Probabilistic Theory Of Mean Field Games With Applications I Ii

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Probabilistic Theory of Mean Field Games with Applications II

Author : René Carmona
Publisher : Springer
ISBN 13 : 3319564366
Total Pages : 712 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Probabilistic Theory of Mean Field Games with Applications II by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications II written by René Carmona and published by Springer. This book was released on 2018-03-08 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : René Carmona
Publisher : Springer
ISBN 13 : 3319589202
Total Pages : 728 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Probabilistic Theory of Mean Field Games with Applications I by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications I written by René Carmona and published by Springer. This book was released on 2018-03-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : René Carmona
Publisher : Springer
ISBN 13 : 9783319598208
Total Pages : 0 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis Probabilistic Theory of Mean Field Games with Applications I-II by : René Carmona

Download or read book Probabilistic Theory of Mean Field Games with Applications I-II written by René Carmona and published by Springer. This book was released on 2018-05-02 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Mean Field Type Control Theory

Author : Alain Bensoussan
Publisher : Springer Science & Business Media
ISBN 13 : 1461485088
Total Pages : 132 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Mean Field Games and Mean Field Type Control Theory by : Alain Bensoussan

Download or read book Mean Field Games and Mean Field Type Control Theory written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mean Field Games

Author : Yves Achdou
Publisher : Springer Nature
ISBN 13 : 3030598373
Total Pages : 316 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Mean Field Games by : Yves Achdou

Download or read book Mean Field Games written by Yves Achdou and published by Springer Nature. This book was released on 2021-01-19 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mean Field Games

Author : François Delarue
Publisher : American Mathematical Society
ISBN 13 : 1470455862
Total Pages : 284 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Mean Field Games by : François Delarue

Download or read book Mean Field Games written by François Delarue and published by American Mathematical Society. This book was released on 2021-12-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Agostino Capponi
Publisher : Cambridge University Press
ISBN 13 : 1009034030
Total Pages : 743 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Machine Learning and Data Sciences for Financial Markets by : Agostino Capponi

Download or read book Machine Learning and Data Sciences for Financial Markets written by Agostino Capponi and published by Cambridge University Press. This book was released on 2023-04-30 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Game Theory and Its Applications

Author : Akio Matsumoto
Publisher : Springer
ISBN 13 : 443154786X
Total Pages : 265 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Game Theory and Its Applications by : Akio Matsumoto

Download or read book Game Theory and Its Applications written by Akio Matsumoto and published by Springer. This book was released on 2015-09-08 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book integrates the fundamentals, methodology, and major application fields of noncooperative and cooperative games including conflict resolution. The topics addressed in the book are discrete and continuous games including games represented by finite trees; matrix and bimatrix games as well as oligopolies; cooperative solution concepts; games under uncertainty; dynamic games and conflict resolution. The methodology is illustrated by carefully chosen examples, applications and case studies which are selected from economics, social sciences, engineering, the military and homeland security. This book is highly recommended to readers who are interested in the in-depth and up-to-date integration of the theory and ever-expanding application areas of game theory.

The Master Equation and the Convergence Problem in Mean Field Games

Author : Pierre Cardaliaguet
Publisher : Princeton University Press
ISBN 13 : 0691190712
Total Pages : 224 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Master Equation and the Convergence Problem in Mean Field Games by : Pierre Cardaliaguet

Download or read book The Master Equation and the Convergence Problem in Mean Field Games written by Pierre Cardaliaguet and published by Princeton University Press. This book was released on 2019-08-13 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : Rene Carmona
Publisher : SIAM
ISBN 13 : 1611974240
Total Pages : 263 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications by : Rene Carmona

Download or read book Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications written by Rene Carmona and published by SIAM. This book was released on 2016-02-18 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : Jean-François Chassagneux
Publisher : American Mathematical Society
ISBN 13 : 1470453754
Total Pages : 136 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria by : Jean-François Chassagneux

Download or read book A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria written by Jean-François Chassagneux and published by American Mathematical Society. This book was released on 2022-11-10 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Vassili N. Kolokoltsov
Publisher : Springer
ISBN 13 : 3030123715
Total Pages : 196 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security by : Vassili N. Kolokoltsov

Download or read book Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security written by Vassili N. Kolokoltsov and published by Springer. This book was released on 2019-03-30 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrete Probability Models and Methods

Author : Pierre Brémaud
Publisher : Springer
ISBN 13 : 3319434764
Total Pages : 561 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Discrete Probability Models and Methods by : Pierre Brémaud

Download or read book Discrete Probability Models and Methods written by Pierre Brémaud and published by Springer. This book was released on 2017-01-31 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book.

Stochastic Control Theory

Author : Makiko Nisio
Publisher : Springer
ISBN 13 : 4431551239
Total Pages : 263 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Stochastic Control Theory by : Makiko Nisio

Download or read book Stochastic Control Theory written by Makiko Nisio and published by Springer. This book was released on 2014-11-27 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic introduction to the optimal stochastic control theory via the dynamic programming principle, which is a powerful tool to analyze control problems. First we consider completely observable control problems with finite horizons. Using a time discretization we construct a nonlinear semigroup related to the dynamic programming principle (DPP), whose generator provides the Hamilton–Jacobi–Bellman (HJB) equation, and we characterize the value function via the nonlinear semigroup, besides the viscosity solution theory. When we control not only the dynamics of a system but also the terminal time of its evolution, control-stopping problems arise. This problem is treated in the same frameworks, via the nonlinear semigroup. Its results are applicable to the American option price problem. Zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games are studied via a nonlinear semigroup related to DPP (the min-max principle, to be precise). Using semi-discretization arguments, we construct the nonlinear semigroups whose generators provide lower and upper Isaacs equations. Concerning partially observable control problems, we refer to stochastic parabolic equations driven by colored Wiener noises, in particular, the Zakai equation. The existence and uniqueness of solutions and regularities as well as Itô's formula are stated. A control problem for the Zakai equations has a nonlinear semigroup whose generator provides the HJB equation on a Banach space. The value function turns out to be a unique viscosity solution for the HJB equation under mild conditions. This edition provides a more generalized treatment of the topic than does the earlier book Lectures on Stochastic Control Theory (ISI Lecture Notes 9), where time-homogeneous cases are dealt with. Here, for finite time-horizon control problems, DPP was formulated as a one-parameter nonlinear semigroup, whose generator provides the HJB equation, by using a time-discretization method. The semigroup corresponds to the value function and is characterized as the envelope of Markovian transition semigroups of responses for constant control processes. Besides finite time-horizon controls, the book discusses control-stopping problems in the same frameworks.

The Master Equation and the Convergence Problem in Mean Field Games

Author : Pierre Cardaliaguet
Publisher : Princeton University Press
ISBN 13 : 0691193711
Total Pages : 224 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Master Equation and the Convergence Problem in Mean Field Games by : Pierre Cardaliaguet

High-Dimensional Probability

Author : Roman Vershynin
Publisher : Cambridge University Press
ISBN 13 : 1108415199
Total Pages : 299 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis High-Dimensional Probability by : Roman Vershynin

Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.