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Author : Jean-François Chassagneux,Dan Crisan,François Delarue
Publisher : American Mathematical Society
Page : 136 pages
File Size : 54,7 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470453756
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Author : François Delarue
Publisher : American Mathematical Society
Page : 284 pages
File Size : 54,8 Mb
Release : 2021-12-14
Category : Mathematics
ISBN : 9781470455866
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 : André Gil Henriques,David Penneys,James E. Tener
Publisher : American Mathematical Society
Page : 100 pages
File Size : 48,5 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470455408
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Author : Giorgio Fabbri,Fausto Gozzi,Andrzej Święch
Publisher : Springer
Page : 916 pages
File Size : 47,8 Mb
Release : 2017-06-22
Category : Mathematics
ISBN : 9783319530673
Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite dimension. Readers from other fields who want to learn the basic theory will also find it useful. The prerequisites are: standard functional analysis, the theory of semigroups of operators and its use in the study of PDEs, some knowledge of the dynamic programming approach to stochastic optimal control problems in finite dimension, and the basics of stochastic analysis and stochastic equations in infinite-dimensional spaces.
Author : Jean-François Chassagneux,Hinesh Chotai,Mirabelle Muûls
Publisher : Springer
Page : 104 pages
File Size : 46,5 Mb
Release : 2017-10-05
Category : Mathematics
ISBN : 9783319631158
In Mathematical Finance, the authors consider a mathematical model for the pricing of emissions permits. The model has particular applicability to the European Union Emissions Trading System (EU ETS) but could also be used to consider the modeling of other cap-and-trade schemes. As a response to the risk of Climate Change, carbon markets are currently being implemented in regions worldwide and already represent more than $30 billion. However, scientific, and particularly mathematical, studies of these carbon markets are needed in order to expose their advantages and shortcomings, as well as allow their most efficient implementation. This Brief reviews mathematical properties such as the existence and uniqueness of solutions for the pricing problem, stability of solutions and their behavior. These fit into the theory of fully coupled forward-backward stochastic differential equations (FBSDEs) with irregular coefficients. The authors present a numerical algorithm to compute the solution to these non-standard FBSDEs. They also carry out a case study of the UK energy market. This involves estimating the parameters to be used in the model using historical data and then solving a pricing problem using the aforementioned numerical algorithm. The Brief is of interest to researchers in stochastic processes and their applications, and environmental and energy economics. Most sections are also accessible to practitioners in the energy sector and climate change policy-makers.
Author : Yves Achdou,Pierre Cardaliaguet,François Delarue,Alessio Porretta,Filippo Santambrogio
Publisher : Springer Nature
Page : 316 pages
File Size : 40,5 Mb
Release : 2021-01-19
Category : Mathematics
ISBN : 9783030598372
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 : Henri Berestycki,Grégoire Nadin
Publisher : American Mathematical Society
Page : 282 pages
File Size : 53,8 Mb
Release : 2022-11-10
Category : Mathematics
ISBN : 9781470454296
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Author : Jang Soo Kim,Kyu-Hwan Lee,Se-jin Oh
Publisher : American Mathematical Society
Page : 100 pages
File Size : 40,8 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470459949
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Author : Tarek M. Elgindi,In-Jee Jeong
Publisher : American Mathematical Society
Page : 102 pages
File Size : 42,7 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470456825
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Author : Fan Gao,Freydoon Shahidi,Dani Szpruch
Publisher : American Mathematical Society
Page : 148 pages
File Size : 45,5 Mb
Release : 2023-03-10
Category : Mathematics
ISBN : 9781470456818
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Author : David A. Croydon,Tsuyoshi Kato,Makiko Sasada,Satoshi Tsujimoto
Publisher : American Mathematical Society
Page : 114 pages
File Size : 55,5 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470456337
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Author : Akinari Hoshi,Ming-chang Kang,Aiichi Yamasaki
Publisher : American Mathematical Society
Page : 150 pages
File Size : 54,7 Mb
Release : 2023-03-09
Category : Mathematics
ISBN : 9781470460228
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Author : François Ledrappier,Lin Shu
Publisher : American Mathematical Society
Page : 164 pages
File Size : 42,6 Mb
Release : 2023-01-18
Category : Mathematics
ISBN : 9781470455422
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Author : Sebastian Casalaina-Martin,Samuel Grushevsky,Klaus Hulek,Radu Laza
Publisher : American Mathematical Society
Page : 112 pages
File Size : 51,9 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781470460204
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Author : Guozhen Lu,Lu Zhang,Jiawei Shen
Publisher : American Mathematical Society
Page : 100 pages
File Size : 46,9 Mb
Release : 2023-01-18
Category : Mathematics
ISBN : 9781470455378
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