Probabilistic Theory Of Mean Field Games With Applications I PDF Download
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| Author | : René Carmona |
| Publisher | : Springer |
| Total Pages | : 728 |
| Release | : 2018-03-01 |
| Genre | : Mathematics |
| ISBN | : 3319589202 |
Download Probabilistic Theory of Mean Field Games with Applications I Book in PDF, ePub and Kindle
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.
| Author | : René Carmona |
| Publisher | : Springer |
| Total Pages | : 712 |
| Release | : 2018-03-08 |
| Genre | : Mathematics |
| ISBN | : 3319564366 |
Download Probabilistic Theory of Mean Field Games with Applications II Book in PDF, ePub and Kindle
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.
| Author | : René Carmona |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2018-05-02 |
| Genre | : Mathematics |
| ISBN | : 9783319598208 |
Download Probabilistic Theory of Mean Field Games with Applications I-II Book in PDF, ePub and Kindle
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.
| Author | : Yves Achdou |
| Publisher | : Springer Nature |
| Total Pages | : 316 |
| Release | : 2021-01-19 |
| Genre | : Mathematics |
| ISBN | : 3030598373 |
Download Mean Field Games Book in PDF, ePub and Kindle
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.
| Author | : François Delarue |
| Publisher | : American Mathematical Society |
| Total Pages | : 284 |
| Release | : 2021-12-14 |
| Genre | : Mathematics |
| ISBN | : 1470455862 |
Download Mean Field Games Book in PDF, ePub and Kindle
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.
| Author | : Agostino Capponi |
| Publisher | : Cambridge University Press |
| Total Pages | : 743 |
| Release | : 2023-04-30 |
| Genre | : Mathematics |
| ISBN | : 1009034030 |
Download Machine Learning and Data Sciences for Financial Markets Book in PDF, ePub and Kindle
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.
| Author | : Jean-François Chassagneux |
| Publisher | : American Mathematical Society |
| Total Pages | : 136 |
| Release | : 2022-11-10 |
| Genre | : Mathematics |
| ISBN | : 1470453754 |
Download A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria Book in PDF, ePub and Kindle
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| Author | : Pierre Cardaliaguet |
| Publisher | : Princeton University Press |
| Total Pages | : 224 |
| Release | : 2019-08-13 |
| Genre | : Mathematics |
| ISBN | : 0691193711 |
Download The Master Equation and the Convergence Problem in Mean Field Games Book in PDF, ePub and Kindle
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population. While it originated in economics, this theory now has applications in areas as diverse as mathematical finance, crowd phenomena, epidemiology, and cybersecurity. Because mean field games concern the interactions of infinitely many players in an optimal control framework, one expects them to appear as the limit for Nash equilibria of differential games with finitely many players as the number of players tends to infinity. This book rigorously establishes this convergence, which has been an open problem until now. The limit of the system associated with differential games with finitely many players is described by the so-called master equation, a nonlocal transport equation in the space of measures. After defining a suitable notion of differentiability in the space of measures, the authors provide a complete self-contained analysis of the master equation. Their analysis includes the case of common noise problems in which all the players are affected by a common Brownian motion. They then go on to explain how to use the master equation to prove the mean field limit. This groundbreaking book presents two important new results in mean field games that contribute to a unified theoretical framework for this exciting and fast-developing area of mathematics.
| Author | : Rene Carmona |
| Publisher | : SIAM |
| Total Pages | : 263 |
| Release | : 2016-02-18 |
| Genre | : Mathematics |
| ISBN | : 1611974240 |
Download Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications Book in PDF, ePub and Kindle
The goal of this textbook is to introduce students to the stochastic analysis tools that play an increasing role in the probabilistic approach to optimization problems, including stochastic control and stochastic differential games. While optimal control is taught in many graduate programs in applied mathematics and operations research, the author was intrigued by the lack of coverage of the theory of stochastic differential games. This is the first title in SIAM?s Financial Mathematics book series and is based on the author?s lecture notes. It will be helpful to students who are interested in stochastic differential equations (forward, backward, forward-backward); the probabilistic approach to stochastic control (dynamic programming and the stochastic maximum principle); and mean field games and control of McKean?Vlasov dynamics. The theory is illustrated by applications to models of systemic risk, macroeconomic growth, flocking/schooling, crowd behavior, and predatory trading, among others.
| Author | : Pierre Cardaliaguet |
| Publisher | : Springer |
| Total Pages | : 218 |
| Release | : 2018-12-22 |
| Genre | : Mathematics |
| ISBN | : 3030019470 |
Download PDE Models for Multi-Agent Phenomena Book in PDF, ePub and Kindle
This volume covers selected topics addressed and discussed during the workshop “PDE models for multi-agent phenomena,” which was held in Rome, Italy, from November 28th to December 2nd, 2016. The content mainly focuses on kinetic equations and mean field games, which provide a solid framework for the description of multi-agent phenomena. The book includes original contributions on the theoretical and numerical study of the MFG system: the uniqueness issue and finite difference methods for the MFG system, MFG with state constraints, and application of MFG to market competition. The book also presents new contributions on the analysis and numerical approximation of the Fokker-Planck-Kolmogorov equations, the isotropic Landau model, the dynamical approach to the quantization problem and the asymptotic methods for fully nonlinear elliptic equations. Chiefly intended for researchers interested in the mathematical modeling of collective phenomena, the book provides an essential overview of recent advances in the field and outlines future research directions.
