The Economics of Inaction: Stochastic Control Models with Fixed Costs - Hardcover

Stokey, Nancy L.

Hardcover

ISBN 10: 0691135053 ISBN 13: 9780691135052

Verlag: Princeton Univers. Press, 2008

Inhaltsangabe

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. In The 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.

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Nancy L. Stokey

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"Fixed adjustment costs are pervasive in economic modeling and until this book there was no place where the needed tools were developed in a way that was accessible to a broad group of economists. Now there is. This brilliantly lucid book is self-contained, first developing the mathematical preliminaries and then using the tools in a number of illustrative economic applications. I advise economists to add this book to their bookshelf."--Edward C. Prescott, Nobel Laureate in Economics

"Stochastic control problems arise everywhere in modern economics. The Economics of Inaction gives a wonderful treatment for students and practitioners alike. It is rigorous yet clear, concise yet thorough. Inaction would not be the optimal decision about this book: read it now!"--Avinash Dixit, Princeton University

"Nancy Stokey has given us a clear, elegant, and rigorous distillation of why and how we should delay action until the status of a decision problem changes enough. By combining the mathematical apparatus with a wealth of applications to production, macroeconomics, and other fields, this book immediately becomes the definitive treatment. It will be the stepping stone into the subject for almost every interested researcher."--Darrell Duffie, Graduate School of Business, Stanford University

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The Economics of Inaction

Stochastic Control Models with Fixed CostsBy Nancy L. Stokey

Princeton University Press

Copyright © 2009 Princeton University Press
All right reserved.
ISBN: 978-0-691-13505-2

Contents

Preface.............................................................................ix1 Introduction......................................................................1Notes...............................................................................12I Mathematical Preliminaries......................................................152 Stochastic Processes, Brownian Motions, and Diffusions............................172.1. Random Variables and Stochastic Processes......................................172.2. Independence...................................................................182.3. Wiener Processes and Brownian Motions..........................................192.4. Random Walk Approximation of a Brownian Motion.................................202.5. Stopping Times.................................................................242.6. Strong Markov Property.........................................................242.7. Diffusions.....................................................................252.8. Discrete Approximation of an Ornstein-Uhlenbeck Process........................27Notes...............................................................................283 Stochastic Integrals and Ito's Lemma..............................................303.1. The Hamilton-Jacobi-Bellman Equation...........................................313.2. Stochastic Integrals...........................................................343.3. Ito's Lemma....................................................................373.4. Geometric Brownian Motion......................................................383.5. Occupancy Measure and Local Time...............................................413.6. Tanaka's Formula...............................................................433.7. The Kolmogorov Backward Equation...............................................473.8. The Kolmogorov Forward Equation................................................50Notes...............................................................................514 Martingales.......................................................................534.1. Definition and Examples........................................................534.2. Martingales Based on Eigenvalues...............................................574.3. The Wald Martingale............................................................584.4. Sub- and Supermartingales......................................................604.5. Optional Stopping Theorem......................................................634.6. Optional Stopping Theorem, Extended............................................674.7. Martingale Convergence Theorem.................................................70Notes...............................................................................745 Useful Formulas for Brownian Motions..............................................755.1. Stopping Times Defined by Thresholds...........................................785.2. Expected Values for Wald Martingales...........................................795.3. The Functions [psi] and [psi]..................................................825.4. ODEs for Brownian Motions......................................................875.5. Solutions for Brownian Motions When r = 0......................................885.6. Solutions for Brownian Motions When r > 0......................................935.7. ODEs for Diffusions............................................................985.8. Solutions for Diffusions When r = 0............................................985.9. Solutions for Diffusions When r > 0............................................102Notes...............................................................................106II Impulse Control Models..........................................................1076 Exercising an Option..............................................................1096.1. The Deterministic Problem......................................................1106.2. The Stochastic Problem: A Direct Approach......................................1166.3. Using the Hamilton-Jacobi-Bellman Equation.....................................1196.4. An Example.....................................................................125Notes...............................................................................1287 Models with Fixed Costs...........................................................1297.1. A Menu Cost Model..............................................................1307.2. Preliminary Results............................................................1337.3. Optimizing: A Direct Approach..................................................1367.4. Using the Hamilton-Jacobi-Bellman Equation.....................................1407.5. Random Opportunities for Costless Adjustment...................................1457.6. An Example.....................................................................146Notes...............................................................................1528 Models with Fixed and Variable Costs..............................................1538.1. An Inventory Model.............................................................1548.2. Preliminary Results............................................................1578.3. Optimizing: A Direct Approach..................................................1608.4. Using the Hamilton-Jacobi-Bellman Equation.....................................1628.5. Long-Run Averages..............................................................1648.6. Examples.......................................................................1668.7. Strictly Convex Adjustment Costs...............................................174Notes...............................................................................1759 Models with Continuous Control Variables..........................................1769.1. Housing and Portfolio Choice with No Transaction Cost..........................1789.2. The Model with Transaction Costs...............................................1829.3. Using the Hamilton-Jacobi-Bellman Equation.....................................1849.4. Extensions.....................................................................191Notes...............................................................................196III Instantaneous Control Models....................................................19710 Regulated Brownian Motion........................................................19910.1. One- and Two-Sided Regulators.................................................20110.2. Discounted Values.............................................................20510.3. The Stationary Distribution...................................................21210.4. An Inventory Example..........................................................218Notes...............................................................................22411 Investment: Linear and Convex Adjustment Costs...................................22511.1. Investment with Linear Costs..................................................22711.2. Investment with Convex Adjustment Costs.......................................23211.3. Some Special Cases............................................................23611.4. Irreversible Investment.......................................................23911.5. Irreversible Investment with Two...

Details zur Ausgabe

• Verlag: Princeton Univers. Press
• Erscheinungsdatum: 2008
• Sprache: Englisch
• ISBN 10: 0691135053
• ISBN 13: 9780691135052
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 322
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: gpsr@libri.de; gpsr@libri.de; ; Friedensallee 273; Hamburg; 22763; Deutschland