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Optimal Control Problems Arising in Mathematical Economics de Alexander J. Zaslavski

Optimal Control Problems Arising in Mathematical Economics: Monographs in Mathematical Economics, cartea 5

Autor Alexander J. Zaslavski
en Limba Engleză Paperback – 30 iun 2023
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 Robinson–Solow–Srinivasan  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 Robinson–Solow–Srinivasan 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. 3–6. 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. 7–9. 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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Specificații

ISBN-13: 9789811693007
ISBN-10: 9811693005
Ilustrații: XI, 378 p. 1 illus.
Dimensiuni: 155 x 235 mm
Greutate: 0.55 kg
Ediția:1st ed. 2022
Editura: Springer Nature Singapore
Colecția Springer
Seria Monographs in Mathematical Economics

Locul publicării:Singapore, Singapore

Cuprins

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.

Recenzii

“This is an excellent monograph on a very important subject: optimal control in mathematical economics. It is based on many related contributions. including the author's work and expertise.” (Gheorghe Moroșanu, zbMATH 1497.49001, 2022)

Notă biografică

Alexander J. Zaslavski, Department of Mathematics, Technion – Israel Institute of Technology, Rishon LeZion, Israel.LeZion, IsraelLeZion, IsraelLeZion, IsraelLeZion, Israel

Textul de pe ultima copertă

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 Robinson–Solow–Srinivasan  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 Robinson–Solow–Srinivasan model. In Chap. 2 we introduce the first class of optimal control problems andstudy its turnpike property. This class of problems is also discussed in Chaps. 3–6. 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. 7–9. 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 toa model of knowledge-based endogenous economic growth and show  the existence of trajectories of unbounded economic growth and provide estimates for the growth rate.

Caracteristici

Develops the turnpike theory for a new class of optimal control problems related to a general model of economic growth Expounds the turnpike theory for a new class of autonomous optimal control problems related to the RSS model Studies the stability of the turnpike phenomenon for the new classes of optimal control problems