Probabilistic Theory Of Mean Field Games With Applications I
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Probabilistic Theory Of Mean Field Games With Applications I
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01
Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume I of the book is entirely devoted to the theory of mean field games without a common noise. The first half of the volume provides a self-contained introduction to mean field games, starting from concrete illustrations of games with a finite number of players, and ending with ready-for-use solvability results. Readers are provided with the tools necessary for the solution of forward-backward stochastic differential equations of the McKean-Vlasov type at the core of the probabilistic approach. The second half of this volume focuses on the main principles of analysis on the Wasserstein space. It includes Lions' approach to the Wasserstein differential calculus, and the applications of its results to the analysis of stochastic mean field control problems. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Probabilistic Theory Of Mean Field Games With Applications Ii
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-08
Probabilistic Theory Of Mean Field Games With Applications Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-08 with Mathematics categories.
This two-volume book offers a comprehensive treatment of the probabilistic approach to mean field game models and their applications. The book is self-contained in nature and includes original material and applications with explicit examples throughout, including numerical solutions. Volume II tackles the analysis of mean field games in which the players are affected by a common source of noise. The first part of the volume introduces and studies the concepts of weak and strong equilibria, and establishes general solvability results. The second part is devoted to the study of the master equation, a partial differential equation satisfied by the value function of the game over the space of probability measures. Existence of viscosity and classical solutions are proven and used to study asymptotics of games with finitely many players. Together, both Volume I and Volume II will greatly benefit mathematical graduate students and researchers interested in mean field games. The authors provide a detailed road map through the book allowing different access points for different readers and building up the level of technical detail. The accessible approach and overview will allow interested researchers in the applied sciences to obtain a clear overview of the state of the art in mean field games.
Probabilistic Theory Of Mean Field Games With Applications I Ii
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-05-02
Probabilistic Theory Of Mean Field Games With Applications I Ii written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-02 with Mathematics categories.
This two-volume set offers an expansive overview of the probabilistic approach to game models and their applications. Considered the first comprehensive treatment of the theory of mean field games, much of the content is original and has been designed especially for the purpose of this book. Volume I of the set is entirely devoted to the theory of mean field games without a common noise, whereas Volume II analyzes mean field games in which the players are subject to games with a common noise. Together, both Volume I and Volume II will benefit researchers in the field as well as PhD and graduate students working on the subject due to the self-contained nature and applications with explicit examples throughout.
Mean Field Games
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Author : Yves Achdou
language : en
Publisher: Springer Nature
Release Date : 2021-01-19
Mean Field Games written by Yves Achdou and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Mathematics categories.
This volume provides an introduction to the theory of Mean Field Games, suggested by J.-M. Lasry and P.-L. Lions in 2006 as a mean-field model for Nash equilibria in the strategic interaction of a large number of agents. Besides giving an accessible presentation of the main features of mean-field game theory, the volume offers an overview of recent developments which explore several important directions: from partial differential equations to stochastic analysis, from the calculus of variations to modeling and aspects related to numerical methods. Arising from the CIME Summer School "Mean Field Games" held in Cetraro in 2019, this book collects together lecture notes prepared by Y. Achdou (with M. Laurière), P. Cardaliaguet, F. Delarue, A. Porretta and F. Santambrogio. These notes will be valuable for researchers and advanced graduate students who wish to approach this theory and explore its connections with several different fields in mathematics.
Machine Learning And Data Sciences For Financial Markets
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Author : Agostino Capponi
language : en
Publisher: Cambridge University Press
Release Date : 2023-06-01
Machine Learning And Data Sciences For Financial Markets written by Agostino Capponi 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 2023-06-01 with Mathematics categories.
Leveraging the research efforts of more than sixty experts in the area, this book reviews cutting-edge practices in machine learning for financial markets. Instead of seeing machine learning as a new field, the authors explore the connection between knowledge developed by quantitative finance over the past forty years and techniques generated by the current revolution driven by data sciences and artificial intelligence. The text is structured around three main areas: 'Interactions with investors and asset owners,' which covers robo-advisors and price formation; 'Risk intermediation,' which discusses derivative hedging, portfolio construction, and machine learning for dynamic optimization; and 'Connections with the real economy,' which explores nowcasting, alternative data, and ethics of algorithms. Accessible to a wide audience, this invaluable resource will allow practitioners to include machine learning driven techniques in their day-to-day quantitative practices, while students will build intuition and come to appreciate the technical tools and motivation for the theory.
Mean Field Games
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Author : François Delarue
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-14
Mean Field Games written by François Delarue and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
This volume is based on lectures delivered at the 2020 AMS Short Course “Mean Field Games: Agent Based Models to Nash Equilibria,” held January 13–14, 2020, in Denver, Colorado. Mean field game theory offers a robust methodology for studying large systems of interacting rational agents. It has been extraordinarily successful and has continued to develop since its inception. The six chapters that make up this volume provide an overview of the subject, from the foundations of the theory to applications in economics and finance, including computational aspects. The reader will find a pedagogical introduction to the main ingredients, from the forward-backward mean field game system to the master equation. Also included are two detailed chapters on the connection between finite games and mean field games, with a pedestrian description of the different methods available to solve the convergence problem. The volume concludes with two contributions on applications of mean field games and on existing numerical methods, with an opening to machine learning techniques.
Carleman Estimates In Mean Field Games
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Author : Michael V. Klibanov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-06-02
Carleman Estimates In Mean Field Games written by Michael V. Klibanov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-02 with Mathematics categories.
This book provides a comprehensive exploration of Mean Field Games (MFG) theory, a mathematical framework for modeling the collective behavior of rational agents in complex systems. MFG theory can govern a range of societal phenomena, including finance, sociology, machine learning, and economics. The focus is on the system of two coupled nonlinear parabolic partial differential equations (PDEs) that define the Mean Field Games System. The book covers key theoretical topics such as solution stability and uniqueness, with a particular emphasis on Carleman estimates, which are used to estimate solution errors based on noise in the input data. It also introduces the theory of Ill-Posed and Inverse Problems within MFG theory. Both theoretical and numerical aspects of forward and inverse problems are explored through Carleman estimates, offering a rigorous foundation for researchers and practitioners in applied mathematics and related fields. This book offers a rigorous approach to Carleman estimates, a key element of Mean Field Games theory, making it an essential resource for researchers, graduate students, and professionals looking to apply this powerful framework to complex, real-world systems.
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data
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Author : Chenchen Mou
language : en
Publisher: American Mathematical Society
Release Date : 2024-12-13
Wellposedness Of Second Order Master Equations For Mean Field Games With Nonsmooth Data written by Chenchen Mou and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-13 with Mathematics categories.
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A Probabilistic Approach To Classical Solutions Of The Master Equation For Large Population Equilibria
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Author : Jean-François Chassagneux
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-10
A Probabilistic Approach To Classical Solutions Of The Master Equation For Large Population Equilibria written by Jean-François Chassagneux and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-10 with Mathematics categories.
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S Minaire De Probabilit S Lii
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Author : Catherine Donati-Martin
language : en
Publisher: Springer Nature
Release Date : 2025-07-14
S Minaire De Probabilit S Lii written by Catherine Donati-Martin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-14 with Mathematics categories.
The last! This volume closes the Séminaire de Probabilités, a long and rich series that started in 1966 under the name Séminaire de Probabilités de Strasbourg. In addition to a tribute to our colleague Dominique Lépingle, who passed away in December 2021, it presents a selection of texts that reflect recent research streams in probability, including material on random matrices, rough analysis, Markov processes, and subordinators. The featured contributors are J. Bacckhoff, Q. Berger, L. Betencourt, E. Bodiot, A. Bonami, A. Cox, S. Dallaporta, M. Defosseux, F. Delarue, N. Demni, M. Février, A. Grass, B. Hass, M. Huesmann, L. I. Hernandez Ruíz, E. Kahn, L. Miclo, W. Salkeld, and M. Zani.