Optimal Control Theory with Applications in Economics
Optimal Control Theory with Applications in Economics

Author: Thomas A. Weber

Publisher: MIT Press

Published: 2011-09-30

Total Pages: 387

ISBN-13: 0262015730

DOWNLOAD EBOOK

A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.

Optimal Control Theory
Optimal Control Theory

Author: Suresh P. Sethi

Publisher: Taylor & Francis US

Published: 2006

Total Pages: 536

ISBN-13: 9780387280929

DOWNLOAD EBOOK

Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as a foundation for the book, which the authors have applied to business management problems developed from their research and classroom instruction. Sethi and Thompson have provided management science and economics communities with a thoroughly revised edition of their classic text on Optimal Control Theory. The new edition has been completely refined with careful attention to the text and graphic material presentation. Chapters cover a range of topics including finance, production and inventory problems, marketing problems, machine maintenance and replacement, problems of optimal consumption of natural resources, and applications of control theory to economics. The book contains new results that were not available when the first edition was published, as well as an expansion of the material on stochastic optimal control theory.

Foundations of Dynamic Economic Analysis
Foundations of Dynamic Economic Analysis

Author: Michael Ralph Caputo

Publisher: Cambridge University Press

Published: 2005-01-17

Total Pages: 596

ISBN-13: 9780521603683

DOWNLOAD EBOOK

Foundations of Dynamic Economic Analysis presents a modern and thorough exposition of the fundamental mathematical formalism used to study optimal control theory, i.e., continuous time dynamic economic processes, and to interpret dynamic economic behavior. The style of presentation, with its continual emphasis on the economic interpretation of mathematics and models, distinguishes it from several other excellent texts on the subject. This approach is aided dramatically by introducing the dynamic envelope theorem and the method of comparative dynamics early in the exposition. Accordingly, motivated and economically revealing proofs of the transversality conditions come about by use of the dynamic envelope theorem. Furthermore, such sequencing of the material naturally leads to the development of the primal-dual method of comparative dynamics and dynamic duality theory, two modern approaches used to tease out the empirical content of optimal control models. The stylistic approach ultimately draws attention to the empirical richness of optimal control theory, a feature missing in virtually all other textbooks of this type.

Dynamic Optimization, Second Edition
Dynamic Optimization, Second Edition

Author: Morton I. Kamien

Publisher: Courier Corporation

Published: 2013-04-17

Total Pages: 402

ISBN-13: 0486310280

DOWNLOAD EBOOK

Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.

Optimal Control Theory and Static Optimization in Economics
Optimal Control Theory and Static Optimization in Economics

Author: Daniel Léonard

Publisher: Cambridge University Press

Published: 1992-01-31

Total Pages: 372

ISBN-13: 9780521337465

DOWNLOAD EBOOK

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purpose of the book is to draw the parallel between optimal control theory and static optimization. Chapter 1 provides an extensive treatment of constrained and unconstrained maximization, with emphasis on economic insight and applications. Starting from basic concepts, it derives and explains important results, including the envelope theorem and the method of comparative statics. This chapter may be used for a course in static optimization. The book is largely self-contained. No previous knowledge of differential equations is required.

The Hamiltonian Approach to Dynamic Economics
The Hamiltonian Approach to Dynamic Economics

Author: David Cass

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 212

ISBN-13: 1483266850

DOWNLOAD EBOOK

The Hamiltonian Approach to Dynamic Economics focuses on the application of the Hamiltonian approach to dynamic economics and attempts to provide some unification of the theory of heterogeneous capital. Emphasis is placed on the stability of long-run steady-state equilibrium in models of heterogeneous capital accumulation. Generalizations of the Samuelson-Scheinkman approach are also given. Moreover, conditions are sought on the geometry of the Hamiltonian function (that is, on static technology) that suffice to preserve under (not necessarily small) perturbation the basic properties of the Hamiltonian dynamical system. Comprised of eight essays, this book begins with an introduction to Hamiltonian dynamics in economics, followed by a discussion on optimal steady states of n-sector growth models when utility is discounted. Optimal growth and decentralized or descriptive growth models in both continuous and discrete time are treated as applications of Hamiltonian dynamics. Theproblem of optimal growth with zero discounting is considered, with emphasis on a steepness condition on the Hamiltonian function. The general problem of decentralized growth with instantaneously adjusted expectations about price changes is also analyzed, along with the global asymptotic stability of optimal control systems with applications to the theory of economic growth. This monograph will be of value to mathematicians and economists.

Dynamic Systems Modelling and Optimal Control
Dynamic Systems Modelling and Optimal Control

Author: Victoria Miroshnik

Publisher: Springer

Published: 2016-04-29

Total Pages: 193

ISBN-13: 1137508957

DOWNLOAD EBOOK

Dynamic Systems Modelling and Optimal Control explores the applications of oil field development, energy system modelling, resource modelling, time varying control of dynamic system of national economy, and investment planning.

Optimal Control of the Growth of Wealth of Nations
Optimal Control of the Growth of Wealth of Nations

Author: E.N. Chukwu

Publisher: CRC Press

Published: 2003-01-23

Total Pages: 412

ISBN-13: 9780415269667

DOWNLOAD EBOOK

Students and researchers in applied mathematics and applied economics can use this introductory-level graduate text. It looks at the current problems of the development of the global economy by studying the dynamics of key economic variables, such as gross national product, interest rates, employment, value of capital stock, prices (inflation) and balance of payments. Validation of the model is attempted using the economic time series of several countries. The constructed models explain the macroeconomic data of nations as dynamic games of pursuit, which are equivalent to "control" problems and are used to study mathematical optimal control of the growth of the wealth of nations. This invaluable reference for graduates and researchers compares the extent of government intervention in the economy with private firms to ensure the controllability of the economy.

Dynamic Modelling and Control of National Economies 1989
Dynamic Modelling and Control of National Economies 1989

Author: N.M. Christodoulakis

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 599

ISBN-13: 1483298825

DOWNLOAD EBOOK

The Symposium aimed at analysing and solving the various problems of representation and analysis of decision making in economic systems starting from the level of the individual firm and ending up with the complexities of international policy coordination. The papers are grouped into subject areas such as game theory, control methods, international policy coordination and the applications of artificial intelligence and experts systems as a framework in economic modelling and control. The Symposium therefore provides a wide range of important information for those involved or interested in the planning of company and national economics.