricing models in mathematical finance thathave been developed and published since the seminal work of Blackand Scholes
Measure, Probability, and Mathematical Finance: AProblem-Oriented Approach is an ideal textbook for introductoryquantitative courses in business, economics, and mathematicalfinance at the upper-undergraduate and graduate levels. The book isalso a useful reference for readers who need to build theirmathematical skills in order to better understand the mathematicaltheory of derivative pricing models.

Autoren/Hrsg.

Gan, Guojun

Ma, Chaoqun

Xie, Hong

Inhaltsverzeichnis

Preface xvii
Financial Glossary xxii
Part I Measure Theory
1 Sets and Sequences 3
2 Measures 15
3 Extension of Measures 29
4 Lebesgue-Stieltjes Measures 37
5 Measurable Functions 47
6 Lebesgue Integration 57
7 The Radon-Nikodym Theorem 77
8 L¯P Spaces 85
9 Convergence 97
10 Product Measures 113
Part II Probability Theory
11 Events and Random Variables 127
12 Independence 141
13 Expectation 161
14 Conditional Expectation 173
15 Inequalities 189
16 Law of Large Numbers 199
17 Characteristic Functions 217
18 Discrete Distributions 227
19 Continuous Distributions 239
20 Central Limit Theorems 257
Part III Stochastic Processes
21 Stochastic Processes 271
22 Martingales 291
23 Stopping Times 301
24 Martingale Inequalities 321
25 Martingale Convergence Theorems 333
26 Random Walks 343
27 Poisson Processes 357
28 Brownian Motion 373
29 Markov Processes 389
30 Lévy Processes 401
Part IV Stochastic Calculus
31 The Wiener Integral 421
32 The Itô Integral 431
33 Extension of the Itô Integral 453
34 Martingale Stochastic Integrals 463
35 The Itô Formula 477
36 Martingale Representation Theorem 495
37 Change of Measure 503
38 Stochastic Differential Equations 515
39 Diffusion 531
40 The Feynman-Kac Formula 547
Part V Stochastic Financial Models
41 Discrete-Time Models 561
42 Black-Scholes Option Pricing Models 579
43 Path-Dependent Options 593
44 American Options 609
45 Short Rate Models 629
46 Instantaneous Forward Rate Models 647
47 LIBOR Market Models 667
References 687
List of Symbols 703
Subject Index 707

Über Autor(innen)

GUOJUN GAN, PHD, ASA, is Director ofQuantitative Modeling and Model Efficiency at Manulife Financial,Canada. His research interests include empirical corporate finance,actuarial science, risk management, data mining, and big dataanalysis.
CHAOQUN MA, PHD, is Professor and Dean ofthe School of Business Administration at Hunan University, China.The recipient of First Prize in Outstanding Achievements inTeaching in 2009, Dr. Ma's research interests includefinancial engineering, risk management, and data mining.
HONG XIE, PHD, is Adjunct Professor in theDepartment of Mathematics and Statistics at York University as wellas Vice President of Models and Analytics at Manulife Financial,Canada. Dr. Xie is on the Board of Directors for theCanadian-Chinese Finance Association, and his research interestsinclude financial engineering, mathematical finance, and partialdifferential equations.