Stochastic Optimization in Continuous Time

by Fwu-Ranq Chang

• ISBN13: 9780521541947
• ISBN10: 0521541948
• Edition: Revised
• Format: Paperback
• Copyright: 2009-10-01
• Publisher: Cambridge University Press

Summary

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

Introduction

Stochastic processes

Conditional expectation

Notes and further readings

Wiener processes

Introduction

A Heuristic approach

Markov processes

Wiener processes

Notes and further readings

Stochastic calculus

Introduction

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

Introduction

Bellman equation

Economic applications

Extension: recursive utility

Notes and further readings

How to solve it

Introduction

HARA functions

Divine revelation

Symmetry

The substitution method

Matingale representation method

Inverse optimum method

Notes and further readings

Boundaries and absorbing barriers

Introduction

Nonnegativity constraint

Other constraints

Stopping rules - certainty case

The expected discount factor

Optimal stopping times

Notes and further readings

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