Optimal control problems arising in mathematical economics / Alexander J. Zaslavski.
Zaslavski, Alexander J.
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
DOI https://doi.org/10.1007/978-981-16-9298-7
Imprint Singapore : Springer, 2022.
Language English
Description 1 online resource (387 pages)
Other Standard Identifiers 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
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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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.

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