Optimal Control Theory And Static Optimization In Economics
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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.
Optimal Control Theory And Static Optimization In Economics
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Author : D. Léonard
language : en
Publisher:
Release Date : 1998
Optimal Control Theory And Static Optimization In Economics written by D. Léonard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
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.
Optimal Control Theory
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Author : Suresh P. Sethi
language : en
Publisher: Springer Nature
Release Date : 2022-01-03
Optimal Control Theory written by Suresh P. Sethi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-03 with Business & Economics categories.
This new 4th edition offers an introduction to optimal control theory and its diverse applications in management science and economics. It introduces students to the concept of the maximum principle in continuous (as well as discrete) time by combining dynamic programming and Kuhn-Tucker theory. While some mathematical background is needed, the emphasis of the book is not on mathematical rigor, but on modeling realistic situations encountered in business and economics. It applies optimal control theory to the functional areas of management including finance, production and marketing, as well as the economics of growth and of natural resources. In addition, it features material on stochastic Nash and Stackelberg differential games and an adverse selection model in the principal-agent framework. Exercises are included in each chapter, while the answers to selected exercises help deepen readers’ understanding of the material covered. Also included are appendices of supplementary material on the solution of differential equations, the calculus of variations and its ties to the maximum principle, and special topics including the Kalman filter, certainty equivalence, singular control, a global saddle point theorem, Sethi-Skiba points, and distributed parameter systems. Optimal control methods are used to determine optimal ways to control a dynamic system. The theoretical work in this field serves as the foundation for the book, in which the author applies it to business management problems developed from his own research and classroom instruction. The new edition has been refined and updated, making it a valuable resource for graduate courses on applied optimal control theory, but also for financial and industrial engineers, economists, and operational researchers interested in applying dynamic optimization in their fields.
Optimal Control Theory
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Author : Zhongjing Ma
language : en
Publisher: Springer Nature
Release Date : 2021-01-30
Optimal Control Theory written by Zhongjing Ma and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-30 with Technology & Engineering categories.
This book focuses on how to implement optimal control problems via the variational method. It studies how to implement the extrema of functional by applying the variational method and covers the extrema of functional with different boundary conditions, involving multiple functions and with certain constraints etc. It gives the necessary and sufficient condition for the (continuous-time) optimal control solution via the variational method, solves the optimal control problems with different boundary conditions, analyzes the linear quadratic regulator & tracking problems respectively in detail, and provides the solution of optimal control problems with state constraints by applying the Pontryagin’s minimum principle which is developed based upon the calculus of variations. And the developed results are applied to implement several classes of popular optimal control problems and say minimum-time, minimum-fuel and minimum-energy problems and so on. As another key branch of optimal control methods, it also presents how to solve the optimal control problems via dynamic programming and discusses the relationship between the variational method and dynamic programming for comparison. Concerning the system involving individual agents, it is also worth to study how to implement the decentralized solution for the underlying optimal control problems in the framework of differential games. The equilibrium is implemented by applying both Pontryagin’s minimum principle and dynamic programming. The book also analyzes the discrete-time version for all the above materials as well since the discrete-time optimal control problems are very popular in many fields.
Optimal Control Models In Finance
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Author : Ping Chen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18
Optimal Control Models In Finance written by Ping Chen 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 2006-06-18 with Mathematics categories.
This book reports initial efforts in providing some useful extensions in - nancial modeling; further work is necessary to complete the research agenda. The demonstrated extensions in this book in the computation and modeling of optimal control in finance have shown the need and potential for further areas of study in financial modeling. Potentials are in both the mathematical structure and computational aspects of dynamic optimization. There are needs for more organized and coordinated computational approaches. These ext- sions will make dynamic financial optimization models relatively more stable for applications to academic and practical exercises in the areas of financial optimization, forecasting, planning and optimal social choice. This book will be useful to graduate students and academics in finance, mathematical economics, operations research and computer science. Prof- sional practitioners in the above areas will find the book interesting and inf- mative. The authors thank Professor B.D. Craven for providing extensive guidance and assistance in undertaking this research. This work owes significantly to him, which will be evident throughout the whole book. The differential eq- tion solver “nqq” used in this book was first developed by Professor Craven. Editorial assistance provided by Matthew Clarke, Margarita Kumnick and Tom Lun is also highly appreciated. Ping Chen also wants to thank her parents for their constant support and love during the past four years.
Foundations Of Dynamic Economic Analysis
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Author : Michael R. Caputo
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-10
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 2005-01-10 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.
Integral And Inverse Reinforcement Learning For Optimal Control Systems And Games
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Author : Bosen Lian
language : en
Publisher: Springer Nature
Release Date : 2024-03-05
Integral And Inverse Reinforcement Learning For Optimal Control Systems And Games written by Bosen Lian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-05 with Technology & Engineering categories.
Integral and Inverse Reinforcement Learning for Optimal Control Systems and Games develops its specific learning techniques, motivated by application to autonomous driving and microgrid systems, with breadth and depth: integral reinforcement learning (RL) achieves model-free control without system estimation compared with system identification methods and their inevitable estimation errors; novel inverse RL methods fill a gap that will help them to attract readers interested in finding data-driven model-free solutions for inverse optimization and optimal control, imitation learning and autonomous driving among other areas. Graduate students will find that this book offers a thorough introduction to integral and inverse RL for feedback control related to optimal regulation and tracking, disturbance rejection, and multiplayer and multiagent systems. For researchers, it provides a combination of theoretical analysis, rigorous algorithms, and a wide-ranging selection of examples. The book equips practitioners working in various domains – aircraft, robotics, power systems, and communication networks among them – with theoretical insights valuable in tackling the real-world challenges they face.
Fundamental Economics Volume Ii
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Author : Mukul Majumdar
language : en
Publisher: EOLSS Publications
Release Date : 2010-12-12
Fundamental Economics Volume Ii written by Mukul Majumdar and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-12 with categories.
Fundamental Economics in two volumes is a component of Encyclopedia of Social Sciences and Humanities in the global Encyclopedia of Life Support Systems (EOLSS), which is an integrated compendium of twenty one Encyclopedias. The Theme discusses on Fundamental Economics, Walrasian and Non-Walrasian Microeconomics, Strategic Behavior, The Economics of Bargaining, Economic Exernalities, Public Goods, Macroeconomics, Decision Making Under Uncertainty, Development Economics and many other related topics. These two volumes are aimed at the following five major target audiences: University and College Students Educators, Professional Practitioners, Research Personnel and Policy Analysts, Managers, and Decision Makers, NGOs and GOs.
Differential Games In Industrial Economics
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Author : Luca Lambertini
language : en
Publisher:
Release Date : 2018-04-26
Differential Games In Industrial Economics written by Luca Lambertini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Business & Economics categories.
A comprehensive and self-contained exposition of the applications of optimal control and differential game theory to industrial organisation and trade.