Mathematics for economics and finance:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London ; New York, NY
Routledge
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xxiii, 520 S. Illustrationen, Diagramme |
| ISBN: | 9780415573030 9780415573047 |
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MARC
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| 100 | 1 | |a Harrison, Michael J. |d 1944- |e Verfasser |0 (DE-588)170843114 |4 aut | |
| 245 | 1 | 0 | |a Mathematics for economics and finance |c Michael Harrison and Patrick Waldron |
| 264 | 1 | |a London ; New York, NY |b Routledge |c 2011 | |
| 300 | |a xxiii, 520 S. |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Economics |x Mathematical models | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Economics, Mathematics | |
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| 700 | 1 | |a Waldron, Patrick |d 1963- |e Verfasser |0 (DE-588)171618122 |4 aut | |
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Record in the Search Index
| _version_ | 1804143685169840128 |
|---|---|
| adam_text | Contents
List of figures
ix
List of tables
xi
Foreword
xiii
Preface
xv
Acknowledgements
xvii
List of abbreviations
xviii
Notation and preliminaries
xix
Part I
MATHEMATICS
Introduction
3
1
Systems of linear equations and matrices
5
1.1 Introduction
5
1.2
Linear equations and examples
5
1.3
Matrix operations
11
1.4
Rules of matrix algebra
14
1.5
Some special types of matrix and associated rules
15
2
Determinants
30
2.1
Introduction
30
2.2
Preliminaries
30
2.3
Definition and properties
31
2.4
Co-factor expansions of determinants
34
2.5
Solution of systems of equations
39
3
Eigenvalues and eigenvectors
53
3.1
Introduction
53
3.2
Definitions and illustration
53
3.3
Computation
54
3.4
Unit eigenvalues
58
3.5
Similar matrices
59
3.6
Diagonalization
59
vi
Contents
4
Conic
sections,
quadratic forms and definite
matrices
71
4.1
Introduction
71
4.2
Conic sections
71
4.3
Quadratic
f
orms
76
4.4
Definite matrices
77
5
Vectors and vector spaces
88
5.7
Introduction
88
5.2
Vectors in 2-space and 3-space
88
5.3
n-Dimensional
Euclidean vector spaces
100
5.4
General vector spaces
101
6
Linear transformations
128
6.1
Introduction
128
6.2
Definitions and illustrations
128
6.3
Properties of linear transformations
131
6.4
Linear transformations
from W
to Rm
137
6.5
Matrices of linear transformations
138
7
Foundations for vector calculus
143
7.1
Introduction
143
7.2
Affine
combinations, sets, hulls and functions
143
7.3
Convex combinations, sets, hulls andfiinctions
146
7.4
Subsets of
n-dimensional
spaces
148
7.5
Basic topology
154
7.6
Supporting and separating
hyperplane
theorems
157
7.7
Visualizing functions of several variables
158
7.8
Limits and continuity
159
7.9
Fundamental theorem of calculus
162
8
Difference equations
167
8.1
Introduction
167
8.2
Definitions and classifications
167
8.3
Linear, first-order difference equations
172
8.4
Linear, autonomous, higher-order difference equations
181
8.5
Systems of linear difference equations
189
9
Vector calculus
202
9.1
Introduction
202
9.2
Partial and total derivatives
202
9.3
Chain rule and product rule
207
9.4
Elasticities
211
9.5
Directional
derivatives
and tangent
hyperplanes 213
9.6
Taylor s theorem; deterministic version
217
9.7
Multiple integration
224
9.8
Implicit function theorem
236
Contents
vii
10
Convexity and optimization
244
10.1
Introduction
244
10.2
Convexity and concavity
244
10.3
Unconstrained optimization
257
10.4
Equality-constrained optimization
261
10.5
Inequality-constrained optimization
270
10.6
Duality
278
Part II
APPLICATIONS
Introduction
287
11
Macroeconomic applications
289
11.1
Introduction
289
11.2
Dynamic linear macroeconomic models
289
11.3
Input-output analysis
294
12
Single-period choice under certainty
299
12.1
Introduction
299
12.2
Definitions
299
12.3
Axioms
301
12.4
The consumer s problem audits dual
307
12.5
General equilibrium theory
316
12.6
Welfare theorems
323
13
Probability theory
334
13.1
Introduction
334
13.2
Sample spaces and random variables
334
13.3
Applications
338
13.4
Vector spaces of random variables
343
13.5
Random vectors
345
13.6
Expectations and moments
347
13.7
Multivariate normal distribution
351
13.8
Estimation and forecasting
354
13.9
Taylor s theorem: stochastic version
355
13.10
Jensen s inequality
356
14
Quadratic programming and econometric applications
371
14.1
Introduction
371
14.2
Algebra and geometry of ordinary least squares
371
14.3
Canonical quadratic programming problem
377
14.4
Stochastic difference equations
382
15
Multi-period choice under certainty
394
15.1
Introduction
394
15.2
Measuring rates of return
394
viii Contents
15.3
Multi-period general equilibrium
400
15.4
Term structure of interest rates
401
16
Single-period choice under uncertainty
415
16.1
Introduction
415
16.2
Motivation
415
16.3
Pricing state-contingent claims
416
16.4
The expected-utility paradigm
423
16.5
Risk aversion
429
16.6
Arbitrage, risk neutrality and the efficient markets hypothesis
434
16.7
Uncovered interest rate parity:
Siegel s
paradox revisited
436
16.8
Mean-variance paradigm
440
16.9
Other non-expected-utility approaches
442
17
Portfolio theory
448
17.1
Introduction
448
17.2
Preliminaries
448
17.3
Single-period portfolio choice problem
450
17.4
Mathematics of the portfolio frontier
457
17.5
Market equilibrium and the capital asset pricing model
478
17.6
Multi-currency considerations
487
Notes
493
References
501
Index
505
|
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| institution | BVB |
| isbn | 9780415573030 9780415573047 |
| language | English |
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| physical | xxiii, 520 S. Illustrationen, Diagramme |
| publishDate | 2011 |
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| publisher | Routledge |
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| spelling | Harrison, Michael J. 1944- Verfasser (DE-588)170843114 aut Mathematics for economics and finance Michael Harrison and Patrick Waldron London ; New York, NY Routledge 2011 xxiii, 520 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematisches Modell Wirtschaft Economics Mathematical models Finance Mathematical models Economics, Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd rswk-swf Finanzmathematik (DE-588)4017195-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Finanzmathematik (DE-588)4017195-4 s Wirtschaftsmathematik (DE-588)4066472-7 s b DE-604 Waldron, Patrick 1963- Verfasser (DE-588)171618122 aut Erscheint auch als Online-Ausgabe 978-0-203-82999-8 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020875127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harrison, Michael J. 1944- Waldron, Patrick 1963- Mathematics for economics and finance Mathematisches Modell Wirtschaft Economics Mathematical models Finance Mathematical models Economics, Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| subject_GND | (DE-588)4066472-7 (DE-588)4017195-4 (DE-588)4123623-3 |
| title | Mathematics for economics and finance |
| title_auth | Mathematics for economics and finance |
| title_exact_search | Mathematics for economics and finance |
| title_full | Mathematics for economics and finance Michael Harrison and Patrick Waldron |
| title_fullStr | Mathematics for economics and finance Michael Harrison and Patrick Waldron |
| title_full_unstemmed | Mathematics for economics and finance Michael Harrison and Patrick Waldron |
| title_short | Mathematics for economics and finance |
| title_sort | mathematics for economics and finance |
| topic | Mathematisches Modell Wirtschaft Economics Mathematical models Finance Mathematical models Economics, Mathematics Wirtschaftsmathematik (DE-588)4066472-7 gnd Finanzmathematik (DE-588)4017195-4 gnd |
| topic_facet | Mathematisches Modell Wirtschaft Economics Mathematical models Finance Mathematical models Economics, Mathematics Wirtschaftsmathematik Finanzmathematik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020875127&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT harrisonmichaelj mathematicsforeconomicsandfinance AT waldronpatrick mathematicsforeconomicsandfinance |