Economics of Inaction Stochastic Control Models with Fixed Costs

ISBN-10: 0691135053
ISBN-13: 9780691135052
Edition: 2009
Authors: Nancy L. Stokey
List price: $72.50
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Description: In economic situations where action entails a fixed cost, inaction is the norm. Action is taken infrequently, and adjustments are large when they occur. Interest in economic models that exhibit ''lumpy'' behavior of this kind has exploded in recent  More...

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Book details

List price: $72.50
Copyright year: 2009
Publisher: Princeton University Press
Publication date: 11/9/2008
Binding: Hardcover
Pages: 320
Size: 6.25" wide x 9.25" long x 1.00" tall
Weight: 1.298
Language: English

In economic situations where action entails a fixed cost, inaction is the norm. Action is taken infrequently, and adjustments are large when they occur. Interest in economic models that exhibit ''lumpy'' behavior of this kind has exploded in recent years, spurred by growing evidence that it is typical in many important economic decisions, including price setting, investment, hiring, durable goods purchases, and portfolio management. InThe Economics of Inaction, leading economist Nancy Stokey shows how the tools of stochastic control can be applied to dynamic problems of decision making under uncertainty when fixed costs are present. Stokey provides a self-contained, rigorous, and clear treatment of two types of models, impulse and instantaneous control. She presents the relevant results about Brownian motion and other diffusion processes, develops methods for analyzing each type of problem, and discusses applications to price setting, investment, and durable goods purchases. This authoritative book will be essential reading for graduate students and researchers in macroeconomics.

Preface
Introduction
Notes
Mathematical Preliminaries
Stochastic Processes, Brownian Motions, and Diffusions
Random Variables and Stochastic Processes
Independence
Wiener Processes and Brownian Motions
Random Walk Approximation of a Brownian Motion
Stopping Times
Strong Markov Property
Diffusions
Discrete Approximation of an Ornstein-Uhlenbeck Process
Notes
Stochastic Integrals and Ito's Lemma
The Hamilton-Jacobi-Bellman Equation
Stochastic Integrals
Ito's Lemma
Geometric Brownian Motion
Occupancy Measure and Local Time
Tanaka's Formula
The Kolmogorov Backward Equation
The Kolmogorov Forward Equation
Notes
Martingales
Definition and Examples
Martingales Based on Eigenvalues
The Wald Martingale
Sub- and Supermartingales
Optional Stopping Theorem
Optional Stopping Theorem, Extended
Martingale Convergence Theorem
Notes
Useful Formulas for Brownian Motions
Stopping Times Defined by Thresholds
Expected Values for Wald Martingales
The Functions [psi] and [Psi]
ODEs for Brownian Motions
Solutions for Brownian Motions When r = 0
Solutions for Brownian Motions When r > 0
ODEs for Diffusions
Solutions for Diffusions When r = 0
Solutions for Diffusions When r > 0
Notes
Impulse Control Models
Exercising an Option
The Deterministic Problem
The Stochastic Problem: A Direct Approach
Using the Hamilton-Jacobi-Bellman Equation
An Example
Notes
Models with Fixed Costs
A Menu Cost Model
Preliminary Results
Optimizing: A Direct Approach
Using the Hamilton-Jacobi-Bellman Equation
Random Opportunities for Costless Adjustment
An Example
Notes
Models with Fixed and Variable Costs
An Inventory Model
Preliminary Results
Optimizing: A Direct Approach
Using the Hamilton-Jacobi-Bellman Equation
Long-Run Averages
Examples
Strictly Convex Adjustment Costs
Notes
Models with Continuous Control Variables
Housing and Portfolio Choice with No Transaction Cost
The Model with Transaction Costs
Using the Hamilton-Jacobi-Bellman Equation
Extensions
Notes
Instantaneous Control Models
Regulated Brownian Motion
One- and Two-Sided Regulators
Discounted Values
The Stationary Distribution
An Inventory Example
Notes
Investment: Linear and Convex Adjustment Costs
Investment with Linear Costs
Investment with Convex Adjustment Costs
Some Special Cases
Irreversible Investment
Irreversible Investment with Two Shocks
A Two-Sector Economy
Notes
Aggregation
An Aggregate Model with Fixed Costs
The Economic Environment
An Economy with Monetary Neutrality
An Economy with a Phillips Curve
Optimizing Behavior and the Phillips Curve
Motivating the Loss Function
Notes
Continuous Stochastic Processes
Modes of Convergence
Continuous Stochastic Processes
Wiener Measure
Nondifferentiability of Sample Paths
Notes
Optional Stopping Theorem
Stopping with a Uniform Bound, T < N
Stopping with Pr { T < [infinity]} = 1
Notes
References
Index

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