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| optimal transport methods in economics: Optimal Transport Methods in Economics Alfred Galichon, 2018-08-14 Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike |
| optimal transport methods in economics: Optimal Transport Methods in Economics Alfred Galichon, 2016-08-23 Optimal Transport Methods in Economics is the first textbook on the subject written especially for students and researchers in economics. Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. Authoritative and accessible, Optimal Transport Methods in Economics also features numerous exercises throughout that help you develop your mathematical agility, deepen your computational skills, and strengthen your economic intuition. The first introduction to the subject written especially for economists Includes programming examples Features numerous exercises throughout Ideal for students and researchers alike |
| optimal transport methods in economics: Optimal Transport for Applied Mathematicians Filippo Santambrogio, 2015-10-17 This monograph presents a rigorous mathematical introduction to optimal transport as a variational problem, its use in modeling various phenomena, and its connections with partial differential equations. Its main goal is to provide the reader with the techniques necessary to understand the current research in optimal transport and the tools which are most useful for its applications. Full proofs are used to illustrate mathematical concepts and each chapter includes a section that discusses applications of optimal transport to various areas, such as economics, finance, potential games, image processing and fluid dynamics. Several topics are covered that have never been previously in books on this subject, such as the Knothe transport, the properties of functionals on measures, the Dacorogna-Moser flow, the formulation through minimal flows with prescribed divergence formulation, the case of the supremal cost, and the most classical numerical methods. Graduate students and researchers in both pure and applied mathematics interested in the problems and applications of optimal transport will find this to be an invaluable resource. |
| optimal transport methods in economics: Computational Optimal Transport Gabriel Peyre, Marco Cuturi, 2019-02-12 The goal of Optimal Transport (OT) is to define geometric tools that are useful to compare probability distributions. Their use dates back to 1781. Recent years have witnessed a new revolution in the spread of OT, thanks to the emergence of approximate solvers that can scale to sizes and dimensions that are relevant to data sciences. Thanks to this newfound scalability, OT is being increasingly used to unlock various problems in imaging sciences (such as color or texture processing), computer vision and graphics (for shape manipulation) or machine learning (for regression, classification and density fitting). This monograph reviews OT with a bias toward numerical methods and their applications in data sciences, and sheds lights on the theoretical properties of OT that make it particularly useful for some of these applications. Computational Optimal Transport presents an overview of the main theoretical insights that support the practical effectiveness of OT before explaining how to turn these insights into fast computational schemes. Written for readers at all levels, the authors provide descriptions of foundational theory at two-levels. Generally accessible to all readers, more advanced readers can read the specially identified more general mathematical expositions of optimal transport tailored for discrete measures. Furthermore, several chapters deal with the interplay between continuous and discrete measures, and are thus targeting a more mathematically-inclined audience. This monograph will be a valuable reference for researchers and students wishing to get a thorough understanding of Computational Optimal Transport, a mathematical gem at the interface of probability, analysis and optimization. |
| optimal transport methods in economics: Optimal Transport Gershon Wolansky, 2021-01-18 This book focuses on problems at the interplay between the theory of partitions and optimal transport with a view toward applications. Topics covered include problems related to stable marriages and stable partitions, multipartitions, optimal transport for measures and optimal partitions, and finally cooperative and noncooperative partitions. All concepts presented are illustrated by examples from game theory, economics, and learning. |
| optimal transport methods in economics: A Handbook of Transport Economics André de Palma, Robin Lindsey, Emile Quinet, Roger Vickerman, 2011-01-01 'This Handbook is a stellar compilation of up-to-date knowledge about the important topics in transport economics. Authors include the very best in the field, and they cover the most important topics for today's research and policy applications. Individual chapters contain sound, readable, well referenced explanations of each topic's history and current status. I cannot think of a better place to start for anyone wanting to become current in the field or in any of its parts.' – Kenneth Small, University of California-Irvine, US Bringing together insights and perspectives from close to 70 of the world's leading experts in the field, this timely Handbook provides an up-to-date guide to the most recent and state-of-the-art advances in transport economics. The comprehensive coverage includes topics such as the relationship between transport and the spatial economy, recent advances in travel demand analysis, the external costs of transport, investment appraisal, pricing, equity issues, competition and regulation, the role of public–private partnerships and the development of policy in local bus services, rail, air and maritime transport. This Handbook is designed both for use on postgraduate and advanced undergraduate courses and as a reference for anyone working in the field. It also complements the textbook Principles of Transport Economics. |
| optimal transport methods in economics: Topics in Optimal Transportation Cédric Villani, 2003 Cedric Villani's book is a lucid and very readable documentation of the tremendous recent analytic progress in ``optimal mass transportation'' theory and of its diverse and unexpected applications in optimization, nonlinear PDE, geometry, and mathematical physics. --Lawrence C. Evans, University of California at Berkeley In 1781, Gaspard Monge defined the problem of ``optimal transportation'', or the transferring of mass with the least possible amount of work, with applications to engineering in mind. In 1942, Leonid Kantorovich applied the newborn machinery of linear programming to Monge's problem, with applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection theorem on the set of measure preserving maps, with applications to fluid mechanics in mind. Each of these contributions marked the beginning of a whole mathematical theory, with many unexpected ramifications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse horizons, including probability theory, functional analysis, isoperimetry, partial differential equations, and even meteorology. Originating from a graduate course, the present volume is at once an introduction to the field of optimal transportation and a survey of the research on the topic over the last 15 years. The book is intended for graduate students and researchers, and it covers both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis. |
| optimal transport methods in economics: The Economics of Urban Transportation Kenneth A. Small, Erik T. Verhoef, 2007-10-18 This timely new edition of Kenneth A. Small’s seminal textbook Urban Transportation Economics, co-authored with Erik T. Verhoef, has been fully updated, covering new areas such as parking policies, reliability of travel times, and the privatization of transportation services, as well as updated treatments of congestion modelling, environmental costs, and transit subsidies. Rigorous in approach and making use of real-world data and econometric techniques, it contains case studies from a range of countries including congestion charging in Norway, Singapore and the UK, light rail in the Netherlands and freeway tolls in the US. Small and Verhoef cover all basic topics needed for any application of economics to transportation: forecasting the demand for transportation services under alternative policies measuring all the costs including those incurred by users setting prices under practical constraints choosing and evaluating investments in basic facilities designing ways in which the private and public sectors interact to provide services. This book will be of great interest to students with basic calculus and some knowledge of economic theory who are engaged with transportation economics, planning and, or engineering, travel demand analysis, and many related fields. It will also be essential reading for researchers in any aspect of urban transportation. |
| optimal transport methods in economics: Demand Functions and the Slutsky Matrix. (PSME-7), Volume 7 Sydney N. Afriat, 2014-07-14 The utility idea has had a long history in economics, especially in the explanation of demand and in welfare economics. In a comprehensive survey and critique of the Slutsky theory and the pattern to which it belongs in the economic context, S. N. Afriat offers a resolution of questions central to its main idea, including sufficient conditions as well. Originally published in 1980. 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. |
| optimal transport methods in economics: Geographical Disadvantage Anthony Venables, Nuno Limão, 1999 What effect does distance have on costs for economies at different locations? Exports and imports of final and intermediate goods bear transport costs that increase with distance. Production and trade depend on factor endowments and factor intensities as well as on distance and the transport intensities of different goods--Cover. |
| optimal transport methods in economics: Microeconomics Samuel Bowles, 2004 Drawing upon recent advances in evolutionary game theory, contract theory, behavioural experiments and modeling of dynamic processes, Bowles develops a theory about the interraction between economic institutions and individual behaviour. |
| optimal transport methods in economics: Chicago Price Theory Sonia Jaffe, Robert Minton, Casey B. Mulligan, Kevin M. Murphy, 2019-09-10 Price theory is a powerful analytical toolkit for measuring, explaining, and predicting human behavior in the marketplace. This incisive textbook provides an essential introduction to the subject, offering a diverse array of practical methods that empower students to learn by doing. |
| optimal transport methods in economics: Principles of Transport Economics Emile Quinet, Roger William Vickerman, 2004 Transport continues to present considerable challenges for both policymakers and economists throughout the world. This book provides a rigorous analytical approach to transport economics and transport policy, showing how economic principles can be applied to problems and practical solutions derived. As well as providing detailed coverage on the conventional topics of demand, costs, market structure, externalities, investment appraisal and regulation, the book also examines the wider role of transport in the economy as a whole. In addition, the authors address the important link between transport and issues of location, urban and regional development, and economic growth. Throughout the book there are frequent references to policy issues at both the national and EU level, complemented by a comprehensive discussion on the different ways in which policy has evolved in various European countries. The concluding chapter draws together some of the problems encountered in moving from the theories and models developed in the book to the actual implementation of specific policy measures. The authors believe that only policies based on a thorough understanding of the economics of transport can help solve some of the pressing problems facing governments across Europe. This unique book addresses a wide range of issues and makes use of cutting-edge data to provide a set of universal tools to analyse and inform policy at all levels. It assumes only a basic knowledge of economics and will be essential reading for students at advanced undergraduate and postgraduate level following courses on transport economics, regional science, urban studies and geography. It will also prove a valuable source of reference for policymakers involved in the provision and regulation of transport and researchers interested in transport planning and policy. |
| optimal transport methods in economics: Economics and Operational Research M. H. Beilby, 2014-05-10 Economics and Operational Research explores the possible connections of the organization of human and material resources by concentrating on the interpretations of management decisions at various levels in the economy. This book discusses economics and mathematics as an analytical tool. Organized into 10 chapters, this book begins with an overview of how consumers manage their own budgets and how manufacturers select their production processes. This text then described generally how consumers and producers react to each other. Other chapters consider the problem of the transportation of goods through busy road networks and the efficiency attained through central planning. This book discusses as well the control of congestion that arises through decentralization and the construction of an overall planning model. The final chapter discusses the important aspects of national planning, wherein the collection of all consumers and producers makes up one large economic system. This book is a valuable resource for management and engineering personnel. |
| optimal transport methods in economics: Discrete Choice Methods with Simulation Kenneth Train, 2009-07-06 This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing. |
| optimal transport methods in economics: Social and Economic Networks Matthew O. Jackson, 2010-11-01 Networks of relationships help determine the careers that people choose, the jobs they obtain, the products they buy, and how they vote. The many aspects of our lives that are governed by social networks make it critical to understand how they impact behavior, which network structures are likely to emerge in a society, and why we organize ourselves as we do. In Social and Economic Networks, Matthew Jackson offers a comprehensive introduction to social and economic networks, drawing on the latest findings in economics, sociology, computer science, physics, and mathematics. He provides empirical background on networks and the regularities that they exhibit, and discusses random graph-based models and strategic models of network formation. He helps readers to understand behavior in networked societies, with a detailed analysis of learning and diffusion in networks, decision making by individuals who are influenced by their social neighbors, game theory and markets on networks, and a host of related subjects. Jackson also describes the varied statistical and modeling techniques used to analyze social networks. Each chapter includes exercises to aid students in their analysis of how networks function. This book is an indispensable resource for students and researchers in economics, mathematics, physics, sociology, and business. |
| optimal transport methods in economics: An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows Alessio Figalli, Federico Glaudo, 2023-05-15 This book provides a self-contained introduction to optimal transport, and it is intended as a starting point for any researcher who wants to enter into this beautiful subject. The presentation focuses on the essential topics of the theory: Kantorovich duality, existence and uniqueness of optimal transport maps, Wasserstein distances, the JKO scheme, Otto's calculus, and Wasserstein gradient flows. At the end, a presentation of some selected applications of optimal transport is given. Suitable for a course at the graduate level, the book also includes an appendix with a series of exercises along with their solutions. The second edition contains a number of additions, such as a new section on the Brunn–Minkowski inequality, new exercises, and various corrections throughout the text. |
| optimal transport methods in economics: The Business Cycle Howard J. Sherman, 2014-07-14 Are the recurring recessions of the capitalist world merely short-term adjustments to changing economic circumstances in a system that tends, in general, toward equilibrium? In this accessible study of the business cycle, Howard Sherman makes a powerful case that recessions and painful involuntary unemployment are endogenous to capitalism. Drawing especially on the work of Wesley Clair Mitchell, Karl Marx, and John M. Keynes, Sherman explains why the nature of the business cycle produces serious economic loss and misery during its contraction phase, just as it produces growth in its expansion phase. Originally published in 1991. 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. |
| optimal transport methods in economics: Applied Transport Economics Stuart Cole, 2005 Revised and updated to cover developments and thinking in transport economics, the book examines the application of economics techniques first, to commercial transport operations, second, to public policy issues and third, to the role of transport in its wider economic context. |
| optimal transport methods in economics: Recent Developments in Transport Economics Kenneth John Button, Kenneth Button, 2003 The past decade has seen both some new trends in the economics of transportation and the reinforcement of work from previous periods. Econometrics and innovative programming techniques have developed the work on production efficiency and interest in demand analysis has continued. Of increasing importance in recent years are the environmental implications of transportation as well as safety and security concerns. Economists are also addressing the problems of congestion with particular regard to new policy initiatives which tie transportation more closely to land-use patterns and telecommunications. In this volume Kenneth Button brings together some of the most significant previously published articles by leading academics in all these crucial areas. |
| optimal transport methods in economics: Microeconometrics A. Colin Cameron, Pravin K. Trivedi, 2005-05-09 This book provides the most comprehensive treatment to date of microeconometrics, the analysis of individual-level data on the economic behavior of individuals or firms using regression methods for cross section and panel data. The book is oriented to the practitioner. A basic understanding of the linear regression model with matrix algebra is assumed. The text can be used for a microeconometrics course, typically a second-year economics PhD course; for data-oriented applied microeconometrics field courses; and as a reference work for graduate students and applied researchers who wish to fill in gaps in their toolkit. Distinguishing features of the book include emphasis on nonlinear models and robust inference, simulation-based estimation, and problems of complex survey data. The book makes frequent use of numerical examples based on generated data to illustrate the key models and methods. More substantially, it systematically integrates into the text empirical illustrations based on seven large and exceptionally rich data sets. |
| optimal transport methods in economics: Lecture Notes in Microeconomic Theory Ariel Rubinstein, 2012-03-04 Ariel Rubinstein's well-known lecture notes on microeconomics—now fully revised and expanded This book presents Ariel Rubinstein's lecture notes for the first part of his well-known graduate course in microeconomics. Developed during the fifteen years that Rubinstein taught the course at Tel Aviv University, Princeton University, and New York University, these notes provide a critical assessment of models of rational economic agents, and are an invaluable supplement to any primary textbook in microeconomic theory. In this fully revised and expanded second edition, Rubinstein retains the striking originality and deep simplicity that characterize his famously engaging style of teaching. He presents these lecture notes with a precision that gets to the core of the material, and he places special emphasis on the interpretation of key concepts. Rubinstein brings this concise book thoroughly up to date, covering topics like modern choice theory and including dozens of original new problems. Written by one of the world's most respected and provocative economic theorists, this second edition of Lecture Notes in Microeconomic Theory is essential reading for students, teachers, and research economists. Fully revised, expanded, and updated Retains the engaging style and method of Rubinstein's well-known lectures Covers topics like modern choice theory Features numerous original new problems—including 21 new review problems Solutions manual (available only to teachers) can be found at: http://gametheory.tau.ac.il/microTheory/. |
| optimal transport methods in economics: Applications of Optimal Transport to Economics and Related Topics Vladik Kreinovich, Woraphon Yamaka, Supanika Leurcharusmee, 2024-11-09 Often, when a new successful data processing techniques appears in one of the application areas, it then proves to be useful in many other areas. This was the case of optimal transportation techniques: these techniques were first developed for transportation problems, but now they have been shown to be successful in many statistical applications, including applications to economics. These techniques are the main focus of this book, but this book also contain papers that use other techniques, ranging from more traditional statistical approaches to more recent ones such as stochastic frontier methods, multivariable quantiles, random forest, and deep learning. Applications include all aspects of economics, from production (including agricultural) to trade (including international) and finances, with relation to issues of crime (including computer crime and cyberbullying), demographics, economic freedom, environment, health, and tourism. We hope that this volume will: help practitioners to become better knowledgeable of the state-of-the-art econometric techniques, especially optimal transport techniques, and help researchers to further develop these important research directions. We want to thank all the authors for their contributions and all anonymous referees for their thorough analysis and helpful comments. The publication of this volume was partly supported by the Faculty of Economics of the Chiang Mai University, Thailand. Our thanks to the leadership and staff of the Chiang Mai University for providing crucial support. Our special thanks to Prof. Hung T. Nguyen for his valuable advice and constant support. |
| optimal transport methods in economics: The Construction of Optimal Stated Choice Experiments Deborah J. Street, Leonie Burgess, 2007-07-20 The most comprehensive and applied discussion of stated choice experiment constructions available The Construction of Optimal Stated Choice Experiments provides an accessible introduction to the construction methods needed to create the best possible designs for use in modeling decision-making. Many aspects of the design of a generic stated choice experiment are independent of its area of application, and until now there has been no single book describing these constructions. This book begins with a brief description of the various areas where stated choice experiments are applicable, including marketing and health economics, transportation, environmental resource economics, and public welfare analysis. The authors focus on recent research results on the construction of optimal and near-optimal choice experiments and conclude with guidelines and insight on how to properly implement these results. Features of the book include: Construction of generic stated choice experiments for the estimation of main effects only, as well as experiments for the estimation of main effects plus two-factor interactions Constructions for choice sets of any size and for attributes with any number of levels A discussion of designs that contain a none option or a common base option Practical techniques for the implementation of the constructions Class-tested material that presents theoretical discussion of optimal design Complete and extensive references to the mathematical and statistical literature for the constructions Exercise sets in most chapters, which reinforce the understanding of the presented material The Construction of Optimal Stated Choice Experiments serves as an invaluable reference guide for applied statisticians and practitioners in the areas of marketing, health economics, transport, and environmental evaluation. It is also ideal as a supplemental text for courses in the design of experiments, decision support systems, and choice models. A companion web site is available for readers to access web-based software that can be used to implement the constructions described in the book. |
| optimal transport methods in economics: Optimal Transportation and Applications Luigi Ambrosio, Luis A. Caffarelli, Yann Brenier, Giuseppe Buttazzo, Cédric Villani, 2003-01-01 Leading researchers in the field of Optimal Transportation, with different views and perspectives, contribute to this Summer School volume: Monge-Ampère and Monge-Kantorovich theory, shape optimization and mass transportation are linked, among others, to applications in fluid mechanics granular material physics and statistical mechanics, emphasizing the attractiveness of the subject from both a theoretical and applied point of view. The volume is designed to become a guide to researchers willing to enter into this challenging and useful theory. |
| optimal transport methods in economics: Mass Transportation Problems Svetlozar T. Rachev, Ludger Rüschendorf, 2006-05-17 The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis. |
| optimal transport methods in economics: Quantitative Methods in Economics and Finance Tomas Kliestik, Katarina Valaskova, Maria Kovacova, 2021-04-08 The purpose of the Special Issue “Quantitative Methods in Economics and Finance” of the journal Risks was to provide a collection of papers that reflect the latest research and problems of pricing complex derivates, simulation pricing, analysis of financial markets, and volatility of exchange rates in the international context. This book can be used as a reference for academicians and researchers who would like to discuss and introduce new developments in the field of quantitative methods in economics and finance and explore applications of quantitative methods in other business areas. |
| optimal transport methods in economics: Real Analysis with Economic Applications Efe A. Ok, 2011-09-05 There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory. |
| optimal transport methods in economics: Markov Processes Stewart N. Ethier, Thomas G. Kurtz, 2009-09-25 The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. [A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference. -American Scientist There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings. -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook. -Journal of Statistical Physics Markov Processes presents several different approaches to proving weak approximation theorems for Markov processes, emphasizing the interplay of methods of characterization and approximation. Martingale problems for general Markov processes are systematically developed for the first time in book form. Useful to the professional as a reference and suitable for the graduate student as a text, this volume features a table of the interdependencies among the theorems, an extensive bibliography, and end-of-chapter problems. |
| optimal transport methods in economics: Revealed Preference Theory Christopher P. Chambers, Federico Echenique, 2016-01-05 The theory of revealed preference has a long, distinguished tradition in economics but lacked a systematic presentation of the theory until now. This book deals with basic questions in economic theory and studies situations in which empirical observations are consistent or inconsistent with some of the best known economic theories. |
| optimal transport methods in economics: Lectures on Optimal Transport Luigi Ambrosio, Elia Brué, Daniele Semola, 2024-12-28 This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations. This is the second edition of the book, first published in 2018. It includes refinement of proofs, an updated bibliography and a more detailed discussion of minmax principles, with the aim of giving two fully self-contained proofs of Kantorovich duality. |
| optimal transport methods in economics: The Theory of Transportation Charles Horton Cooley, 1893 |
| optimal transport methods in economics: The Theory of Linear Economic Models David Gale, 1960 |
| optimal transport methods in economics: Operations Research in Transportation Systems A.S. Belenky, 1998-08-31 The scientific monograph of a survey kind presented to the reader's attention deals with fundamental ideas and basic schemes of optimization methods that can be effectively used for solving strategic planning and operations manage ment problems related, in particular, to transportation. This monograph is an English translation of a considerable part of the author's book with a similar title that was published in Russian in 1992. The material of the monograph embraces methods of linear and nonlinear programming; nonsmooth and nonconvex optimization; integer programming, solving problems on graphs, and solving problems with mixed variables; rout ing, scheduling, solving network flow problems, and solving the transportation problem; stochastic programming, multicriteria optimization, game theory, and optimization on fuzzy sets and under fuzzy goals; optimal control of systems described by ordinary differential equations, partial differential equations, gen eralized differential equations (differential inclusions), and functional equations with a variable that can assume only discrete values; and some other methods that are based on or adjoin to the listed ones. |
| optimal transport methods in economics: The Best Use of Economic Resources Leonid Vitalʹevich Kantorovich, 1965 |
| optimal transport methods in economics: Optimal Transport Statistics for Economics and Related Topics Nguyen Ngoc Thach, Vladik Kreinovich, Doan Thanh Ha, Nguyen Duc Trung, 2023-10-31 This volume emphasizes techniques of optimal transport statistics, but it also describes and uses other econometric techniques, ranging from more traditional statistical techniques to more innovative ones such as quantiles (in particular, multidimensional quantiles), maximum entropy approach, and machine learning. Applications range from general analysis of GDP growth, stock market, and consumer prices to analysis of specific sectors of economics (construction, credit and banking, energy, health, labor, textile, tourism, international trade) to specific issues affecting economy such as bankruptcy, effect of Covid-19 pandemic, effect of pollution, effect of gender, cryptocurrencies, and the existence of shadow economy. Papers presented in this volume also cover data processing techniques, with economic and financial application being the unifying theme. This volume shows what has been achieved, but even more important are remaining open problems. We hope that this volume will: ˆ inspire practitioners to learn how to apply state-of-the-art techniques, especially techniques of optimal transport statistics, to economic and financial problems, and ˆ inspire researchers to further improve the existing techniques and to come up with new techniques for studying economic and financial phenomena. |
| optimal transport methods in economics: Optimal Transport Cedric Villani, 2016-04-01 The field of optimal transport has made breathtaking forays into various other domains of mathematics. This book presents a broad overview of this area. PhD students or researchers can read the entire book without any prior knowledge of the field. |
| optimal transport methods in economics: Transport System Optimization and Pricing Jan Owen Jansson, 1984 |
| optimal transport methods in economics: Credible Asset Allocation, Optimal Transport Methods, and Related Topics Songsak Sriboonchitta, Vladik Kreinovich, Woraphon Yamaka, 2022-07-29 This book describes state-of-the-art economic ideas and how these ideas can be (and are) used to make economic decision (in particular, to optimally allocate assets) and to gauge the results of different economic decisions (in particular, by using optimal transport methods). Special emphasis is paid to machine learning techniques (including deep learning) and to different aspects of quantum econometrics—when quantum physics and quantum computing models are techniques are applied to study economic phenomena. Applications range from more traditional economic areas to more non-traditional topics such as economic aspects of tourism, cryptocurrencies, telecommunication infrastructure, and pandemic. This book helps student to learn new techniques, practitioners to become better knowledgeable of the state-of-the-art econometric techniques, and researchers to further develop these important research directions |
| optimal transport methods in economics: The Use of Entropy Maximising Models in the Theory of Trip Distribution, Mode Split and Route Split Alan Geoffrey Wilson, 1968 |
OPTIMAL Definition & Meaning - Merriam-Webster
The meaning of OPTIMAL is most desirable or satisfactory : optimum. How to use optimal in a sentence.
OPTIMAL | English meaning - Cambridge Dictionary
OPTIMAL definition: 1. best; most likely to bring success or advantage: 2. best; most likely to bring success or…. Learn more.
80 Synonyms & Antonyms for OPTIMAL | Thesaurus.com
Find 80 different ways to say OPTIMAL, along with antonyms, related words, and example sentences at Thesaurus.com.
optimal adjective - Definition, pictures, pronunciation and usage …
Definition of optimal adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
OPTIMAL definition and meaning | Collins English Dictionary
optimal in American English (ˈɑptəməl ) adjective most favorable or desirable; best; optimum
Optimal - definition of optimal by The Free Dictionary
1. the most favorable point, degree, or amount of something for obtaining a given result. 2. the most favorable conditions for the growth of an organism. 3. the best result obtainable under …
OPTIMAL Definition & Meaning | Dictionary.com
Optimal definition: optimum.. See examples of OPTIMAL used in a sentence.
optimal - WordReference.com Dictionary of English
the most favorable point, degree, or amount of something for obtaining a certain result. best: optimum conditions for growth. n. the best or most favorable point, degree, amount, etc., as of …
'Optimum' vs. 'Optimal' | Merriam-Webster
Optimal and optimum both mean “best or most effective,” as in “plants that grow tall under optimal conditions” and “for optimum results, let the paint dry overnight.” You may consider either …
optimal - Wiktionary, the free dictionary
Apr 7, 2025 · optimal (not comparable) The best, most favourable or desirable, especially under some restriction. Finding the optimal balance between features and price is a common …
OPTIMAL Definition & Meaning - Merriam-Webster
The meaning of OPTIMAL is most desirable or satisfactory : optimum. How to use optimal in a sentence.
OPTIMAL | English meaning - Cambridge Dictionary
OPTIMAL definition: 1. best; most likely to bring success or advantage: 2. best; most likely to bring success or…. Learn more.
80 Synonyms & Antonyms for OPTIMAL | Thesaurus.com
Find 80 different ways to say OPTIMAL, along with antonyms, related words, and example sentences at Thesaurus.com.
optimal adjective - Definition, pictures, pronunciation and usage …
Definition of optimal adjective in Oxford Advanced Learner's Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.
OPTIMAL definition and meaning | Collins English Dictionary
optimal in American English (ˈɑptəməl ) adjective most favorable or desirable; best; optimum
Optimal - definition of optimal by The Free Dictionary
1. the most favorable point, degree, or amount of something for obtaining a given result. 2. the most favorable conditions for the growth of an organism. 3. the best result obtainable under …
OPTIMAL Definition & Meaning | Dictionary.com
Optimal definition: optimum.. See examples of OPTIMAL used in a sentence.
optimal - WordReference.com Dictionary of English
the most favorable point, degree, or amount of something for obtaining a certain result. best: optimum conditions for growth. n. the best or most favorable point, degree, amount, etc., as of …
'Optimum' vs. 'Optimal' | Merriam-Webster
Optimal and optimum both mean “best or most effective,” as in “plants that grow tall under optimal conditions” and “for optimum results, let the paint dry overnight.” You may consider either …
optimal - Wiktionary, the free dictionary
Apr 7, 2025 · optimal (not comparable) The best, most favourable or desirable, especially under some restriction. Finding the optimal balance between features and price is a common …
