Жанры
Авторы
Контакты
О сайте
Книжные новинки
Популярные книги
Найти
Главная
Авторы
Daniel J. Duffy
Numerical Methods in Computational Finance
Читать книгу Numerical Methods in Computational Finance - Daniel J. Duffy - Страница 1
Оглавление
Предыдущая
Следующая
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
...
98
Оглавление
Купить и скачать книгу
Вернуться на страницу книги Numerical Methods in Computational Finance
Оглавление
Страница 1
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Страница 7
Numerical Methods in Computational Finance A Partial Differential Equation (PDE/FDM) Approach
Страница 9
Preface
Who Should Read this Book?
Страница 12
CHAPTER 1 Real Analysis Foundations for this Book
1.1 INTRODUCTION AND OBJECTIVES
1.2 CONTINUOUS FUNCTIONS
1.2.1 Formal Definition of Continuity
Definition 1.1
1.2.2 An Example
1.2.3 Uniform Continuity
1.2.4 Classes of Discontinuous Functions
1.3 DIFFERENTIAL CALCULUS
1.3.1 Taylor's Theorem
1.3.2 Big O and Little o Notation
Definition 1.2
(O-Notation)
.
Definition 1.3
(O-Notation)
.
1.4 PARTIAL DERIVATIVES
1.5 FUNCTIONS AND IMPLICIT FORMS
1.6 METRIC SPACES AND CAUCHY SEQUENCES
1.6.1 Metric Spaces
1.6.2 Cauchy Sequences
1.6.3 Lipschitz Continuous Functions
1.7 SUMMARY AND CONCLUSIONS
CHAPTER 2 Ordinary Differential Equations (ODEs), Part 1
2.1 INTRODUCTION AND OBJECTIVES
2.2 BACKGROUND AND PROBLEM STATEMENT
2.2.1 Qualitative Properties of the Solution and Maximum Principle
2.2.2 Rationale and Generalisations
2.3 DISCRETISATION OF INITIAL VALUE PROBLEMS: FUNDAMENTALS
2.3.1 Common Schemes
2.3.2 Discrete Maximum Principle
2.4 SPECIAL SCHEMES
2.4.1 Exponential Fitting
2.4.2 Scalar Non-Linear Problems and Predictor-Corrector Method
2.4.3 Extrapolation
2.5 FOUNDATIONS OF DISCRETE TIME APPROXIMATIONS
2.6 STIFF ODEs
2.7 INTERMEZZO: EXPLICIT SOLUTIONS
2.8 SUMMARY AND CONCLUSIONS
CHAPTER 3 Ordinary Differential Equations (ODEs), Part 2
3.1 INTRODUCTION AND OBJECTIVES
3.2 EXISTENCE AND UNIQUENESS RESULTS
3.2.1 An Example
3.3 OTHER MODEL EXAMPLES
3.3.1 Bernoulli ODE
3.3.2 Riccati ODE
3.3.3 Predator-Prey Models
3.3.4 Logistic Function
3.4 EXISTENCE THEOREMS FOR STOCHASTIC DIFFERENTIAL EQUATIONS (SDEs)
3.4.1 Stochastic Differential Equations (SDEs)
3.5 NUMERICAL METHODS FOR ODES
3.5.1 Code Samples in Python
3.6 THE RICCATI EQUATION
3.6.1 Finite Difference Schemes
3.7 MATRIX DIFFERENTIAL EQUATIONS
3.7.1 Transition Rate Matrices and Continuous Time Markov Chains
3.8 SUMMARY AND CONCLUSIONS
CHAPTER 4 An Introduction to Finite Dimensional Vector Spaces
4.1 SHORT INTRODUCTION AND OBJECTIVES
4.1.1 Notation
4.2 WHAT IS A VECTOR SPACE?
4.3 SUBSPACES
4.4 LINEAR INDEPENDENCE AND BASES
4.5 LINEAR TRANSFORMATIONS
4.5.1 Invariant Subspaces
4.5.2 Rank and Nullity
Eigenvalues (Characteristic Roots) and Eigenvectors (Characteristic Vectors)
4.6 SUMMARY AND CONCLUSIONS
CHAPTER 5 Guide to Matrix Theory and Numerical Linear Algebra
5.1 INTRODUCTION AND OBJECTIVES
5.2 FROM VECTOR SPACES TO MATRICES
5.2.1 Sums and Scalar Products of Linear Transformations
5.3 INNER PRODUCT SPACES
5.3.1 Orthonormal Basis
5.4 FROM VECTOR SPACES TO MATRICES
5.4.1 Some Examples
5.5 FUNDAMENTAL MATRIX PROPERTIES
5.6 ESSENTIAL MATRIX TYPES
5.6.1 Nilpotent and Related Matrices
5.6.2 Normal Matrices
5.6.3 Unitary and Orthogonal Matrices
5.6.4 Positive Definite Matrices
5.6.5 Non-Negative Matrices
5.6.6 Irreducible Matrices
5.6.7 Other Kinds of Matrices
5.7 THE CAYLEY TRANSFORM
Appendix : The Schrödinger Equation
5.8 SUMMARY AND CONCLUSIONS
{buyButton}
Подняться наверх
