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Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems

Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems
Author: Jingrui Sun
Publisher: Springer Nature
Total Pages: 138
Release: 2020-06-29
Genre: Mathematics
ISBN: 3030483061
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Download Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems Book in PDF, ePub and Kindle

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

Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions
Author: Jingrui Sun
Publisher: Springer Nature
Total Pages: 129
Release: 2020-06-29
Genre: Mathematics
ISBN: 3030209229
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Download Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions Book in PDF, ePub and Kindle

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.

Matrix Riccati Equations in Control and Systems Theory

Matrix Riccati Equations in Control and Systems Theory
Author: Hisham Abou-Kandil
Publisher: Birkhäuser
Total Pages: 584
Release: 2012-12-06
Genre: Science
ISBN: 3034880812
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Download Matrix Riccati Equations in Control and Systems Theory Book in PDF, ePub and Kindle

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.

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

Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications
Author: Rene Carmona
Publisher: SIAM
Total Pages: 265
Release: 2016-02-18
Genre: Mathematics
ISBN: 1611974240
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Download Lectures on BSDEs, Stochastic Control, and Stochastic Differential Games with Financial Applications Book in PDF, ePub and Kindle

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 Games and Mean Field Type Control Theory

Mean Field Games and Mean Field Type Control Theory
Author: Alain Bensoussan
Publisher: Springer Science & Business Media
Total Pages: 132
Release: 2013-10-16
Genre: Science
ISBN: 1461485088
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​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. ​

Modeling, Stochastic Control, Optimization, and Applications

Modeling, Stochastic Control, Optimization, and Applications
Author: George Yin
Publisher: Springer
Total Pages: 599
Release: 2019-07-16
Genre: Mathematics
ISBN: 3030254984
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Download Modeling, Stochastic Control, Optimization, and Applications Book in PDF, ePub and Kindle

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.

LQ Dynamic Optimization and Differential Games

LQ Dynamic Optimization and Differential Games
Author: Jacob Engwerda
Publisher: John Wiley & Sons
Total Pages: 514
Release: 2005-06-17
Genre: Business & Economics
ISBN: 9780470015247
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Download LQ Dynamic Optimization and Differential Games Book in PDF, ePub and Kindle

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.

Mean-Field-Type Games for Engineers

Mean-Field-Type Games for Engineers
Author: JULIAN. TEMBINE BARREIRO-GOMEZ (HAMIDOU.)
Publisher: CRC Press
Total Pages: 528
Release: 2021-11-24
Genre:
ISBN: 9780367566128
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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.

Stochastic Analysis and Applications

Stochastic Analysis and Applications
Author: Fred Espen Benth
Publisher: Springer Science & Business Media
Total Pages: 672
Release: 2007-04-24
Genre: Mathematics
ISBN: 3540708472
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Download Stochastic Analysis and Applications Book in PDF, ePub and Kindle

The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over presented the newest developments within the exciting and fast growing field of stochastic analysis. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion.

The Master Equation and the Convergence Problem in Mean Field Games

The Master Equation and the Convergence Problem in Mean Field Games
Author: Pierre Cardaliaguet
Publisher: Princeton University Press
Total Pages: 224
Release: 2019-08-13
Genre: Mathematics
ISBN: 0691190712
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Download The Master Equation and the Convergence Problem in Mean Field Games Book in PDF, ePub and Kindle

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.