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Author: Nguyen Ngoc Thach Publisher: Springer Nature ISBN: 3031357639 Category : Technology & Engineering Languages : en Pages : 712
Book Description
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.
Author: Nguyen Ngoc Thach Publisher: Springer Nature ISBN: 3031357639 Category : Technology & Engineering Languages : en Pages : 712
Book Description
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.
Author: Alfred Galichon Publisher: Princeton University Press ISBN: 0691183465 Category : Business & Economics Languages : en Pages : 184
Book Description
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
Author: Victor M. Panaretos Publisher: Springer Nature ISBN: 3030384381 Category : Mathematics Languages : en Pages : 157
Book Description
This open access book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation. Further to reviewing state-of-the-art aspects, it also provides an accessible introduction to the fundamentals of this current topic, as well as an overview that will serve as an invitation and catalyst for further research. Statistics in Wasserstein spaces represents an emerging topic in mathematical statistics, situated at the interface between functional data analysis (where the data are functions, thus lying in infinite dimensional Hilbert space) and non-Euclidean statistics (where the data satisfy nonlinear constraints, thus lying on non-Euclidean manifolds). The Wasserstein space provides the natural mathematical formalism to describe data collections that are best modeled as random measures on Euclidean space (e.g. images and point processes). Such random measures carry the infinite dimensional traits of functional data, but are intrinsically nonlinear due to positivity and integrability restrictions. Indeed, their dominating statistical variation arises through random deformations of an underlying template, a theme that is pursued in depth in this monograph.
Author: Songsak Sriboonchitta Publisher: Springer Nature ISBN: 3030972739 Category : Technology & Engineering Languages : en Pages : 762
Book Description
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
Author: Filippo Santambrogio Publisher: Birkhäuser ISBN: 3319208284 Category : Mathematics Languages : en Pages : 353
Book Description
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.
Author: Cédric Villani Publisher: American Mathematical Soc. ISBN: 1470467267 Category : Education Languages : en Pages : 370
Book Description
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.
Author: Cédric Villani Publisher: Springer Science & Business Media ISBN: 3540710507 Category : Mathematics Languages : en Pages : 970
Book Description
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.
Author: Luigi Ambrosio Publisher: Springer Nature ISBN: 3030721620 Category : Mathematics Languages : en Pages : 250
Book Description
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.
Author: Nguyen Ngoc Thach Publisher: Springer Nature ISBN: 3030986896 Category : Technology & Engineering Languages : en Pages : 865
Book Description
This book overviews latest ideas and developments in financial econometrics, with an emphasis on how to best use prior knowledge (e.g., Bayesian way) and how to best use successful data processing techniques from other application areas (e.g., from quantum physics). The book also covers applications to economy-related phenomena ranging from traditionally analyzed phenomena such as manufacturing, food industry, and taxes, to newer-to-analyze phenomena such as cryptocurrencies, influencer marketing, COVID-19 pandemic, financial fraud detection, corruption, and shadow economy. This book will inspire practitioners to learn how to apply state-of-the-art Bayesian, quantum, and related techniques to economic and financial problems and inspire researchers to further improve the existing techniques and come up with new techniques for studying economic and financial phenomena. The book will also be of interest to students interested in latest ideas and results.
Author: Marc Bernot Publisher: Springer Science & Business Media ISBN: 3540693149 Category : Business & Economics Languages : en Pages : 204
Book Description
The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.
Author: Nguyen Ngoc Thach
Author: Nguyen Ngoc Thach
Author: Alfred Galichon
Author: Victor M. Panaretos
Author: Songsak Sriboonchitta
Author: Filippo Santambrogio
Author: Cédric Villani
Author: Cédric Villani
Author: Luigi Ambrosio
Author: Nguyen Ngoc Thach
Author: Marc Bernot