The economics of inaction : stochastic control models with fixed costs / Nancy L. Stokey.

Format:

Book

Author/Creator:

Stokey, Nancy L.

Contributor:

Class of 1891 Department of Arts Fund.

Language:

English

Subjects (All):

Econometric models.

Brownian movements.

Physical Description:

ix, 308 pages : illustrations ; 25 cm

Place of Publication:

Princeton : Princeton University Press, [2009]

Contents:

I Mathematical Preliminaries 15

2 Stochastic Processes, Brownian Motions, and Diffusions 17

2.1 Random Variables and Stochastic Processes 17

2.2 Independence 18

2.3 Wiener Processes and Brownian Motions 19

2.4 Random Walk Approximation of a Brownian Motion 20

2.5 Stopping Times 24

2.6 Strong Markov Property 24

2.7 Diffusions 25

2.8 Discrete Approximation of an Ornstein-Uhlenbeck Process 27

3 Stochastic Integrals and Ito's Lemma 30

3.1 The Hamilton-Jacobi-Bellman Equation 31

3.2 Stochastic Integrals 34

3.3 Ito's Lemma 37

3.4 Geometric Brownian Motion 38

3.5 Occupancy Measure and Local Time 41

3.6 Tanaka's Formula 43

3.7 The Kolmogorov Backward Equation 47

3.8 The Kolmogorov Forward Equation 50

4 Martingales 53

4.1 Definition and Examples 53

4.2 Martingales Based on Eigenvalues 57

4.3 The Wald Martingale 58

4.4 Sub- and Supermartingales 60

4.5 Optional Stopping Theorem 63

4.6 Optional Stopping Theorem, Extended 67

4.7 Martingale Convergence Theorem 70

5 Useful Formulas for Brownian Motions 75

5.1 Stopping Times Defined by Thresholds 78

5.2 Expected Values for Wald Martingales 79

5.3 The Functions [psi] and [Psi] 82

5.4 ODEs for Brownian Motions 87

5.5 Solutions for Brownian Motions When r = 0 88

5.6 Solutions for Brownian Motions When r > 0 93

5.7 ODEs for Diffusions 98

5.8 Solutions for Diffusions When r = 0 98

5.9 Solutions for Diffusions When r > 0 102

II Impulse Control Models 107

6 Exercising an Option 109

6.1 The Deterministic Problem 110

6.2 The Stochastic Problem: A Direct Approach 116

6.3 Using the Hamilton-Jacobi-Bellman Equation 119

7 Models with Fixed Costs 129

7.1 A Menu Cost Model 130

7.2 Preliminary Results 133

7.3 Optimizing: A Direct Approach 136

7.4 Using the Hamilton-Jacobi-Bellman Equation 140

7.5 Random Opportunities for Costless Adjustment 145

8 Models with Fixed and Variable Costs 153

8.1 An Inventory Model 154

8.2 Preliminary Results 157

8.3 Optimizing: A Direct Approach 160

8.4 Using the Hamilton-Jacobi-Bellman Equation 162

8.5 Long-Run Averages 164

8.7 Strictly Convex Adjustment Costs 174

9 Models with Continuous Control Variables 176

9.1 Housing and Portfolio Choice with No Transaction Cost 178

9.2 The Model with Transaction Costs 182

9.3 Using the Hamilton-Jacobi-Bellman Equation 184

9.4 Extensions 191

III Instantaneous Control Models 197

10 Regulated Brownian Motion 199

10.1 One- and Two-Sided Regulators 201

10.2 Discounted Values 205

10.3 The Stationary Distribution 212

10.4 An Inventory Example 218

11 Investment: Linear and Convex Adjustment Costs 225

11.1 Investment with Linear Costs 227

11.2 Investment with Convex Adjustment Costs 232

11.3 Some Special Cases 236

11.4 Irreversible Investment 239

11.5 Irreversible Investment with Two Shocks 243

11.6 A Two-Sector Economy 247

IV Aggregation 251

12 An Aggregate Model with Fixed Costs 253

12.1 The Economic Environment 256

12.2 An Economy with Monetary Neutrality 259

12.3 An Economy with a Phillips Curve 261

12.4 Optimizing Behavior and the Phillips Curve 265

12.5 Motivating the Loss Function 278

A Continuous Stochastic Processes 283

A.1 Modes of Convergence 283

A.2 Continuous Stochastic Processes 285

A.3 Wiener Measure 287

A.4 Nondifferentiability of Sample Paths 288

B Optional Stopping Theorem 290

B.1 Stopping with a Uniform Bound, T < N 290

B.2 Stopping with Pr { T < [infinity]} = 1 292.

Notes:

Includes bibliographical references (pages 295-302) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Class of 1891 Department of Arts Fund.

ISBN:

9780691135052

0691135053

OCLC:

225852519

Publisher Number:

99934989361