Mathematics for Economics and Finance.

The aim of this book is to bring students of economics and finance who have only an introductory background in mathematics up to a quite advanced level in the subject, thus preparing them for the core mathematical demands of econometrics, economic theory, quantitative finance and mathematical econom...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Harrison, Michael
Otros Autores: Waldron, Patrick
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Hoboken : Taylor & Francis, 2011.
Temas:
Economics > Mathematical models.
Finance > Mathematical models.
Economics, Mathematical.
Économie politique > Modèles mathématiques.
Finances > Modèles mathématiques.
BUSINESS & ECONOMICS > Economics > Theory.
Economics, Mathematical
Economics > Mathematical models
Finance > Mathematical models
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: Introduction
  • 1. Systems of linear equations and matrices
  • 1.1. Introduction
  • 1.2. Linear equations and examples
  • 1.3. Matrix operations
  • 1.4. Rules of matrix algebra
  • 1.5. Some special types of matrix and associated rules
  • 2. Determinants
  • 2.1. Introduction
  • 2.2. Preliminaries
  • 2.3. Definition and properties
  • 2.4. Co-factor expansions of determinants
  • 2.5. Solution of systems of equations
  • 3. Eigenvalues and eigenvectors
  • 3.1. Introduction
  • 3.2. Definitions and illustration
  • 3.3. Computation
  • 3.4. Unit eigenvalues
  • 3.5. Similar matrices
  • 3.6. Diagonalization
  • 4. Conic sections, quadratic forms and definite matrices
  • 4.1. Introduction
  • 4.2. Conic sections
  • 4.3. Quadratic forms
  • 4.4. Definite matrices
  • 5. Vectors and vector spaces
  • 5.1. Introduction
  • 5.2. Vectors in 2-space and 3-space
  • 5.3. n-Dimensional Euclidean vector spaces
  • 5.4. General vector spaces
  • 6. Linear transformations
  • 6.1. Introduction
  • 6.2. Definitions and illustrations
  • 6.3. Properties of linear transformations
  • 6.4. Linear transformations from Rn to Rm
  • 6.5. Matrices of linear transformations
  • 7. Foundations for vector calculus
  • 7.1. Introduction
  • 7.2. Affine combinations, sets, hulls and functions
  • 7.3. Convex combinations, sets, hulls and functions
  • 7.4. Subsets of n-dimensional spaces
  • 7.5. Basic topology
  • 7.6. Supporting and separating hyperplane theorems
  • 7.7. Visualizing functions of several variables
  • 7.8. Limits and continuity
  • 7.9. Fundamental theorem of calculus
  • 8. Difference equations
  • 8.1. Introduction
  • 8.2. Definitions and classifications
  • 8.3. Linear, first-order difference equations
  • 8.4. Linear, autonomous, higher-order difference equations
  • 8.5. Systems of linear difference equations
  • Note continued: 9. Vector calculus
  • 9.1. Introduction
  • 9.2. Partial and total derivatives
  • 9.3. Chain rule and product rule
  • 9.4. Elasticities
  • 9.5. Directional derivatives and tangent hyperplanes
  • 9.6. Taylor's theorem: deterministic version
  • 9.7. Multiple integration
  • 9.8. Implicit function theorem
  • 10. Convexity and optimization 244
  • 10.1. Introduction
  • 10.2. Convexity and concavity
  • 10.3. Unconstrained optimization
  • 10.4. Equality-constrained optimization
  • 10.5. Inequality-constrained optimization
  • 10.6. Duality
  • Introduction
  • 11. Macroeconomic applications
  • 11.1. Introduction
  • 11.2. Dynamic linear macroeconomic models
  • 11.3. Input-output analysis
  • 12. Single-period choice under certainty
  • 12.1. Introduction
  • 12.2. Definitions
  • 12.3. Axioms
  • 12.4. consumer's problem and its dual
  • 12.5. General equilibrium theory
  • 12.6. Welfare theorems
  • 13. Probability theory
  • 13.1. Introduction
  • 13.2. Sample spaces and random variables
  • 13.3. Applications
  • 13.4. Vector spaces of random variables
  • 13.5. Random vectors
  • 13.6. Expectations and moments
  • 13.7. Multivariate normal distribution
  • 13.8. Estimation and forecasting
  • 13.9. Taylor's theorem: stochastic version
  • 13.10. Jensen's inequality
  • 14. Quadratic programming and econometric applications
  • 14.1. Introduction
  • 14.2. Algebra and geometry of ordinary least squares
  • 14.3. Canonical quadratic programming problem
  • 14.4. Stochastic difference equations
  • 15. Multi-period choice under certainty
  • 15.1. Introduction
  • 15.2. Measuring rates of return
  • 15.3. Multi-period general equilibrium
  • 15.4. Term structure of interest rates
  • 16. Single-period choice under uncertainty
  • ^ 16.1. Introduction
  • 16.2. Motivation
  • 16.3. Pricing state-contingent claims
  • Note continued: 16.4. expected-utility paradigm
  • 16.5. Risk aversion
  • 16.6. Arbitrage, risk neutrality and the efficient markets hypothesis
  • 16.7. Uncovered interest rate parity: Siegel's paradox revisited
  • 16.8. Mean[-]variance paradigm
  • 16.9. Other non-expected-utility approaches
  • 17. Portfolio theory
  • 17.1. Introduction
  • 17.2. Preliminaries
  • 17.3. Single-period portfolio choice problem
  • 17.4. Mathematics of the portfolio frontier
  • 17.5. Market equilibrium and the capital asset pricing model
  • 17.6. Multi-currency considerations.

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