Control Theory Methods In Economics
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Control Theory Methods In Economics
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Author : Jati Sengupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Control Theory Methods In Economics written by Jati Sengupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
Control theory methods in economics have historically developed over three phases. The first involved basically the feedback control rules in a deterministic framework which were applied in macrodynamic models for analyzing stabilization policies. The second phase raised the issues of various types of inconsistencies in deterministic optimal control models due to changing information and other aspects of stochasticity. Rational expectations models have been extensively used in this plan to resolve some of the inconsistency problems. The third phase has recently focused on the various aspects of adaptive control. where stochasticity and information adaptivity are introduced in diverse ways e.g .• risk adjustment and risk sensitivity of optimal control, recursive updating rules via Kalman filtering and weighted recursive least squares and variable structure control methods in nonlinear framework. Problems of efficient econometric estimation of optimal control models have now acquired significant importance. This monograph provides an integrated view of control theory methods, synthesizing the three phases from feedback control to stochastic control and from stochastic control to adaptive control. Aspects of econometric estimation are strongly emphasized here, since these are very important in empirical applications in economics.
Optimal Control Theory And Static Optimization In Economics
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Author : Daniel Léonard
language : en
Publisher: Cambridge University Press
Release Date : 1992-01-31
Optimal Control Theory And Static Optimization In Economics written by Daniel Léonard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-31 with Business & Economics categories.
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.
Control Theory Methods In Economics
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Author : Jati Sengupta
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31
Control Theory Methods In Economics written by Jati Sengupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-31 with Business & Economics categories.
Control theory methods in economics have historically developed over three phases. The first involved basically the feedback control rules in a deterministic framework which were applied in macrodynamic models for analyzing stabilization policies. The second phase raised the issues of various types of inconsistencies in deterministic optimal control models due to changing information and other aspects of stochasticity. Rational expectations models have been extensively used in this plan to resolve some of the inconsistency problems. The third phase has recently focused on the various aspects of adaptive control. where stochasticity and information adaptivity are introduced in diverse ways e.g .• risk adjustment and risk sensitivity of optimal control, recursive updating rules via Kalman filtering and weighted recursive least squares and variable structure control methods in nonlinear framework. Problems of efficient econometric estimation of optimal control models have now acquired significant importance. This monograph provides an integrated view of control theory methods, synthesizing the three phases from feedback control to stochastic control and from stochastic control to adaptive control. Aspects of econometric estimation are strongly emphasized here, since these are very important in empirical applications in economics.
Foundations Of Dynamic Economic Analysis
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Author : Michael R. Caputo
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-17
Foundations Of Dynamic Economic Analysis written by Michael R. Caputo and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-17 with Business & Economics categories.
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.
Optimal Control Theory
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Author : Suresh P. Sethi
language : en
Publisher: Taylor & Francis US
Release Date : 2005-09-06
Optimal Control Theory written by Suresh P. Sethi and has been published by Taylor & Francis US this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-06 with Business & Economics categories.
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.
Mathematical Methods Of Game And Economic Theory
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Author : Jean-Pierre Aubin
language : en
Publisher: Courier Corporation
Release Date : 2007-01-01
Mathematical Methods Of Game And Economic Theory written by Jean-Pierre Aubin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.
Geometric Optimal Control
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Author : Heinz Schättler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-26
Geometric Optimal Control written by Heinz Schättler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-26 with Mathematics categories.
This book gives a comprehensive treatment of the fundamental necessary and sufficient conditions for optimality for finite-dimensional, deterministic, optimal control problems. The emphasis is on the geometric aspects of the theory and on illustrating how these methods can be used to solve optimal control problems. It provides tools and techniques that go well beyond standard procedures and can be used to obtain a full understanding of the global structure of solutions for the underlying problem. The text includes a large number and variety of fully worked out examples that range from the classical problem of minimum surfaces of revolution to cancer treatment for novel therapy approaches. All these examples, in one way or the other, illustrate the power of geometric techniques and methods. The versatile text contains material on different levels ranging from the introductory and elementary to the advanced. Parts of the text can be viewed as a comprehensive textbook for both advanced undergraduate and all level graduate courses on optimal control in both mathematics and engineering departments. The text moves smoothly from the more introductory topics to those parts that are in a monograph style were advanced topics are presented. While the presentation is mathematically rigorous, it is carried out in a tutorial style that makes the text accessible to a wide audience of researchers and students from various fields, including the mathematical sciences and engineering. Heinz Schättler is an Associate Professor at Washington University in St. Louis in the Department of Electrical and Systems Engineering, Urszula Ledzewicz is a Distinguished Research Professor at Southern Illinois University Edwardsville in the Department of Mathematics and Statistics.
Optimal Control Of Nonlinear Processes
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Author : Dieter Grass
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-24
Optimal Control Of Nonlinear Processes written by Dieter Grass and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-24 with Business & Economics categories.
Dynamic optimization is rocket science – and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin’s Maximum Principle – that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.
Primer On Optimal Control Theory
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Author : Jason L. Speyer
language : en
Publisher: SIAM
Release Date : 2010-05-13
Primer On Optimal Control Theory written by Jason L. Speyer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-13 with Mathematics categories.
A rigorous introduction to optimal control theory, which will enable engineers and scientists to put the theory into practice.
Developments Of Control Theory For Economic Analysis
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Author : Carlo Carraro
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Developments Of Control Theory For Economic Analysis written by Carlo Carraro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
Giovanni Castellani Rector of the University of Venice This book contains the Proceedings of the Conference on "Economic Policy and Control Theory" which was held at the University of Venice (Italy) on 27 January-l February 1985. The goal of the Conference was to survey the main developments of control theory in economics, by emphasizing particularly new achievements in the analysis of dynamic economic models by con trol methods. The development of control theory is strictly related to the development of science and technology in the last forty years. Control theory was indeed applied mainly in engineering, and only in the sixties economists started using control methods for analys ing economic problems, even if some preliminary economic applica tions of calculus of variations, from which control theory was then developed, date back to the twenties. Applications of control theory in economics also had to solve new, complicated, problems, like those encountered in optimal growth models, or like the determination of the appropriate inter temporal social welfare function, of the policy horizon and the relative final state of the system, of the appropriate discount factor. Furthermore, the uncertainty characterizing economic models had to be taken into account, thus giving rise to the development of stochastic control theory in economics.