Book description
Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance.
Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance.
This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance.
Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one's further understanding of mathematical finance.
Table of contents
- Title Page
- Copyright
- Dedication
- Preface
- Prologue
- About the Authors
- Chapter 1: General Probability Theory
- Chapter 2: Wiener Process
- Chapter 3: Stochastic Differential Equations
- Chapter 4: Change of Measure
- Chapter 5: Poisson Process
-
Appendix A: Mathematics Formulae
- Indices
- Surds
- Exponential and Natural Logarithm
- Quadratic Equation
- Binomial Formula
- Series
- Summation
- Trigonometric Functions
- Hyperbolic Functions
- Complex Numbers
- Derivatives
- Standard Differentiations
- Taylor Series
- Maclaurin Series
- Landau Symbols and Asymptotics
- L'Hospital Rule
- Indefinite Integrals
- Standard Indefinite Integrals
- Definite Integrals
- Derivatives of Definite Integrals
- Integration by Parts
- Integration by Substitution
- Gamma Function
- Beta Function
- Convex Function
- Dirac Delta Function
- Heaviside Step Function
- Fubini's Theorem
-
Appendix B: Probability Theory Formulae
- Probability Concepts
- Bayes' Rule
- Indicator Function
- Discrete Random Variables
- Univariate Case
- Bivariate Case
- Continuous Random Variables
- Univariate Case
- Bivariate Case
- Properties of Expectation and Variance
- Properties of Moment Generating and Characteristic Functions
- Correlation Coefficient
- Convolution
- Discrete Distributions
- Continuous Distributions
- Integrable and Square Integrable Random Variables
- Convergence of Random Variables
- Relationship Between Modes of Convergence
- Dominated Convergence Theorem
- Monotone Convergence Theorem
- The Weak Law of Large Numbers
- The Strong Law of Large Numbers
- The Central Limit Theorem
- Appendix C: Differential Equations Formulae
- Bibliography
- Notation
- Index
- End User License Agreement
Product information
- Title: Problems and Solutions in Mathematical Finance: Stochastic Calculus, Volume I
- Author(s):
- Release date: November 2014
- Publisher(s): Wiley
- ISBN: 9781119965831
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