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...
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| Other Authors: | , |
| Format: | eBook |
| Language: | English |
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Hoboken, New Jersey
Wiley
2013
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| Series: | The Frank J. Fabozzi series
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| Collection: | O'Reilly - Collection details see MPG.ReNa |
Table of Contents:
- 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
- Includes bibliographical references and index
- 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
- 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