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 fourvolume 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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