Optimal control problems arising in mathematical economics / Alexander J. Zaslavski.
2022
QA402.3
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Title
Optimal control problems arising in mathematical economics / Alexander J. Zaslavski.
Author
Zaslavski, Alexander J.
ISBN
9789811692987 (electronic bk.)
981169298X (electronic bk.)
9789811692970
9811692971
981169298X (electronic bk.)
9789811692970
9811692971
Publication Details
Singapore : Springer, 2022.
Language
English
Description
1 online resource (387 pages)
Item Number
10.1007/978-981-16-9298-7 doi
Call Number
QA402.3
Dewey Decimal Classification
515.642
Summary
This book is devoted to the study of two large classes of discrete-time optimal control problems arising in mathematical economics. Nonautonomous optimal control problems of the first class are determined by a sequence of objective functions and sequence of constraint maps. They correspond to a general model of economic growth. We are interested in turnpike properties of approximate solutions and in the stability of the turnpike phenomenon under small perturbations of objective functions and constraint maps. The second class of autonomous optimal control problems corresponds to another general class of models of economic dynamics which includes the RobinsonSolowSrinivasan model as a particular case. In Chap. 1 we discuss turnpike properties for a large class of discrete-time optimal control problems studied in the literature and for the RobinsonSolowSrinivasan model. In Chap. 2 we introduce the first class of optimal control problems and study its turnpike property. This class of problems is also discussed in Chaps. 36. In Chap. 3 we study the stability of the turnpike phenomenon under small perturbations of the objective functions. Analogous results for problems with discounting are considered in Chap. 4. In Chap. 5 we study the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. Analogous results for problems with discounting are established in Chap. 6. The results of Chaps. 5 and 6 are new. The second class of problems is studied in Chaps. 79. In Chap. 7 we study the turnpike properties. The stability of the turnpike phenomenon under small perturbations of the objective functions is established in Chap. 8. In Chap. 9 we establish the stability of the turnpike phenomenon under small perturbations of the objective functions and the constraint maps. The results of Chaps. 8 and 9 are new. In Chap. 10 we study optimal control problems related to a model of knowledge-based endogenous economic growth and show the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.
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Includes bibliographical references and index.
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Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 13, 2022).
Series
Monographs in mathematical economics ; v. 5.
Available in Other Form
Optimal Control Problems Arising in Mathematical Economics.
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Table of Contents
Preface-1. Introduction
2. Turnpike Conditions for Optimal Control Systems
3. Nonautonomous Problems with Perturbed Objective Functions
4. Nonautonomous Problems with Discounting
5. Stability of the Turnpike Phenomenon for Nonautonomous Problems
6. Stability of the Turnpike for Nonautonomous Problems with Discounting
7. Turnpike Properties for Autonomous Problems
8. Autonomous Problems with Perturbed Objective Functions
9. Stability Results for Autonomous Problems
10. Models with Unbounded Endogenous Economic Growth-Reference
Index.
2. Turnpike Conditions for Optimal Control Systems
3. Nonautonomous Problems with Perturbed Objective Functions
4. Nonautonomous Problems with Discounting
5. Stability of the Turnpike Phenomenon for Nonautonomous Problems
6. Stability of the Turnpike for Nonautonomous Problems with Discounting
7. Turnpike Properties for Autonomous Problems
8. Autonomous Problems with Perturbed Objective Functions
9. Stability Results for Autonomous Problems
10. Models with Unbounded Endogenous Economic Growth-Reference
Index.