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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000004736116 | HB135 C42 2004 | Open Access Book | Book | Searching... |
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Summary
Summary
First published in 2004, this is a rigorous but user-friendly book on the application of stochastic control theory to economics. A distinctive feature of the book is that mathematical concepts are introduced in a language and terminology familiar to graduate students of economics. The standard topics of many mathematics, economics and finance books are illustrated with real examples documented in the economic literature. Moreover, the book emphasises the dos and don'ts of stochastic calculus, cautioning the reader that certain results and intuitions cherished by many economists do not extend to stochastic models. A special chapter (Chapter 5) is devoted to exploring various methods of finding a closed-form representation of the value function of a stochastic control problem, which is essential for ascertaining the optimal policy functions. The book also includes many practice exercises for the reader. Notes and suggested readings are provided at the end of each chapter for more references and possible extensions.
Table of Contents
| 1 Probability theory |
| 1.1 Introduction |
| 1.2 Stochastic processes |
| 1.3 Conditional expectation |
| 1.4 Notes and further readings |
| 2 Wiener processes |
| 2.1 Introduction |
| 2.2 A Heuristic approach |
| 2.3 Markov processes |
| 2.4 Wiener processes |
| 2.5 Notes and further readings |
| 3 Stochastic calculus |
| 3.1 Introduction |
| 3.2 A Heuristic approach |
| 3.3 The Ito integral |
| 3.4 Ito's lemma: autonomous case |
| 3.5 Ito's lemma for time-dependent functions |
| 3.6 Notes and further readings |
| 4 Stochastic dynamic programming |
| 4.1 Introduction |
| 4.2 Bellman equation |
| 4.3 Economic applications |
| 4.4 Extension: recursive utility |
| 4.5 Notes and further readings |
| 5 How to solve it |
| 5.1 Introduction |
| 5.2 HARA functions |
| 5.3 Divine revelation |
| 5.4 Symmetry |
| 5.5 The substitution method |
| 5.6 Matingale representation method |
| 5.7 Inverse optimum method |
| 5.8 Notes and further readings |
| 6 Boundaries and absorbing barriers |
| 6.1 Introduction |
| 6.2 Nonnegativity constraint |
| 6.3 Other constraints |
| 6.4 Stopping rules - certainty case |
| 6.5 The expected discount factor |
| 6.6 Optimal stopping times |
| 6.7 Notes and further readings |
