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Mathematical methods for finance : tools for asset and risk management /
The mathematical and statistical tools needed in the rapidly growing quantitative finance field With the rapid growth in quantitative finance, practitioners must achieve a high level of proficiency in math and statistics. Mathematical Methods and Statistical Tools for Finance, part of the Frank J. F...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, New Jersey :
Wiley,
[2013]
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| Colección: | Frank J. Fabozzi series.
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| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- Mathematical Methods for Finance; Contents; Preface; About the Authors; CHAPTER 1 Basic Concepts: Sets, Functions, and Variables; INTRODUCTION; SETS AND SET OPERATIONS; Proper Subsets; Empty Sets; Union of Sets; Intersection of Sets; Elementary Properties of Sets; DISTANCES AND QUANTITIES; n-tuples; Distance; Density of Points; FUNCTIONS; VARIABLES; KEY POINTS; CHAPTER 2 Differential Calculus; INTRODUCTION; LIMITS; CONTINUITY; TOTAL VARIATION; THE NOTION OF DIFFERENTIATION; COMMONLY USED RULES FOR COMPUTING DERIVATIVES; HIGHER-ORDER DERIVATIVES; Application to Bond Analysis.
- Application of the Chain RuleTAYLOR SERIES EXPANSION; Application to Bond Analysis; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 3 Integral Calculus; INTRODUCTION; RIEMANN INTEGRALS; Properties of Riemann Integrals; LEBESGUE-STIELTJES INTEGRALS; INDEFINITE AND IMPROPER INTEGRALS; THE FUNDAMENTAL THEOREM OF CALCULUS; INTEGRAL TRANSFORMS; Laplace Transforms; Fourier Transforms; CALCULUS IN MORE THAN ONE VARIABLE; KEY POINTS; CHAPTER 4 Matrix Algebra; INTRODUCTION; VECTORS AND MATRICES DEFINED; Vectors; Matrices; SQUARE MATRICES; Diagonals and Antidiagonals; Identity Matrix.
- Diagonal MatrixUpper and Lower Triangular Matrix; DETERMINANTS; SYSTEMS OF LINEAR EQUATIONS; LINEAR INDEPENDENCE AND RANK; HANKEL MATRIX; VECTOR AND MATRIX OPERATIONS; Vector Operations; Matrix Operations; FINANCE APPLICATION; EIGENVALUES AND EIGENVECTORS; DIAGONALIZATION AND SIMILARITY; SINGULAR VALUE DECOMPOSITION; KEY POINTS; CHAPTER 5 Probability: Basic Concepts; INTRODUCTION; REPRESENTING UNCERTAINTY WITH MATHEMATICS; PROBABILITY IN A NUTSHELL; OUTCOMES AND EVENTS; PROBABILITY; MEASURE; RANDOM VARIABLES; INTEGRALS; DISTRIBUTIONS AND DISTRIBUTION FUNCTIONS; RANDOM VECTORS.
- STOCHASTIC PROCESSESPROBABILISTIC REPRESENTATION OF FINANCIAL MARKETS; INFORMATION STRUCTURES; FILTRATION; KEY POINTS; CHAPTER 6 Probability: Random Variables and Expectations; INTRODUCTION; CONDITIONAL PROBABILITY AND CONDITIONAL EXPECTATION; MOMENTS AND CORRELATION; COPULA FUNCTIONS; SEQUENCES OF RANDOM VARIABLES; INDEPENDENT AND IDENTICALLY DISTRIBUTED SEQUENCES; SUM OF VARIABLES; GAUSSIAN VARIABLES; APPPROXIMATING THE TAILS OF A PROBABILITY DISTRIBUTION: CORNISH-FISHER EXPANSION AND HERMITE POLYNOMIALS; Cornish-Fisher Expansion; Hermite Polynomials.
- Cornish-Fisher Expansion with Hermite PolynomialsTHE REGRESSION FUNCTION; Linear Regression; FAT TAILS AND STABLE LAWS; Fat Tails; The Class L of Fat-Tailed Distributions; The Law of Large Numbers and the Central Limit Theorem; Stable Distributions; KEY POINTS; CHAPTER 7 Optimization; INTRODUCTION; MAXIMA AND MINIMA; LAGRANGE MULTIPLIERS; NUMERICAL ALGORITHMS; Linear Programming; Quadratic Programming; CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY; STOCHASTIC PROGRAMMING; APPLICATION TO BOND PORTFOLIO: LIABILITY-FUNDING STRATEGIES; Cash Flow Matching; Portfolio Immunization.