Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems
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Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems
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Author : Jingrui Sun
language : en
Publisher: Springer Nature
Release Date : 2020-06-29
Stochastic Linear Quadratic Optimal Control Theory Differential Games And Mean Field Problems written by Jingrui Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-29 with Mathematics categories.
This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
Stochastic Linear Quadratic Optimal Control Theory Open Loop And Closed Loop Solutions
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Author : Jingrui Sun
language : en
Publisher: Springer Nature
Release Date : 2020-06-29
Stochastic Linear Quadratic Optimal Control Theory Open Loop And Closed Loop Solutions written by Jingrui Sun and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-29 with Mathematics categories.
This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents the results in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, it precisely identifies, for the first time, the interconnections between three well-known, relevant issues – the existence of optimal controls, solvability of the optimality system, and solvability of the associated Riccati equation. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
Lectures On Bsdes Stochastic Control And Stochastic Differential Games With Financial Applications
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Author : Rene Carmona
language : en
Publisher: SIAM
Release Date : 2016-02-18
Lectures On Bsdes Stochastic Control And Stochastic Differential Games With Financial Applications written by Rene Carmona and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-18 with Mathematics categories.
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.
Mean Field Type Games For Engineers
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Author : JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.)
language : en
Publisher: CRC Press
Release Date : 2021-11-24
Mean Field Type Games For Engineers written by JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.) and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-24 with categories.
This book comprises an appropriate background to work and do research on mean-field-type control and game theory. It starts with studying the deterministic optimal control and differential linear-quadratic games, and progressively moves to analyzing mean-field-type control and game problems incorporating several stochastic processes.
Matrix Riccati Equations In Control And Systems Theory
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Author : Hisham Abou-Kandil
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Matrix Riccati Equations In Control And Systems Theory written by Hisham Abou-Kandil and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The authors present the theory of symmetric (Hermitian) matrix Riccati equations and contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control. The volume offers a complete treatment of generalized and coupled Riccati equations. It deals with differential, discrete-time, algebraic or periodic symmetric and non-symmetric equations, with special emphasis on those equations appearing in control and systems theory. Extensions to Riccati theory allow to tackle robust control problems in a unified approach. The book makes available classical and recent results to engineers and mathematicians alike. It is accessible to graduate students in mathematics, applied mathematics, control engineering, physics or economics. Researchers working in any of the fields where Riccati equations are used can find the main results with the proper mathematical background.
Mean Field Games And Mean Field Type Control Theory
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Author : Alain Bensoussan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-16
Mean Field Games And Mean Field Type Control Theory written by Alain Bensoussan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-16 with Science categories.
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.
Advances In Dynamic And Mean Field Games
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Author : Joseph Apaloo
language : en
Publisher: Birkhäuser
Release Date : 2018-01-03
Advances In Dynamic And Mean Field Games written by Joseph Apaloo and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-03 with Mathematics categories.
This contributed volume considers recent advances in dynamic games and their applications, based on presentations given at the 17th Symposium of the International Society of Dynamic Games, held July 12-15, 2016, in Urbino, Italy. Written by experts in their respective disciplines, these papers cover various aspects of dynamic game theory including mean-field games, stochastic and pursuit-evasion games, and computational methods for dynamic games. Topics covered include Pedestrian flow in crowded environments Models for climate change negotiations Nash Equilibria for dynamic games involving Volterra integral equations Differential games in healthcare markets Linear-quadratic Gaussian dynamic games Aircraft control in wind shear conditions Advances in Dynamic and Mean-Field Games presents state-of-the-art research in a wide spectrum of areas. As such, it serves as a testament to the continued vitality and growth of the field of dynamic games and their applications. It will be of interest to an interdisciplinary audience of researchers, practitioners, and graduate students.
Modeling Stochastic Control Optimization And Applications
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Author : George Yin
language : en
Publisher: Springer
Release Date : 2019-07-16
Modeling Stochastic Control Optimization And Applications written by George Yin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-16 with Mathematics categories.
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.
Probabilistic Theory Of Mean Field Games With Applications I
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Author : René Carmona
language : en
Publisher: Springer
Release Date : 2018-03-01
Probabilistic Theory Of Mean Field Games With Applications I written by René Carmona and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-01 with Mathematics categories.
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.
Lq Dynamic Optimization And Differential Games
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Author : Jacob Engwerda
language : en
Publisher: John Wiley & Sons
Release Date : 2005-06-17
Lq Dynamic Optimization And Differential Games written by Jacob Engwerda and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-17 with Business & Economics categories.
Game theory is the theory of social situations, and the majority of research into the topic focuses on how groups of people interact by developing formulas and algorithms to identify optimal strategies and to predict the outcome of interactions. Only fifty years old, it has already revolutionized economics and finance, and is spreading rapidly to a wide variety of fields. LQ Dynamic Optimization and Differential Games is an assessment of the state of the art in its field and the first modern book on linear-quadratic game theory, one of the most commonly used tools for modelling and analysing strategic decision making problems in economics and management. Linear quadratic dynamic models have a long tradition in economics, operations research and control engineering; and the author begins by describing the one-decision maker LQ dynamic optimization problem before introducing LQ differential games. Covers cooperative and non-cooperative scenarios, and treats the standard information structures (open-loop and feedback). Includes real-life economic examples to illustrate theoretical concepts and results. Presents problem formulations and sound mathematical problem analysis. Includes exercises and solutions, enabling use for self-study or as a course text. Supported by a website featuring solutions to exercises, further examples and computer code for numerical examples. LQ Dynamic Optimization and Differential Games offers a comprehensive introduction to the theory and practice of this extensively used class of economic models, and will appeal to applied mathematicians and econometricians as well as researchers and senior undergraduate/graduate students in economics, mathematics, engineering and management science.