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Optimal Control Problems Arising in Mathematical Economics (Hardcover, 1st ed. 2022)
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Optimal Control Problems Arising in Mathematical Economics (Hardcover, 1st ed. 2022)
Series: Monographs in Mathematical Economics, 5
Expected to ship within 18 - 22 working days
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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.
General
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