Optimal Transport Methods In Economics
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Optimal Transport Methods In Economics
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Author : Alfred Galichon
language : en
Publisher: Princeton University Press
Release Date : 2018-08-14
Optimal Transport Methods In Economics written by Alfred Galichon and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-14 with Business & Economics categories.
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 For Applied Mathematicians
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Author : Filippo Santambrogio
language : en
Publisher: Birkhäuser
Release Date : 2015-10-17
Optimal Transport For Applied Mathematicians written by Filippo Santambrogio and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-17 with Mathematics categories.
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
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Author : Gabriel Peyre
language : en
Publisher: Foundations and Trends(r) in M
Release Date : 2019-02-12
Computational Optimal Transport written by Gabriel Peyre and has been published by Foundations and Trends(r) in M this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-12 with Computers categories.
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
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Author : André de Palma
language : en
Publisher: Edward Elgar Publishing
Release Date : 2011-01-01
A Handbook Of Transport Economics written by André de Palma and has been published by Edward Elgar Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Transportation categories.
'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.
Topics In Optimal Transportation
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Author : Cédric Villani
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Topics In Optimal Transportation written by Cédric Villani and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Monge-Ampère equations categories.
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.
The Economics Of Urban Transportation
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Author : Kenneth A. Small
language : en
Publisher: Routledge
Release Date : 2007-10-18
The Economics Of Urban Transportation written by Kenneth A. Small and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-18 with Business & Economics categories.
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.
An Invitation To Optimal Transport Wasserstein Distances And Gradient Flows
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Author : Alessio Figalli
language : en
Publisher: European Mathematical Society
Release Date : 2023-05-15
An Invitation To Optimal Transport Wasserstein Distances And Gradient Flows written by Alessio Figalli and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
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.
Applications Of Optimal Transport To Economics And Related Topics
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Author : Vladik Kreinovich
language : en
Publisher: Springer Nature
Release Date : 2024-11-09
Applications Of Optimal Transport To Economics And Related Topics written by Vladik Kreinovich and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-09 with Technology & Engineering categories.
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.
Analysis On Polish Spaces And An Introduction To Optimal Transportation
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Author : D. J. H. Garling
language : en
Publisher: Cambridge University Press
Release Date : 2018
Analysis On Polish Spaces And An Introduction To Optimal Transportation written by D. J. H. Garling and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.
Detailed account of analysis on Polish spaces with a straightforward introduction to optimal transportation.