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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Bibliographic Details
Main Author:	Harrison, Michael
Other Authors:	Waldron, Patrick
Format:	eBook
Language:	English
Published:	Hoboken : Taylor & Francis, 2011.
Subjects:	Economics > Mathematical models. Finance > Mathematical models. Economics, Mathematical. BUSINESS & ECONOMICS > Economics > Theory. Economics, Mathematical Economics > Mathematical models Finance > Mathematical models
Online Access:	Click for online access

Table of Contents:

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.

Mathematics for Economics and Finance.

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