Probabilistic Theory Of Mean Field Games With Applications Ii

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Probabilistic Theory of Mean Field Games with Applications II

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications II Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 700 pages
File Size : 40,8 Mb
Release : 2018-03-08
Category : Mathematics
ISBN : 9783319564364

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Probabilistic Theory of Mean Field Games with Applications II by René Carmona,François Delarue Pdf

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

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications I Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 714 pages
File Size : 54,6 Mb
Release : 2018-03-01
Category : Mathematics
ISBN : 9783319589206

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Probabilistic Theory of Mean Field Games with Applications I by René Carmona,François Delarue Pdf

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 I-II

René Carmona,François Delarue
Probabilistic Theory of Mean Field Games with Applications I II Book PDF

Author : René Carmona,François Delarue
Publisher : Springer
Page : 0 pages
File Size : 52,9 Mb
Release : 2018-05-02
Category : Mathematics
ISBN : 3319598201

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Probabilistic Theory of Mean Field Games with Applications I-II by René Carmona,François Delarue Pdf

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

François Delarue
Mean Field Games Book PDF

Author : François Delarue
Publisher : American Mathematical Society
Page : 284 pages
File Size : 52,9 Mb
Release : 2021-12-14
Category : Mathematics
ISBN : 9781470455866

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Mean Field Games by François Delarue Pdf

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.

Machine Learning and Data Sciences for Financial Markets

Agostino Capponi,Charles-Albert Lehalle
Machine Learning and Data Sciences for Financial Markets Book PDF

Author : Agostino Capponi,Charles-Albert Lehalle
Publisher : Cambridge University Press
Page : 743 pages
File Size : 47,6 Mb
Release : 2023-04-30
Category : Mathematics
ISBN : 9781009034036

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Machine Learning and Data Sciences for Financial Markets by Agostino Capponi,Charles-Albert Lehalle Pdf

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.

A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria

Jean-François Chassagneux,Dan Crisan,François Delarue
A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria Book PDF

Author : Jean-François Chassagneux,Dan Crisan,François Delarue
Publisher : American Mathematical Society
Page : 136 pages
File Size : 41,8 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470453756

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A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria by Jean-François Chassagneux,Dan Crisan,François Delarue Pdf

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Mean Field Games

Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Mean Field Games Book PDF

Author : Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Publisher : Springer Nature
Page : 316 pages
File Size : 40,7 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9783030598372

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Mean Field Games by Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio Pdf

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.

Modeling, Stochastic Control, Optimization, and Applications

George Yin,Qing Zhang
Modeling Stochastic Control Optimization and Applications Book PDF

Author : George Yin,Qing Zhang
Publisher : Springer
Page : 599 pages
File Size : 50,6 Mb
Release : 2019-07-16
Category : Mathematics
ISBN : 9783030254988

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Modeling, Stochastic Control, Optimization, and Applications by George Yin,Qing Zhang Pdf

This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security

Vassili N. Kolokoltsov,Oleg A. Malafeyev
Many Agent Games in Socio economic Systems Corruption Inspection Coalition Building Network Growth Security Book PDF

Author : Vassili N. Kolokoltsov,Oleg A. Malafeyev
Publisher : Springer
Page : 196 pages
File Size : 51,9 Mb
Release : 2019-03-30
Category : Mathematics
ISBN : 9783030123710

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Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security by Vassili N. Kolokoltsov,Oleg A. Malafeyev Pdf

There has been an increase in attention toward systems involving large numbers of small players, giving rise to the theory of mean field games, mean field type control and nonlinear Markov games. Exhibiting various real world problems involving major and minor agents, this book presents a systematic continuous-space approximation approach for mean-field interacting agents models and mean-field games models. After describing Markov-chain methodology and a modeling of mean-field interacting systems, the text presents various structural conditions on the chain to yield respective socio-economic models, focusing on migration models via binary interactions. The specific applications are wide-ranging – including inspection and corruption, cyber-security, counterterrorism, coalition building and network growth, minority games, and investment policies and optimal allocation – making this book relevant to a wide audience of applied mathematicians interested in operations research, computer science, national security, economics, and finance.

Stochastic Stability of Differential Equations

Rafail Khasminskii
Stochastic Stability of Differential Equations Book PDF

Author : Rafail Khasminskii
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 48,9 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9783642232800

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Stochastic Stability of Differential Equations by Rafail Khasminskii Pdf

Since the publication of the first edition of the present volume in 1980, the stochastic stability of differential equations has become a very popular subject of research in mathematics and engineering. To date exact formulas for the Lyapunov exponent, the criteria for the moment and almost sure stability, and for the existence of stationary and periodic solutions of stochastic differential equations have been widely used in the literature. In this updated volume readers will find important new results on the moment Lyapunov exponent, stability index and some other fields, obtained after publication of the first edition, and a significantly expanded bibliography. This volume provides a solid foundation for students in graduate courses in mathematics and its applications. It is also useful for those researchers who would like to learn more about this subject, to start their research in this area or to study the properties of concrete mechanical systems subjected to random perturbations.

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications

Rene Carmona
Lectures on BSDEs Stochastic Control and Stochastic Differential Games with Financial Applications Book PDF

Author : Rene Carmona
Publisher : SIAM
Page : 265 pages
File Size : 55,5 Mb
Release : 2016-02-18
Category : Mathematics
ISBN : 9781611974249

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Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by Rene Carmona Pdf

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.

Handbook of Price Impact Modeling

Kevin T Webster
Handbook of Price Impact Modeling Book PDF

Author : Kevin T Webster
Publisher : CRC Press
Page : 485 pages
File Size : 49,5 Mb
Release : 2023-05-05
Category : Mathematics
ISBN : 9781000877663

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Handbook of Price Impact Modeling by Kevin T Webster Pdf

Handbook of Price Impact Modeling provides practitioners and students with a mathematical framework grounded in academic references to apply price impact models to quantitative trading and portfolio management. Automated trading is now the dominant form of trading across all frequencies. Furthermore, trading algorithm rise introduces new questions professionals must answer, for instance: How do stock prices react to a trading strategy? How to scale a portfolio considering its trading costs and liquidity risk? How to measure and improve trading algorithms while avoiding biases? Price impact models answer these novel questions at the forefront of quantitative finance. Hence, practitioners and students can use this Handbook as a comprehensive, modern view of systematic trading. For financial institutions, the Handbook’s framework aims to minimize the firm’s price impact, measure market liquidity risk, and provide a unified, succinct view of the firm’s trading activity to the C-suite via analytics and tactical research. The Handbook’s focus on applications and everyday skillsets makes it an ideal textbook for a master’s in finance class and students joining quantitative trading desks. Using price impact models, the reader learns how to: Build a market simulator to back test trading algorithms Implement closed-form strategies that optimize trading signals Measure liquidity risk and stress test portfolios for fire sales Analyze algorithm performance controlling for common trading biases Estimate price impact models using public trading tape Finally, the reader finds a primer on the database kdb+ and its programming language q, which are standard tools for analyzing high-frequency trading data at banks and hedge funds. Authored by a finance professional, this book is a valuable resource for quantitative researchers and traders.

Mean Field Games and Mean Field Type Control Theory

Alain Bensoussan,Jens Frehse,Phillip Yam
Mean Field Games and Mean Field Type Control Theory Book PDF

Author : Alain Bensoussan,Jens Frehse,Phillip Yam
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 46,5 Mb
Release : 2013-10-16
Category : Science
ISBN : 9781461485087

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Mean Field Games and Mean Field Type Control Theory by Alain Bensoussan,Jens Frehse,Phillip Yam Pdf

​Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem. ​

The Master Equation and the Convergence Problem in Mean Field Games

Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
The Master Equation and the Convergence Problem in Mean Field Games Book PDF

Author : Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
Publisher : Princeton University Press
Page : 224 pages
File Size : 45,6 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9780691190716

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The Master Equation and the Convergence Problem in Mean Field Games by Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions Pdf

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.

The Master Equation and the Convergence Problem in Mean Field Games

Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
The Master Equation and the Convergence Problem in Mean Field Games Book PDF

Author : Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions
Publisher : Princeton University Press
Page : 224 pages
File Size : 52,7 Mb
Release : 2019-08-13
Category : Mathematics
ISBN : 9780691193717

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The Master Equation and the Convergence Problem in Mean Field Games by Pierre Cardaliaguet,François Delarue,Jean-Michel Lasry,Pierre-Louis Lions Pdf

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.