Dynamic General Equilibrium Modelling: Computational Methods and Applications

Book Description

Modern business cycle theory and growth theory uses stochastic dynamic general equilibrium models. Many mathematical tools are needed to solve these models. The book presents various methods for computing the dynamics of general equilibrium models. In part I, the representative-agent stochastic growth model is solved with the help of value function iteration, linear and linear quadratic approximation methods, parameterised expectations and projection methods. In order to apply these methods, fundamentals from numerical analysis are reviewed in detail. Part II discusses methods for solving heterogeneous-agent economies. In such economies, the distribution of the individual state variables is endogenous. This part of the book also serves as an introduction to the modern theory of distribution economics. Applications include the dynamics of the income distribution over the business cycle or the overlapping-generations model. Through an accompanying home page to this book, computer codes to all applications can be downloaded.

H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control: Foundations & Applications)

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H-Infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach (Systems & Control: Foundations & Applications)
Tamer Basar , and Pierre Bernhard
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817638148

Book Description

One of the major concentrated activities of the past decade in control theory has been the development of the so-called 'H-infinity-optimal control theory', which addresses the issue of worst-case controller design for linear plants subject to unknown disturbances and plant uncertainties.

This second edition features a more streamlined presentation of the results included in the first edition and also contains substantial new material, reflecting new developments in the field since 1991. Among these are the nonlinear theory; connections between H-infinity-optimal control and risk sensitive stochastic control problems; H-infinity filtering for linear and nonlinear systems; and robustness considerations in the presence of regular and singular perturbations. Also included are a rather detailed description of the relationship between frequency-and time-domain approaches to robust controller design, and a complete set of results on the existence of value and characterization of optimal policies in finite- and infinite-horizon LQ differential games.

Book Description

Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics.
Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games)

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Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games)

Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817643990

Book Description

This collection of selected contributions gives an account of recent developments in dynamic game theory and its applications, covering both theoretical advances and new applications of dynamic games in such areas as pursuit-evasion games, ecology, and economics. Written by experts in their respective disciplines, the chapters are an outgrowth of presentations from the 11th International Symposium on Dynamic Games and Applications.

Key topics covered include:

* stochastic and differential games

* dynamic games and their applications in various areas, such as ecology and economics

* numerical methods and algorithms in dynamic games

* zero- and nonzero-sum games

* pursuit-evasion games

* evolutionary game theory and applications

The work will serve as a state-of-the art account of recent advances in dynamic game theory and its applications for researchers, practitioners, and advanced students in applied mathematics, mathematical finance, and engineering.

Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications (Dover Books on Mathematics)

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Stationary and Related Stochastic Processes: Sample Function Properties and Their Applications (Dover Books on Mathematics)
Harald Cramer , and M. Ross Leadbetter
Manufacturer: Dover Publications
ProductGroup: Book
Binding: Paperback

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ASIN: 0486438279

Book Description

This graduate-level text offers a comprehensive account of the general theory of stationary processes, with special emphasis on the properties of sample functions. The text develops the foundations of the general theory of stochastic processes, examines processes with a continuous-time parameter, and applies the general theory to procedures key to the study of stationary processes. 1967 edition.

Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control (Annals of the International Society of Dynamic Games)

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Advances in Dynamic Games: Applications to Economics, Finance, Optimization, and Stochastic Control (Annals of the International Society of Dynamic Games)

Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817643621

Book Description

This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a guide to the vitality and growth of the field and its applications. The selected chapters, written by experts in their respective disciplines, are an outgrowth of presentations originally given at the 9 ^th International Symposium of Dynamic Games and Applications. Featured throughout are useful tools for researchers and practitioners who use game theory for modeling in many disciplines.

Major topics covered include:

* repeated and stochastic games

* differential dynamic games

* optimal stopping games

* applications of dynamic games to economics, finance, and queuing theory

* numerical methods and algorithms for solving dynamic games

* Parrondo’s games and related topics

A valuable reference for practitioners and researchers in dynamic game theory, the book and its diverse applications will also benefit researchers and graduate students in applied mathematics, economics, engineering, systems and control, and environmental science.

Control of Spatially Structured Random Processes and Random Fields with Applications (Nonconvex Optimization and Its Applications)

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Control of Spatially Structured Random Processes and Random Fields with Applications (Nonconvex Optimization and Its Applications)
Ruslan K. Chornei , Hans Daduna , and Pavel S. Knopov
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 0387304096

Book Description

This book is devoted to the study and optimization of spatiotemporal stochastic processes, that is, processes which develop simultaneously in space and time under random influences. These processes are seen to occur almost everywhere when studying the global behavior of complex systems, including:

- Physical and technical systems

- Population dynamics

- Neural networks

- Computer and telecommunication networks

- Complex production networks

- Flexible manufacturing systems

- Logistic networks and transportation systems

-Environmental engineering

Climate modelling and prediction

Earth surface models

Classical stochastic dynamic optimization forms the framework of the book. Taken as a whole, the project undertaken in the book is to establish optimality or near-optimality for Markovian policies in the control of spatiotemporal Markovian processes. The authors apply this general principle to different frameworks of Markovian systems and processes. Depending on the structure of the systems and the surroundings of the model classes the authors arrive at different levels of simplicity for the policy classes which encompass optimal or nearly optimal policies. A set of examples accompanies the theoretical findings, and these examples should demonstrate some important application areas for the theorems discussed.

Conflict-Controlled Processes (Mathematics and Its Applications)

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Conflict-Controlled Processes (Mathematics and Its Applications)
A. Chikrii
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Book Description

This volume advances a new method for the solution of game problems of pursuit-evasion, which efficiently solves a wide range of game problems. In the case of `simple motions' it fully substantiates the classic `parallel pursuit' rule well known on a heuristic level to the designers of control systems. This method can be used for the solution of differential games of group and consecutive pursuit, the problem of complete controllability, and the problem of conflict interaction of a group of controlled objects, both for number under state constraints and under delay of information. These problems are not practically touched upon in other monographs. Some basic notions from functional and convex analysis, theory of set-valued maps and linear control theory are sufficient for understanding the main content of the book. Audience: This book will be of interest to specialists, as well as graduate and postgraduate students in applied mathematics and mechanics, and researchers in the mathematical theory of control, games theory and its applications.

Online Optimization of Large Scale Systems: State of the Art

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Online Optimization of Large Scale Systems: State of the Art

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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Systems Analysis & Design | Computer Science | Computers & Internet | Subjects | Books

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ASIN: 3540424598

Book Description

Whether costs are to be reduced, profits to be maximized, or scarce resources to be used wisely, optimization methods are available to guide decision making. In online optimization the main issue is incomplete data, and the scientific challenge: How well can an online algorithm perform? Can one guarantee solution quality, even without knowing all data in advance? In real-time optimization there is an additional requirement, decisions have to be computed very fast in relation to the time frame of the instance we consider. Online and real-time optimization problems occur in all branches of optimization. These areas have developed their own techniques but they are addressing the same issues: quality, stability, and robustness of the solutions. To fertilize this emerging topic of optimization theory and to foster cooperation between the different branches of optimization, the Deutsche Forschungsgemeinschaft (DFG) has supported a Priority Programme "Online Optimization of Large Systems".

Stochastic and Global Optimization (Nonconvex Optimization and Its Applications)

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Stochastic and Global Optimization (Nonconvex Optimization and Its Applications)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 1402004842

Book Description

This book is dedicated to the 70th birthday of Professor J. Mockus, whose scientific interests include theory and applications of global and discrete optimization, and stochastic programming. The papers for the book were selected because they relate to these topics and also satisfy the criterion of theoretical soundness combined with practical applicability. In addition, the methods for statistical analysis of extremal problems are covered. Although statistical approach to global and discrete optimization is emphasized, applications to optimal design and to mathematical finance are also presented. The results of some subjects (e.g., statistical models based on one-dimensional global optimization) are summarized and the prospects for new developments are justified.
Audience: Practitioners, graduate students in mathematics, statistics, computer science and engineering.

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