Dynamic Optimization

This book explores discrete-time dynamic optimization and provides a detailed introduction to both deterministic and stochastic models. Covering problems with finite and infinite horizon, as well as M

" An excellent financial research tool, this celebrated classic focuses on the methods of solving continuous time problems. The two-part treatment covers the calculus of variations and optimal control

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.

The main purpose of the book is to show how a viscosity approach can be used to tackle control problems in insurance. The problems covered are the maximization of survival probability as well as the m

In this book, a methodology for parameter adaptation in meta-heuristic op-timization methods is proposed. This methodology is based on using met-rics about the population of the meta-heuristic methods

Directions for working with two popular photo editing programs: Photomatix and HDR Efex Pro The specific settings used for each photo are given, along with commentary on why the artist chose those set

Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for prec

A common set of mathematical tools underlies dynamic optimization, dynamic estimation, and filtering. In Recursive Models of Dynamic Linear Economies, Lars Peter Hansen and Thomas Sargent use these to

Focusing on deterministic models in discrete time, this concise yet rigorous textbook provides a clear and systematic introduction to the theory and application of dynamic economic models. It guides students through the most popular model structures and solution concepts, from the simplest dynamic economic models through to complex problems of optimal policy design in dynamic general equilibrium frameworks. Chapters feature theorems and practical hints, and seventy-five worked examples highlight the various methods and results that can be applied in dynamic economic models. Notation and formulation is uniform throughout, so students can easily discern the similarities and differences between various model classes. Chapters include more than sixty exercises for students to self-test their analytical skills, and password-protected solutions are available for instructors on the companion website. Assuming no prior knowledge of dynamic economic analysis or dynamic optimization, this textbo

The book is devoted to systems with discontinuous control. The study of discontinuous dynamic systems is a multifacet problem which embraces mathematical, control theoretic and application aspects. Ti

Intended for an audience of graduate students, executive MBA students, and mid-to upper level government and corporate managers, Design, Analysis and Optimization of Supply Chains: A System Dynamic Ap

This book, first published in 1996, introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. Each chapter contains a number of detailed examples explaining both the theory and its applications for first-year master's and graduate students. 'Cookbook' procedures are accompanied by a discussion of when such methods are guaranteed to be successful, and, equally importantly, when they could fail. Each result in the main body of the text is also accompanied by a complete proof. A preliminary chapter and three appendices are designed to keep the book mathematically self-conta

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 purp

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and

Analysis and Control of Polynomial Dynamic Models with Biological Applications synthesizes three mathematical background areas (graphs, matrices and optimization) to solve problems in the biological s

Andreas Potschka discusses a direct multiple shooting method for dynamic optimization problems constrained by nonlinear, possibly time-periodic, parabolic partial differential equations. In contrast t

This book includes a collection of articles that present recent developments in the fields of optimization and dynamic game theory, economic dynamics, dynamic theory of the firm, and population dynami

In the second edition of this user-friendly book, Olivier de La Grandville provides a clear and original introduction to the theory of economic growth, its mechanisms and its challenges. The book has been fully updated to incorporate several important new results and proofs since the first edition. In addition to a progressive treatment of dynamic optimization, readers will find intuitive derivations of all central equations of the calculus of variations and of optimal control theory. It offers a new solution to the fundamental question: How much should a nation save and invest? La Grandville shows that the optimal savings rule he suggests not only corresponds to the maximization of future welfare flows for society, but also maximizes the value of society's activity, as well as the total remuneration of labour. The rule offers a fresh alternative to dire current predictions about an ever-increasing capital–output ratio and a decrease of the labour share in national income.

This textbook concisely covers math knowledge and tools useful for business and economics studies, including matrix analysis, basic math concepts, general optimization, dynamic optimization, and ordin

This book adopts a linear optimization method and introduces a dynamic optimization simulation model for analyzing synthetic environmental policies as endogenous variables in order to improve the envi

In this book, the authors treat macroeconomic models as composed of large numbers of micro-units or agents of several types and explicitly discuss stochastic dynamic and combinatorial aspects of interactions among them. In mainstream macroeconomics sound microfoundations for macroeconomics have meant incorporating sophisticated intertemporal optimization by representative agents into models. Optimal growth theory, once meant to be normative, is now taught as a descriptive theory in mainstream macroeconomic courses. In neoclassical equilibria flexible prices led the economy to the state of full employment and marginal productivities are all equated. Professors Aoki and Yoshikawa contrariwise show that such equilibria are not possible in economies with a large number of agents of heterogeneous types. They employ a set of statistical dynamical tools via continuous-time Markov chains and statistical distributions of fractions of agents by types available in the new literature of combinator

This book develops dynamic economic models using the perspective and analytic framework provided by psychological learning theory. This framework is used to resolve apparent contradictions between optimization theory, which lies at the heart of all modern economic theory, and day-to-day evidence that short-run economic behaviour cannot reasonably be described solely as the outcome of efficiently implemented self-interest. The author applies this viewpoint to a number of problem areas in which literal applications of maximization theory have not usually proved to be satisfactory. These include analyses of decision-making under uncertainty and gambling behaviour, the role of consumer-oriented advertising in influencing behaviour, the persistence of price dispersions in markets, and inflation.

One of the central questions of economics relates to the coordination of individual units within a large organization to achieve the central objectives of that organization. This book examines the problems involved in allocating resources in an economic system where decision-making is decentralized into the hands of individuals and individual enterprises. The decisions made by these economic agents must be coordinated because the input decisions of some must eventually equal the output decisions of others. Coordination arises naturally out of the mathematical theory of optimization but there is still the question of how it can be achieved in practice with dispersed knowledge. The essays here explore the many facets of this problem. Nine papers are grouped under the title 'Economies with a single maximand'. They include papers on static and dynamic optimization, decentralization within firms, and nonconvexities in optimizing problems. Fourteen papers are concerned with 'Economies with m

This book is the only source that provides comprehensive, current, and correct information on problem solving using modern heuristics. It covers classic methods of optimization, including dynamic prog

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.