The economics of inaction: stochastic control models with fixed costs
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2009
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| Subjects: | |
| Online Access: | Contributor biographical information Publisher description Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | IX, 308 S. graph. Darst. |
| ISBN: | 9780691135052 0691135053 |
Staff View
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| 245 | 1 | 0 | |a The economics of inaction |b stochastic control models with fixed costs |c Nancy L. Stokey |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a IX, 308 S. |b graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
1
Introduction
1
Notes
12
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
Notes
28
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
Notes
51
vi
Contents
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
Notes
74
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
ψ
and
Φ
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
Notes
106
Π
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
6.4.
An Example
125
Notes
128
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
7.6.
An Example
146
Notes
152
8
Models with Fixed and Variable Costs
153
8.1.
An Inventory Model
154
8.2.
Preliminary Results
157
Contents
vii
8.3.
Optimizing:
A Direct
Approach
160
8.4.
Using the Hamiltonjacobi-Bellman Equation
162
8.5.
Long-Run Averages
164
8.6.
Examples
166
8.7.
Strictly Convex Adjustment Costs
174
Notes
175
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
Notes
196
Ш
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
Notes
224
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
Notes
248
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
Notes
280
Contents
A
Contmuous
Stochastic Processes
283
Α.
1.
Modes of Convergence
283
A.2. Continuous Stochastic Processes
285
A.3. Wiener Measure
287
A.4.
Nondifferentìability
of Sample Paths
288
Notes
289
В
Optional Stopping Theorem
290
B.I. Stopping with a Uniform Bound,
Τ
< N
290
B.2. Stopping with Pr
{
Γ
< 00} = 1
292
Notes
294
References
295
Index
303
|
| adam_txt |
Contents
Preface
ix
1
Introduction
1
Notes
12
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
Notes
28
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
Notes
51
vi
Contents
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
Notes
74
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
ψ
and
Φ
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
Notes
106
Π
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
6.4.
An Example
125
Notes
128
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
7.6.
An Example
146
Notes
152
8
Models with Fixed and Variable Costs
153
8.1.
An Inventory Model
154
8.2.
Preliminary Results
157
Contents
vii
8.3.
Optimizing:
A Direct
Approach
160
8.4.
Using the Hamiltonjacobi-Bellman Equation
162
8.5.
Long-Run Averages
164
8.6.
Examples
166
8.7.
Strictly Convex Adjustment Costs
174
Notes
175
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
Notes
196
Ш
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
Notes
224
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
Notes
248
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
Notes
280
Contents
A
Contmuous
Stochastic Processes
283
Α.
1.
Modes of Convergence
283
A.2. Continuous Stochastic Processes
285
A.3. Wiener Measure
287
A.4.
Nondifferentìability
of Sample Paths
288
Notes
289
В
Optional Stopping Theorem
290
B.I. Stopping with a Uniform Bound,
Τ
< N
290
B.2. Stopping with Pr
{
Γ
< 00} = 1
292
Notes
294
References
295
Index
303 |
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| id | DE-604.BV035172992 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:55:03Z |
| indexdate | 2024-07-09T21:26:39Z |
| institution | BVB |
| isbn | 9780691135052 0691135053 |
| language | English |
| lccn | 2008062109 |
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| physical | IX, 308 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Stokey, Nancy L. Verfasser aut The economics of inaction stochastic control models with fixed costs Nancy L. Stokey Princeton, NJ [u.a.] Princeton Univ. Press 2009 IX, 308 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Econometrische modellen gtt Stochastische modellen gtt Ökonometrisches Modell Econometric models Brownian movements Ökonometrisches Modell (DE-588)4043212-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Ökonometrisches Modell (DE-588)4043212-9 s DE-604 http://www.loc.gov/catdir/enhancements/fy0834/2008062109-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0834/2008062109-d.html Publisher description Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016979903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stokey, Nancy L. The economics of inaction stochastic control models with fixed costs Econometrische modellen gtt Stochastische modellen gtt Ökonometrisches Modell Econometric models Brownian movements Ökonometrisches Modell (DE-588)4043212-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| subject_GND | (DE-588)4043212-9 (DE-588)4128328-4 |
| title | The economics of inaction stochastic control models with fixed costs |
| title_auth | The economics of inaction stochastic control models with fixed costs |
| title_exact_search | The economics of inaction stochastic control models with fixed costs |
| title_exact_search_txtP | The economics of inaction stochastic control models with fixed costs |
| title_full | The economics of inaction stochastic control models with fixed costs Nancy L. Stokey |
| title_fullStr | The economics of inaction stochastic control models with fixed costs Nancy L. Stokey |
| title_full_unstemmed | The economics of inaction stochastic control models with fixed costs Nancy L. Stokey |
| title_short | The economics of inaction |
| title_sort | the economics of inaction stochastic control models with fixed costs |
| title_sub | stochastic control models with fixed costs |
| topic | Econometrische modellen gtt Stochastische modellen gtt Ökonometrisches Modell Econometric models Brownian movements Ökonometrisches Modell (DE-588)4043212-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd |
| topic_facet | Econometrische modellen Stochastische modellen Ökonometrisches Modell Econometric models Brownian movements Brownsche Bewegung |
| url | http://www.loc.gov/catdir/enhancements/fy0834/2008062109-b.html http://www.loc.gov/catdir/enhancements/fy0834/2008062109-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016979903&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT stokeynancyl theeconomicsofinactionstochasticcontrolmodelswithfixedcosts |