Optimal Control Problems Arising in Mathematical Economics

ISBN-13: 9789811692970 / Angielski / Twarda / 2022

Alexander J. Zaslavski

Opis

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.

Recenzje

"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 Moro anu, zbMATH 1497.49001, 2022)

Spis treści

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.

O autorze

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

LeZion, Israel

LeZion, Israel

LeZion, Israel

LeZion, Israel