Stochastic Optimization in Continuous Time

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  • Edition: Revised
  • Format: Paperback
  • Copyright: 2009-10-01
  • Publisher: Cambridge University Press
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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 emphasizes 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

Probability theory
Stochastic processes
Conditional expectation
Notes and further readings
Wiener processes
A Heuristic approach
Markov processes
Wiener processes
Notes and further readings
Stochastic calculus
A Heuristic approach
The Ito integral
Ito's lemma: autonomous case
Ito's lemma for time-dependent functions
Notes and further readings
Stochastic dynamic programming
Bellman equation
Economic applications
Extension: recursive utility
Notes and further readings
How to solve it
HARA functions
Divine revelation
The substitution method
Matingale representation method
Inverse optimum method
Notes and further readings
Boundaries and absorbing barriers
Nonnegativity constraint
Other constraints
Stopping rules - certainty case
The expected discount factor
Optimal stopping times
Notes and further readings
Table of Contents provided by Publisher. All Rights Reserved.

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