Probabilistic Theory Of Mean Field Games With Applications I

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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 : 50,6 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 : 45,6 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 : 55,8 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 : 53,6 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 : 48,9 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.

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 : 43,9 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.

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 : 41,9 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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PDE Models for Multi-Agent Phenomena

Pierre Cardaliaguet,Alessio Porretta,Francesco Salvarani
PDE Models for Multi Agent Phenomena Book PDF

Author : Pierre Cardaliaguet,Alessio Porretta,Francesco Salvarani
Publisher : Springer
Page : 218 pages
File Size : 41,8 Mb
Release : 2018-12-22
Category : Mathematics
ISBN : 9783030019471

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PDE Models for Multi-Agent Phenomena by Pierre Cardaliaguet,Alessio Porretta,Francesco Salvarani Pdf

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.

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 : 42,8 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. ​

Stochastic Analysis, Filtering, and Stochastic Optimization

George Yin,Thaleia Zariphopoulou
Stochastic Analysis Filtering and Stochastic Optimization Book PDF

Author : George Yin,Thaleia Zariphopoulou
Publisher : Springer Nature
Page : 466 pages
File Size : 47,7 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9783030985196

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Stochastic Analysis, Filtering, and Stochastic Optimization by George Yin,Thaleia Zariphopoulou Pdf

This volume is a collection of research works to honor the late Professor Mark H.A. Davis, whose pioneering work in the areas of Stochastic Processes, Filtering, and Stochastic Optimization spans more than five decades. Invited authors include his dissertation advisor, past collaborators, colleagues, mentees, and graduate students of Professor Davis, as well as scholars who have worked in the above areas. Their contributions may expand upon topics in piecewise deterministic processes, pathwise stochastic calculus, martingale methods in stochastic optimization, filtering, mean-field games, time-inconsistency, as well as impulse, singular, risk-sensitive and robust stochastic control.

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 : 49,6 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.

Artificial Intelligence in Insurance and Finance

Glenn Fung,Sou Cheng Choi,Luisa Fernanda Polania Cabrera,Victor Wu,Lawrence Kwan Ho Ma
Artificial Intelligence in Insurance and Finance Book PDF

Author : Glenn Fung,Sou Cheng Choi,Luisa Fernanda Polania Cabrera,Victor Wu,Lawrence Kwan Ho Ma
Publisher : Frontiers Media SA
Page : 135 pages
File Size : 40,8 Mb
Release : 2022-01-04
Category : Science
ISBN : 9782889718115

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Artificial Intelligence in Insurance and Finance by Glenn Fung,Sou Cheng Choi,Luisa Fernanda Polania Cabrera,Victor Wu,Lawrence Kwan Ho Ma Pdf

Luisa Fernanda Polania Cabrera is an Experienced Professional at Target Corporation (United States). Victor Wu is a Product Manager at GitLab Inc, San Francisco, United States. Sou-Cheng Choi is a Consulting Principle Data Scientist at Allstate Corporation. Lawrence Kwan Ho Ma is the Founder, Director and Chief Scientist of Valigo Limited and Founder, CEO and Chief Scientist of EMALI.IO Limited. Glenn M. Fung is the Chief Research Scientist at American Family Insurance.

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 : 53,9 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.

Recent Developments in Stochastic Methods and Applications

Albert N. Shiryaev,Konstantin E. Samouylov,Dmitry V. Kozyrev
Recent Developments in Stochastic Methods and Applications Book PDF

Author : Albert N. Shiryaev,Konstantin E. Samouylov,Dmitry V. Kozyrev
Publisher : Springer Nature
Page : 370 pages
File Size : 55,6 Mb
Release : 2021-08-02
Category : Mathematics
ISBN : 9783030832667

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Recent Developments in Stochastic Methods and Applications by Albert N. Shiryaev,Konstantin E. Samouylov,Dmitry V. Kozyrev Pdf

Highlighting the latest advances in stochastic analysis and its applications, this volume collects carefully selected and peer-reviewed papers from the 5th International Conference on Stochastic Methods (ICSM-5), held in Moscow, Russia, November 23-27, 2020. The contributions deal with diverse topics such as stochastic analysis, stochastic methods in computer science, analytical modeling, asymptotic methods and limit theorems, Markov processes, martingales, insurance and financial mathematics, queueing theory and stochastic networks, reliability theory, risk analysis, statistical methods and applications, machine learning and data analysis. The 29 articles in this volume are a representative sample of the 87 high-quality papers accepted and presented during the conference. The aim of the ICSM-5 conference is to promote the collaboration of researchers from Russia and all over the world, and to contribute to the development of the field of stochastic analysis and applications of stochastic models.

Non-Smooth and Complementarity-Based Distributed Parameter Systems

Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich
Non Smooth and Complementarity Based Distributed Parameter Systems Book PDF

Author : Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich
Publisher : Springer Nature
Page : 518 pages
File Size : 55,9 Mb
Release : 2022-02-18
Category : Mathematics
ISBN : 9783030793937

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Non-Smooth and Complementarity-Based Distributed Parameter Systems by Michael Hintermüller,Roland Herzog,Christian Kanzow,Michael Ulbrich,Stefan Ulbrich Pdf

Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.