Book description
An introduction to the mathematical theory and financial models developed and used on Wall Street
Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A ProblemOriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models.
The authors promote a problemsolving approach when applying mathematics in realworld situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features:
A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus
Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems
Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes
Measure, Probability, and Mathematical Finance: A ProblemOriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upperundergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.
Table of contents
 Cover
 Half Title page
 Title page
 Copyright page
 Dedication
 Preface
 Financial Glossary
 Part I: Measure Theory

Part II: Probability Theory
 Chapter 11: Events and Random Variables
 Chapter 12: Independence
 Chapter 13: Expectation
 Chapter 14: Conditional Expectation
 Chapter 15: Inequalities
 Chapter 16: Law of Large Numbers
 Chapter 17: Characteristic Functions
 Chapter 18: Discrete Distributions
 Chapter 19: Continuous Distributions
 Chapter 20: Central Limit Theorems

Part III: Stochastic Processes
 Chapter 21: Stochastic Processes
 Chapter 22: Martingales
 Chapter 23: Stopping Times
 Chapter 24: Martingale Inequalities
 Chapter 25: Martingale Convergence Theorems
 Chapter 26: Random Walks
 Chapter 27: Poisson Processes
 Chapter 28: Brownian Motion
 Chapter 29: Markov Processes
 Chapter 30: Lévy Processes

Part IV: Stochastic Calculus
 Chapter 31: The Wiener Integral
 Chapter 32: The Itô Integral
 Chapter 33: Extension of the Itô Integral
 Chapter 34: Martingale Stochastic Integrals
 Chapter 35: The Itô Formula
 Chapter 36: Martingale Representation Theorem
 Chapter 37: Change of Measure
 Chapter 38: Stochastic Differential Equations
 Chapter 39: Diffusion
 Chapter 40: The FeynmanKac Formula
 Part V: Stochastic Financial Models
 References
 List of Symbols
 Subject Index
Product information
 Title: Measure, Probability, and Mathematical Finance: A ProblemOriented Approach
 Author(s):
 Release date: April 2014
 Publisher(s): Wiley
 ISBN: 9781118831960
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