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Mathematics For Stability And Optimization Of Economic Systems
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Book Synopsis Mathematics for Stability and Optimization of Economic Systems by : Yasuo Murata
Download or read book Mathematics for Stability and Optimization of Economic Systems written by Yasuo Murata and published by Academic Press. This book was released on 2014-05-10 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.
Book Synopsis Dynamic Optimization and Mathematical Economics by : Pan-Tai Liu
Download or read book Dynamic Optimization and Mathematical Economics written by Pan-Tai Liu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: As an outgrowth of the advancement in modern control theory during the past 20 years, dynamic modeling and analysis of economic systems has become an important subject in the study of economic theory. Recent developments in dynamic utility, economic planning, and profit optimiza tion, for example, have been greatly influenced by results in optimal control, stabilization, estimation, optimization under conflicts, multi criteria optimization, control of large-scale systems, etc. The great success that has been achieved so far in utilizing modern control theory in economic systems should be attributed to the effort of control theorists as well as economists. Collaboration between the two groups of researchers has proven to be most successful in many instances; nevertheless, the gap between them has existed for some time. Whereas a control theorist frequently sets up a mathematically feasible model to obtain results that permit economic interpretations, an economist is concerned more with the fidelity of the model in representing a real world problem, and results that are obtained (through possibly less mathematical analysis) are due largely to economic insight. The papers appearing in this volume are divided into three parts. In Part I there are five papers on the application of control theory to economic planning. Part II contains five papers on exploration, exploita tion, and pricing of extractive natural resources. Finally, in Part III, some recent advances in large-scale systems and decentralized control appear.
Book Synopsis Optimization and Stability Theory for Economic Analysis by : Brian Beavis
Download or read book Optimization and Stability Theory for Economic Analysis written by Brian Beavis and published by Cambridge University Press. This book was released on 1990 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability. Both of these are topics central to economic analysis since the latter is so much concerned with the optimizing behaviour of economic agents and the stability of the interaction processes to which this gives rise. The topics covered include convexity, mathematical programming, fixed point theorems, comparative static analysis and duality, the stability of dynamic systems, the calculus of variations and optimal control theory. The authors present a more detailed and wide-ranging discussion of these topics than is to be found in the few books which attempt a similar coverage. Although the text deals with fairly advanced material, the mathematical prerequisites are minimised by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra. A novel feature of the book is that it provides the reader with an understanding and feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. This is achieved through an extensive use of a broad range of economic examples (rather than the numerical/algebraic examples so often found). This is suitable for use in advanced undergraduate and postgraduate courses in economic analysis and should in addition prove a useful reference work for practising economists.
Book Synopsis Mathematical Optimization and Economic Theory by : Michael D. Intriligator
Download or read book Mathematical Optimization and Economic Theory written by Michael D. Intriligator and published by SIAM. This book was released on 2002-01-01 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.
Book Synopsis Optimization in Economics and Finance by : Bruce D. Craven
Download or read book Optimization in Economics and Finance written by Bruce D. Craven and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book.
Book Synopsis Differential Equations, Discrete Systems and Control by : A. Halanay
Download or read book Differential Equations, Discrete Systems and Control written by A. Halanay and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents some of the most important mathematical tools for studying economic models. It contains basic topics concerning linear differential equations and linear discrete-time systems; a sketch of the general theory of nonlinear systems and the stability of equilibria; an introduction to numerical methods for differential equations, and some applications to the solution of nonlinear equations and static optimization. The second part of the book discusses stabilization problems, including optimal stabilization, linear-quadratic optimization and other problems of dynamic optimization, including a proof of the Maximum Principle for general optimal control problems. All these mathematical subjects are illustrated with detailed discussions of economic models. Audience: This text is recommended as auxiliary material for undergraduate and graduate level MBA students, while at the same time it can also be used as a reference by specialists.
Book Synopsis Optimisation and Stability Theory for Economic Analysis by : Brian Beavis
Download or read book Optimisation and Stability Theory for Economic Analysis written by Brian Beavis and published by Cambridge University Press. This book was released on 1990-02-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a coherent and systematic exposition of the mathematical theory of the problems of optimization and stability, both of which are central to economic analysis. Through extensive use of economic examples, the authors provide the economist with a feel for the kinds of mathematical techniques most useful for dealing with particular economic problems. Although the text deals with fairly advanced material, the mathematical prerequisites are minimized by the inclusion of an integrated mathematical review designed to make the text self-contained and accessible to the reader with only an elementary knowledge of calculus and linear algebra.
Book Synopsis The Stability of a Macroeconomic System with Quantity Constraints by : P.van den Heuvel
Download or read book The Stability of a Macroeconomic System with Quantity Constraints written by P.van den Heuvel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Mathematical Economics by : M.C. Kemp
Download or read book Introduction to Mathematical Economics written by M.C. Kemp and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our objectives may be briefly stated. They are two. First, we have sought to provide a compact and digestible exposition of some sub-branches of mathematics which are of interest to economists but which are underplayed in mathematical texts and dispersed in the journal literature. Second, we have sought to demonstrate the usefulness of the mathematics by providing a systematic account of modern neoclassical economics, that is, of those parts of economics from which jointness in production has been excluded. The book is introductory not in the sense that it can be read by any high-school graduate but in the sense that it provides some of the mathematics needed to appreciate modern general-equilibrium economic theory. It is aimed primarily at first-year graduate students and final-year honors students in economics who have studied mathematics at the university level for two years and who, in particular, have mastered a full-year course in analysis and calculus. The book is the outcome of a long correspondence punctuated by periodic visits by Kimura to the University of New South Wales. Without those visits we would never have finished. They were made possible by generous grants from the Leverhulme Foundation, Nagoya City University, and the University of New South Wales. Equally indispensible were the expert advice and generous encouragement of our friends Martin Beckmann, Takashi Negishi, Ryuzo Sato, and Yasuo Uekawa.
Book Synopsis Optimal Control Methods for Linear Discrete-Time Economic Systems by : Y. Murata
Download or read book Optimal Control Methods for Linear Discrete-Time Economic Systems written by Y. Murata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: As our title reveals, we focus on optimal control methods and applications relevant to linear dynamic economic systems in discrete-time variables. We deal only with discrete cases simply because economic data are available in discrete forms, hence realistic economic policies should be established in discrete-time structures. Though many books have been written on optimal control in engineering, we see few on discrete-type optimal control. More over, since economic models take slightly different forms than do engineer ing ones, we need a comprehensive, self-contained treatment of linear optimal control applicable to discrete-time economic systems. The present work is intended to fill this need from the standpoint of contemporary macroeconomic stabilization. The work is organized as follows. In Chapter 1 we demonstrate instru ment instability in an economic stabilization problem and thereby establish the motivation for our departure into the optimal control world. Chapter 2 provides fundamental concepts and propositions for controlling linear deterministic discrete-time systems, together with some economic applica tions and numerical methods. Our optimal control rules are in the form of feedback from known state variables of the preceding period. When state variables are not observable or are accessible only with observation errors, we must obtain appropriate proxies for these variables, which are called "observers" in deterministic cases or "filters" in stochastic circumstances. In Chapters 3 and 4, respectively, Luenberger observers and Kalman filters are discussed, developed, and applied in various directions. Noticing that a separation principle lies between observer (or filter) and controller (cf.
Book Synopsis The stability of a macroeconomic system with quantity constraints by : Paul van den Heuvel
Download or read book The stability of a macroeconomic system with quantity constraints written by Paul van den Heuvel and published by Not Avail. This book was released on 1983 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Giancarlo Gandolfo Publisher :Springer Science & Business Media ISBN 13 :9783540627609 Total Pages :712 pages Book Rating :4.6/5 (276 download)
Book Synopsis Economic Dynamics by : Giancarlo Gandolfo
Download or read book Economic Dynamics written by Giancarlo Gandolfo and published by Springer Science & Business Media. This book was released on 1997 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: Treating the mathematical methods used in the economic dynamics, this book shows how they are utilised to build and analyse dynamical models. Accordingly, the focus is on the methods, and every new mathematical technique introduced is followed by its application to select economic models. The mathematical methods coveredc range from elementary linear difference and differential equations and simultaneous systems to the qualitative analysis of non-linear dynamical systems. Stability considerations are stressed throughout, including many advanced topics. Bifurcation and chaos theory are also dealt with. The reader is guided through a step-by-step analysis of each topic, be it a mathematical method or an economic model. The Study Edition also provides the reader with solutions to the numerous exercises.
Book Synopsis Optimization of Stochastic Systems by : Masanao Aoki
Download or read book Optimization of Stochastic Systems written by Masanao Aoki and published by . This book was released on 1989 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface The first edition of this book was written mainly for audiences with physical science and engineering backgrounds. Nevertheless, it reached some readers with economic and management science training. Analytical training of graduate students in economics and management sciences had progressed much in the last 20 years, and many new research results and optimization algorithms have also become available. My own interest in the meantime has shifted to the analysis of dynamics and optimization problems of economic and management science origin. With these developments and changes, I decided to rewrite much of the first edition to make it more accessible to graduate students and professionals in social sciences. I have also incorporated some new analytic tools that I deem useful in analyzing the dynamic and stochastic problems which confront these readers. I hope that my efforts successfully bring intertemporal optimization problems closer to economics professionals. New topics introduced into this second edition appear mostly in Chapters 2, 4, 5, 6, and 8. Martingales and martingale differences are introduced early in Chapter 2. Some limit theorems and asymptotic properties of linear state space models driven by martingale differences are presented. Because many excellent books are available on martingales and their limit theorems, derivations and proofs are mostly sketchy, and readers are referred to these sources. The results in Chapteer 2 are applied in Chapters 5, 6, and 8, among other places. The notion of dynamic aggregation and its relation to cointegration and error-correction models are developed in Chapter 4. Some recursive parameter estimation schemes and their statistical properties are included in Chapters 5 and 6. Here again, books devoted entirely to these topics are available in the literature, and much had to be omitted to keep the second edition to a manageable size. In an appendix to Chapter 7, a potentially very powerful tool in proving convergence of adaptive schemes is outlined. Rational expectations models and their solution methods are developed in Chapter 8 because of their wide-spread interest to economists. A very important class of problems in sequential decision problems revolves around questions of approximating nonlinear dynamics or more generally complex situations with a sequence of less complex ones. Chapter 9 does not begin to do justice to this class of problems but is included as being suggestive of works to be done. When I first started contemplating the revision of the first edition, I benefited from a list of excellent suggestions from Rick van der Ploeg, though I did not necessarily incorporate all of his suggestions. Conversations with Thomas Sargent and Victor Solo were useful in organizing the material into the form of the second edition. I also benefited from discussions with Hashem Pesaran and correspondences with L. Broze in finalizing Chapter 8. Some material in this book was used as lecture notes in a graduate course in the Department of Economics, University of California, Los Angeles, the winter quarter of 1987. I thank the participants in the course for many useful comments. Key Features * This major revision of the First Edition addresses optimization problems stated in stochastic difference equations, which often contain uncertain or randomly varying parameters * Presents a set of concepts and techniques useful in analyzing or controlling stochastic dynamic processes, with possible incompletely specified characteristics * It discusses basic system properties such as: * Stability and observability * Dynamic programming formulations of optimal and adaptive control problems * Parameter estimation schemes and their convergence behavior * Solution methods for rational expectations models using martingale differences
Book Synopsis Economic Dynamics: Methods and Models by : G Gandolfo
Download or read book Economic Dynamics: Methods and Models written by G Gandolfo and published by Elsevier. This book was released on 1971-01-01 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Economic Dynamics: Methods and Models aims to give a simple but comprehensive treatment of mathematical methods used in economic dynamics and show how they are utilized to build and to analyze dynamic models. The text also focuses on methods, and every mathematical technique introduced is followed by its application to selected models. The book is divided into three different parts. Part I: Different Equations discusses general principles; first-order, second-order, higher-order equations; simultaneous systems; and their economic applications. Part II: Differential Equations also discusses the same areas as those in Part I, but instead features differential equations, as what the section name suggests. Part III: More Advanced Material covers comparative statistics and the comparative principle; stability of equilibrium and Liapunov's second method; and linear mixed differential and difference equations, as well as its other related topics. The text is recommended for mathematicians and economists who have an idea on advanced mathematics and would like to know more about its applications in economics.
Book Synopsis Mathematical Analysis and Optimization for Economists by : Michael J. Panik
Download or read book Mathematical Analysis and Optimization for Economists written by Michael J. Panik and published by CRC Press. This book was released on 2021-09-30 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Mathematical Analysis and Optimization for Economists, the author aims to introduce students of economics to the power and versatility of traditional as well as contemporary methodologies in mathematics and optimization theory; and, illustrates how these techniques can be applied in solving microeconomic problems. This book combines the areas of intermediate to advanced mathematics, optimization, and microeconomic decision making, and is suitable for advanced undergraduates and first-year graduate students. This text is highly readable, with all concepts fully defined, and contains numerous detailed example problems in both mathematics and microeconomic applications. Each section contains some standard, as well as more thoughtful and challenging, exercises. Solutions can be downloaded from the CRC Press website. All solutions are detailed and complete. Features Contains a whole spectrum of modern applicable mathematical techniques, many of which are not found in other books of this type. Comprehensive and contains numerous and detailed example problems in both mathematics and economic analysis. Suitable for economists and economics students with only a minimal mathematical background. Classroom-tested over the years when the author was actively teaching at the University of Hartford. Serves as a beginner text in optimization for applied mathematics students. Accompanied by several electronic chapters on linear algebra and matrix theory, nonsmooth optimization, economic efficiency, and distance functions available for free on www.routledge.com/9780367759018.
Book Synopsis Mathematical Modelling by : Murray S. Klamkin
Download or read book Mathematical Modelling written by Murray S. Klamkin and published by SIAM. This book was released on 1987-01-01 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for classroom use, this book contains short, self-contained mathematical models of problems in the physical, mathematical, and biological sciences first published in the Classroom Notes section of the SIAM Review from 1975-1985. The problems provide an ideal way to make complex subject matter more accessible to the student through the use of concrete applications. Each section has extensive supplementary references provided by the editor from his years of experience with mathematical modelling.
Download or read book Chaotic Dynamics written by Alfredo Medio and published by Cambridge University Press. This book was released on 1992 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The modelling of economic models by means of dynamic systems.
