Optimal Transport Methods in Economics
Optimal Transport Methods in Economics

Author: Alfred Galichon

Publisher: Princeton University Press

Published: 2018-08-14

Total Pages: 184

ISBN-13: 0691183465

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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
Optimal Transport

Author: Cédric Villani

Publisher: Springer Science & Business Media

Published: 2008-10-26

Total Pages: 970

ISBN-13: 3540710507

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At the close of the 1980s, the independent contributions of Yann Brenier, Mike Cullen and John Mather launched a revolution in the venerable field of optimal transport founded by G. Monge in the 18th century, which has made breathtaking forays into various other domains of mathematics ever since. The author presents a broad overview of this area, supplying complete and self-contained proofs of all the fundamental results of the theory of optimal transport at the appropriate level of generality. Thus, the book encompasses the broad spectrum ranging from basic theory to the most recent research results. PhD students or researchers can read the entire book without any prior knowledge of the field. A comprehensive bibliography with notes that extensively discuss the existing literature underlines the book’s value as a most welcome reference text on this subject.

Topics in Optimal Transportation
Topics in Optimal Transportation

Author: Cédric Villani

Publisher: American Mathematical Soc.

Published: 2021-08-25

Total Pages: 370

ISBN-13: 1470467267

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This is the first comprehensive introduction to the theory of mass transportation with its many—and sometimes unexpected—applications. In a novel approach to the subject, the book both surveys the topic and includes a chapter of problems, making it a particularly useful graduate textbook. 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 intended for graduate students and researchers, covering both theory and applications. Readers are only assumed to be familiar with the basics of measure theory and functional analysis.

Optimal Transport for Applied Mathematicians
Optimal Transport for Applied Mathematicians

Author: Filippo Santambrogio

Publisher: Birkhäuser

Published: 2015-10-17

Total Pages: 376

ISBN-13: 3319208284

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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.

Computational Optimal Transport
Computational Optimal Transport

Author: Gabriel Peyre

Publisher: Foundations and Trends(r) in M

Published: 2019-02-12

Total Pages: 272

ISBN-13: 9781680835502

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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.

A Handbook of Transport Economics
A Handbook of Transport Economics

Author: André de Palma

Publisher: Edward Elgar Publishing

Published: 2011-01-01

Total Pages: 929

ISBN-13: 0857930877

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'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.

An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows
An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows

Author: Alessio Figalli

Publisher: European Mathematical Society

Published: 2023-05-15

Total Pages: 0

ISBN-13: 3985470502

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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.

Economics and Operational Research
Economics and Operational Research

Author: M. H. Beilby

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 185

ISBN-13: 1483268748

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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.

The Economics of Urban Transportation
The Economics of Urban Transportation

Author: Kenneth A. Small

Publisher: Taylor & Francis

Published: 2024-06-10

Total Pages: 433

ISBN-13: 135165344X

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This new edition of the seminal textbook The Economics of Urban Transportation incorporates the latest research affecting the design, implementation, pricing, and control of transport systems in towns and cities. The book offers an economic framework for understanding the societal impacts and policy implications of many factors including congestion, traffic safety, climate change, air quality, COVID-19, and newly important developments such as ride-hailing services, electric vehicles, and autonomous vehicles. Rigorous in approach and making use of real-world data and econometric techniques, the third edition features a new chapter on the special challenges of managing the energy that powers transportation systems. It provides fully updated coverage of well-known topics and a rigorous treatment of new ones. All of the basic topics needed to apply economics to urban transportation are included: Forecasting demand for transportation services under various conditions Measuring costs, including those incurred by users and incorporating two new tools to describe congestion in dense urban areas Setting prices under practical constraints Evaluating infrastructure investments Understanding how private and public sectors interact to provide services Written by three of the field’s leading researchers, The Economics of Urban Transportation is essential reading for students, researchers, and practicing professionals in transportation economics, planning, engineering, or related disciplines. With a focus on workable models that can be adapted to future needs, it provides tools for a rapidly changing world.

Dynamic Optimization, Second Edition
Dynamic Optimization, Second Edition

Author: Morton I. Kamien

Publisher: Courier Corporation

Published: 2013-04-17

Total Pages: 402

ISBN-13: 0486310280

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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.