Dynamic Programming of Economic Decisions


Book Description

Dynamic Programming is the analysis of multistage decision in the sequential mode. It is now widely recognized as a tool of great versatility and power, and is applied to an increasing extent in all phases of economic analysis, operations research, technology, and also in mathematical theory itself. In economics and operations research its impact may someday rival that of linear programming. The importance of this field is made apparent through a growing number of publications. Foremost among these is the pioneering work of Bellman. It was he who originated the basic ideas, formulated the principle of optimality, recognized its power, coined the terminology, and developed many of the present applications. Since then mathe maticians, statisticians, operations researchers, and economists have come in, laying more rigorous foundations [KARLIN, BLACKWELL], and developing in depth such application as to the control of stochastic processes [HoWARD, JEWELL]. The field of inventory control has almost split off as an independent branch of Dynamic Programming on which a great deal of effort has been expended [ARRoW, KARLIN, SCARF], [WIDTIN] , [WAGNER]. Dynamic Programming is also playing an in creasing role in modem mathematical control theory [BELLMAN, Adap tive Control Processes (1961)]. Some of the most exciting work is going on in adaptive programming which is closely related to sequential statistical analysis, particularly in its Bayesian form. In this monograph the reader is introduced to the basic ideas of Dynamic Programming.




Forward-Looking Decision Making


Book Description

Individuals and families make key decisions that impact many aspects of financial stability and determine the future of the economy. These decisions involve balancing current sacrifice against future benefits. People have to decide how much to invest in health care, exercise, their diet, and insurance. They must decide how much debt to take on, and how much to save. And they make choices about jobs that determine employment and unemployment levels. Forward-Looking Decision Making is about modeling this individual or family-based decision making using an optimizing dynamic programming model. Robert Hall first reviews ideas about dynamic programs and introduces new ideas about numerical solutions and the representation of solved models as Markov processes. He surveys recent research on the parameters of preferences--the intertemporal elasticity of substitution, the Frisch elasticity of labor supply, and the Frisch cross-elasticity. He then examines dynamic programming models applied to health spending, long-term care insurance, employment, entrepreneurial risk-taking, and consumer debt. Linking theory with data and applying them to real-world problems, Forward-Looking Decision Making uses dynamic optimization programming models to shed light on individual behaviors and their economic implications.




Dynamic Programming of Economic Decisions


Book Description

Textbook on dynamic programming as methodology of operational research and decision making - covers theoretical aspects, mathematical and research methodology, etc. Bibliographys.




Dynamic Programming


Book Description

Humans interact with and are part of the mysterious processes of nature. Inevitably they have to discover how to manage the environment for their long-term survival and benefit. To do this successfully means learning something about the dynamics of natural processes, and then using the knowledge to work with the forces of nature for some desired outcome. These are intriguing and challenging tasks. This book describes a technique which has much to offer in attempting to achieve the latter task. A knowledge of dynamic programming is useful for anyone interested in the optimal management of agricultural and natural resources for two reasons. First, resource management problems are often problems of dynamic optimization. The dynamic programming approach offers insights into the economics of dynamic optimization which can be explained much more simply than can other approaches. Conditions for the optimal management of a resource can be derived using the logic of dynamic programming, taking as a starting point the usual economic definition of the value of a resource which is optimally managed through time. This is set out in Chapter I for a general resource problem with the minimum of mathematics. The results are related to the discrete maximum principle of control theory. In subsequent chapters dynamic programming arguments are used to derive optimality conditions for particular resources.




Dynamic Programming


Book Description

Designed both for those who seek an acquaintance with dynamic programming and for those wishing to become experts, this text is accessible to anyone who's taken a course in operations research. It starts with a basic introduction to sequential decision processes and proceeds to the use of dynamic programming in studying models of resource allocation. Subsequent topics include methods for approximating solutions of control problems in continuous time, production control, decision-making in the face of an uncertain future, and inventory control models. The final chapter introduces sequential decision processes that lack fixed planning horizons, and the supplementary chapters treat data structures and the basic properties of convex functions. 1982 edition. Preface to the Dover Edition.




Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining


Book Description

Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.




Dynamic Optimization, Second Edition


Book Description

Since its initial publication, this text has defined courses in dynamic optimization taught to economics and management science students. The two-part treatment covers the calculus of variations and optimal control. 1998 edition.




Dynamic Economics


Book Description

An integrated approach to the empirical application of dynamic optimization programming models, for students and researchers. This book is an effective, concise text for students and researchers that combines the tools of dynamic programming with numerical techniques and simulation-based econometric methods. Doing so, it bridges the traditional gap between theoretical and empirical research and offers an integrated framework for studying applied problems in macroeconomics and microeconomics. In part I the authors first review the formal theory of dynamic optimization; they then present the numerical tools and econometric techniques necessary to evaluate the theoretical models. In language accessible to a reader with a limited background in econometrics, they explain most of the methods used in applied dynamic research today, from the estimation of probability in a coin flip to a complicated nonlinear stochastic structural model. These econometric techniques provide the final link between the dynamic programming problem and data. Part II is devoted to the application of dynamic programming to specific areas of applied economics, including the study of business cycles, consumption, and investment behavior. In each instance the authors present the specific optimization problem as a dynamic programming problem, characterize the optimal policy functions, estimate the parameters, and use models for policy evaluation. The original contribution of Dynamic Economics: Quantitative Methods and Applications lies in the integrated approach to the empirical application of dynamic optimization programming models. This integration shows that empirical applications actually complement the underlying theory of optimization, while dynamic programming problems provide needed structure for estimation and policy evaluation.




Applications Of Dynamic Programming To Agricultural Decision Problems


Book Description

A collection of articles which provide examples that demonstrate the application of dynamic programming to a wide variety of decision problems in agriculture.




Applied Dynamic Programming


Book Description

This comprehensive study of dynamic programming applied to numerical solution of optimization problems. It will interest aerodynamic, control, and industrial engineers, numerical analysts, and computer specialists, applied mathematicians, economists, and operations and systems analysts. Originally published in 1962. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.