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Dynamic Economic Models And Optimal Control
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Book Synopsis Foundations of Dynamic Economic Analysis by : Michael R. Caputo
Download or read book Foundations of Dynamic Economic Analysis written by Michael R. Caputo and published by Cambridge University Press. This book was released on 2005-01-10 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control Theory with Applications in Economics by : Thomas A. Weber
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Methods in Dynamic Economics by : A. Simonovits
Download or read book Mathematical Methods in Dynamic Economics written by A. Simonovits and published by Springer. This book was released on 2000-06-05 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a concise description of important mathematical methods of dynamics and suitable economic models. It covers discrete as well as continuous-time systems, linear and nonlinear models. Mixing traditional and modern materials, the study covers dynamics with and without optimization, naive and rational expectations, respectively. In addition to standard models of growth and cycles, the book also contains original studies on control of a multisector economy and expectations-driven multicohort economy. Numerous examples, problems (with solutions) and figures complete the book.
Book Synopsis Dynamic Economic Models and Optimal Control by : Gustav Feichtinger
Download or read book Dynamic Economic Models and Optimal Control written by Gustav Feichtinger and published by North Holland. This book was released on 1992 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth issue in a series of volumes on optimal control theory and its economic applications. This volume reflects the important role which optimal control theory and differential games play in economics and management science. They provide powerful tools for the analysis of intertemporal decision processes arising in economics. The first part of the volume deals with optimal control theory and its applications to economics. The second part contains a selection of contributions to applied dynamic game theory. Finally, in the third part the strange behaviour of various nonlinear dynamical systems is investigated. It illustrates the fact that persistent oscillations and chaos play an increasing role in mathematical economics. In addition to including chaos theory a second innovation in this fourth volume of the series is that for the first time selected discussion remarks have been attached as addenda to some of the contributions.
Book Synopsis Dynamic Optimization, Second Edition by : Morton I. Kamien
Download or read book Dynamic Optimization, Second Edition written by Morton I. Kamien and published by Courier Corporation. This book was released on 2013-04-17 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Economic Models and Optimal Control by :
Download or read book Dynamic Economic Models and Optimal Control written by and published by . This book was released on 1992 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimal Control Theory and Static Optimization in Economics by : Daniel Léonard
Download or read book Optimal Control Theory and Static Optimization in Economics written by Daniel Léonard and published by Cambridge University Press. This book was released on 1992-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dynamic Linear Economic Models by : James L. Kenkel
Download or read book Dynamic Linear Economic Models written by James L. Kenkel and published by Routledge. This book was released on 2018-04-09 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1974. This book provides a rigorous and detailed introductory treatment of the theory of difference equations and their applications in the construction and analysis of dynamic economic models. It explains the theory of linear difference equations and various types of dynamic economic models are then analysed. Including plenty of examples of application throughout the text, it will be of use to those working in macroeconomics and econometrics.
Book Synopsis The Hamiltonian Approach to Dynamic Economics by : David Cass
Download or read book The Hamiltonian Approach to Dynamic Economics written by David Cass and published by Academic Press. This book was released on 2014-05-10 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Infinite Horizon Optimal Control by : Dean A. Carlson
Download or read book Infinite Horizon Optimal Control written by Dean A. Carlson and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with various classes of deterministic continuous time optimal control problems wh ich are defined over unbounded time intervala. For these problems, the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts; referred to here as "overtaking", "weakly overtaking", "agreeable plans", etc. ; have been proposed. The motivation for studying these problems arisee primarily from the economic and biological aciences where models of this nature arise quite naturally since no natural bound can be placed on the time horizon when one considers the evolution of the state of a given economy or species. The reeponsibility for the introduction of this interesting class of problems rests with the economiste who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey who, in his seminal work on a theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a "Lagrange problem with unbounded time interval". The advent of modern control theory, particularly the formulation of the famoue Maximum Principle of Pontryagin, has had a considerable impact on the treatment of these models as well as optimization theory in general.
Book Synopsis Optimal Control Theory by : Suresh P. Sethi
Download or read book Optimal Control Theory written by Suresh P. Sethi and published by Taylor & Francis US. This book was released on 2006 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Optimal Control and System Theory in Dynamic Economic Analysis by : Masanao Aoki
Download or read book Optimal Control and System Theory in Dynamic Economic Analysis written by Masanao Aoki and published by North-Holland. This book was released on 1976 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Equations, Stability, and Chaos in Dynamic Economics by : William A. Brock
Download or read book Differential Equations, Stability, and Chaos in Dynamic Economics written by William A. Brock and published by North Holland. This book was released on 1989 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first economics work of its kind offering the economist the opportunity to acquire new and important analytical tools. It introduces the reader to three advanced mathematical methods by presenting both their theoretical bases and their applications to a wide range of economic models. The mathematical methods presented are ordinary differential equations, stability techniques and chaotic dynamics. Topics such as existence, continuation of solutions, uniqueness, dependence on initial data and parameters, linear systems, stability of linear systems, two dimensional phase analysis, local and global stability, the stability manifold, stability of optimal control and empirical tests for chaotic dynamics are covered and their use in economic theory is illustrated in numerous applications. These applications include microeconomic dynamics, investment theory, macroeconomic policies, capital theory, business cycles, financial economics and many others. All chapters conclude with two sections on miscellaneous applications and exercises and further remarks and references. In total the reader will find a valuable guide to over 500 selected references that use differential equations, stability analysis and chaotic dynamics. Graduate students in economics with a special interest in economic theory, economic researchers and applied mathematicians will all benefit from this volume.
Book Synopsis Recursive Methods in Economic Dynamics by : Nancy L. Stokey
Download or read book Recursive Methods in Economic Dynamics written by Nancy L. Stokey and published by Harvard University Press. This book was released on 1989-10-10 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rigorous but brilliantly lucid book presents a self-contained treatment of modern economic dynamics. Stokey, Lucas, and Prescott develop the basic methods of recursive analysis and illustrate the many areas where they can usefully be applied.
Book Synopsis Stochastic Optimal Control in Infinite Dimension by : Giorgio Fabbri
Download or read book Stochastic Optimal Control in Infinite Dimension written by Giorgio Fabbri and published by Springer. This book was released on 2017-06-22 with total page 928 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Book Synopsis Introduction to Dynamic Economic Models by : Brian S. Ferguson
Download or read book Introduction to Dynamic Economic Models written by Brian S. Ferguson and published by . This book was released on 1998 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unnecessary complexity has been avoided, yet the models have been presented in the same general form as they appear in the professional literature.
Book Synopsis Dynamic Economic Analysis by : Milton Harris
Download or read book Dynamic Economic Analysis written by Milton Harris and published by Oxford University Press, USA. This book was released on 1987 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: In industrial organization and labour economics, many of the most interesting recent contributions have encompassed explicit dynamics as well as extensive form games. This book collects and explains a number of the most widely used techniques in dynamic economic analysis.
