Economic Dynamics

Theory and Computation

by Stachurski

ISBN: 9780262304047 | Copyright 2009

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This text provides an introduction to the modern theory of economic dynamics, with emphasis on mathematical and computational techniques for modeling dynamic systems. Written to be both rigorous and engaging, the book shows how sound understanding of the underlying theory leads to effective algorithms for solving real world problems. The material makes extensive use of programming examples to illustrate ideas. These programs help bring to life the abstract concepts in the text. Background in computing and analysis is offered for readers without programming experience or upper-level mathematics. Topics covered in detail include nonlinear dynamic systems, finite-state Markov chains, stochastic dynamic programming, stochastic stability and computation of equilibria. The models are predominantly nonlinear, and the emphasis is on studying nonlinear systems in their original form, rather than by means of rudimentary approximation methods such as linearization. Much of the material is new to economics and improves on existing techniques. For graduate students and those already working in the field, Economic Dynamics will serve as an essential resource.
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Contents (pg. vii)
Preface (pg. xiii)
Common Symbols (pg. xvii)
Chapter 1. Introduction (pg. 1)
Part I. Introduction to Dynamics (pg. 9)
Chapter 2. Introduction to Programming (pg. 11)
2.1 Basic Techniques (pg. 11)
2.2 Program Design (pg. 25)
2.3 Commentary (pg. 33)
Chapter 3. Analysis in Metric Space (pg. 35)
3.1 A First Look at Metric Space (pg. 35)
3.2 Further Properties (pg. 44)
3.3 Commentary (pg. 54)
Chapter 4. Introduction to Dynamics (pg. 55)
4.1 Deterministic Dynamical Systems (pg. 55)
4.2 Finite State Markov Chains (pg. 68)
4.3 Stability of Finite State MCs (pg. 83)
4.4 Commentary (pg. 96)
Chapter 5. Further Topics for Finite MCs (pg. 99)
5.1 Optimization (pg. 99)
5.2 MCs and SRSs (pg. 107)
5.3 Commentary (pg. 116)
Chapter 6. Infinite State Space (pg. 117)
6.1 First Steps (pg. 117)
6.2 Optimal Growth, Infinite State (pg. 133)
6.3 Stochastic Speculative Price (pg. 145)
6.4 Commentary (pg. 156)
Part II. Advanced Techniques (pg. 157)
Chapter 7. Integration (pg. 159)
7.1 Measure Theory (pg. 159)
7.2 Definition of the Integral (pg. 171)
7.3 Properties of the Integral (pg. 178)
7.4 Commentary (pg. 186)
Chapter 8. Density Markov Chains (pg. 187)
8.1 Outline (pg. 187)
8.2 Stability (pg. 197)
8.3 Commentary (pg. 210)
Chapter 9. Measure-Theoretic Probability (pg. 211)
9.1 Random Variables (pg. 211)
9.2 General State Markov Chains (pg. 218)
9.3 Commentary (pg. 227)
Chapter 10. Stochastic DynamicProgramming (pg. 229)
10.1 Theory (pg. 229)
10.2 Numerical Methods (pg. 238)
10.3 Commentary (pg. 246)
Chapter 11. Stochastic Dynamics (pg. 247)
11.1 Notions of Convergence (pg. 247)
11.2 Stability: Analytical Methods (pg. 257)
11.3 Stability: Probabilistic Methods (pg. 271)
11.4 Commentary (pg. 293)
Chapter 12. More Stochastic Dynamic Programming (pg. 295)
12.1 Monotonicity and Concavity (pg. 295)
12.2 Unbounded Rewards (pg. 306)
12.3 Commentary (pg. 312)
Part III. Appendixes (pg. 315)
Appendix A: Real Analysis (pg. 317)
A.1 The Nuts and Bolts (pg. 317)
A.2 The Real Numbers (pg. 327)
Appendix B: Chapter Appendixes (pg. 339)
B.1 Appendix to Chapter 3 (pg. 339)
B.2 Appendix to Chapter 4 (pg. 342)
B.3 Appendix to Chapter 6 (pg. 344)
B.4 Appendix to Chapter 8 (pg. 345)
B.5 Appendix to Chapter 10 (pg. 347)
B.6 Appendix to Chapter 11 (pg. 349)
B.7 Appendix to Chapter 12 (pg. 350)
Bibliography (pg. 357)
Index (pg. 367)

John Stachurski

John Stachurski is Professor of Economics at the Australian National University and the author of Economic Dynamics: Theory and Computation (MIT Press).


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