Stochastic And Differential Games
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Stochastic And Differential Games
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Author : Martino Bardi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic And Differential Games written by Martino Bardi 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 2012-12-06 with Mathematics categories.
The theory of two-person, zero-sum differential games started at the be ginning of the 1960s with the works of R. Isaacs in the United States and L.S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P.P. Varaiya, E. Roxin, R.J. Elliott and N.J. Kalton, N.N. Krasovskii, and A.I. Subbotin (see their book Po sitional Differential Games, Nauka, 1974, and Springer, 1988), and L.D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M.G. Crandall and P.-L.
Stochastic Differential Games Theory And Applications
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Author : Kandethody M. Ramachandran
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-05
Stochastic Differential Games Theory And Applications written by Kandethody M. Ramachandran 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 2012-01-05 with Mathematics categories.
The subject theory is important in finance, economics, investment strategies, health sciences, environment, industrial engineering, etc.
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.
Stochastic And Differential Games
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Author : Martino Bardi
language : en
Publisher:
Release Date : 1999
Stochastic And Differential Games written by Martino Bardi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Differential games categories.
The theory of two-person, zero-sum differential games started at the be- ginning of the 1960s with the works of R. Isaacs in the United States and L. S. Pontryagin and his school in the former Soviet Union. Isaacs based his work on the Dynamic Programming method. He analyzed many special cases of the partial differential equation now called Hamilton- Jacobi-Isaacs-briefiy HJI-trying to solve them explicitly and synthe- sizing optimal feedbacks from the solution. He began a study of singular surfaces that was continued mainly by J. Breakwell and P. Bernhard and led to the explicit solution of some low-dimensional but highly nontriv- ial games; a recent survey of this theory can be found in the book by J. Lewin entitled Differential Games (Springer, 1994). Since the early stages of the theory, several authors worked on making the notion of value of a differential game precise and providing a rigorous derivation of the HJI equation, which does not have a classical solution in most cases; we mention here the works of W. Fleming, A. Friedman (see his book, Differential Games, Wiley, 1971), P. P. Varaiya, E. Roxin, R. J. Elliott and N. J. Kalton, N. N. Krasovskii, and A. I.Subbotin (see their book Po- sitional Differential Games, Nauka, 1974, and Springer, 1988), and L. D. Berkovitz. A major breakthrough was the introduction in the 1980s of two new notions of generalized solution for Hamilton-Jacobi equations, namely, viscosity solutions, by M. G. Crandall and P. -L.
Cooperative Stochastic Differential Games
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Author : David W.K. Yeung
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-11
Cooperative Stochastic Differential Games written by David W.K. Yeung 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 2006-05-11 with Business & Economics categories.
Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.
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.
Differential Games In Economics And Management Science
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Author : Engelbert Dockner
language : en
Publisher: Cambridge University Press
Release Date : 2000-11-16
Differential Games In Economics And Management Science written by Engelbert Dockner and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-16 with Business & Economics categories.
A comprehensive, self-contained survey of the theory and applications of differential games, one of the most commonly used tools for modelling and analysing economics and management problems which are characterised by both multiperiod and strategic decision making. Although no prior knowledge of game theory is required, a basic knowledge of linear algebra, ordinary differential equations, mathematical programming and probability theory is necessary. Part One presents the theory of differential games, starting with the basic concepts of game theory and going on to cover control theoretic models, Markovian equilibria with simultaneous play, differential games with hierarchical play, trigger strategy equilibria, differential games with special structures, and stochastic differential games. Part Two offers applications to capital accumulation games, industrial organization and oligopoly games, marketing, resources and environmental economics.
Advances In Dynamic Games
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Author : Michèle Breton
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-18
Advances In Dynamic Games written by Michèle Breton 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 2010-11-18 with Mathematics categories.
This book focuses on various aspects of dynamic game theory, presenting state-of-the-art research and serving as a testament to the vitality and growth of the field of dynamic games and their applications. The selected contributions, written by experts in their respective disciplines, are outgrowths of presentations originally given at the 13th International Symposium of Dynamic Games and Applications held in Wrocław. The book covers a variety of topics, ranging from theoretical developments in game theory and algorithmic methods to applications, examples, and analysis in fields as varied as environmental management, finance and economics, engineering, guidance and control, and social interaction.
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.
Multicriteria Decision Making And Differential Games
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Author : George Leitmann
language : en
Publisher: Springer
Release Date : 2013-12-19
Multicriteria Decision Making And Differential Games written by George Leitmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Science categories.
This volume is a collection of contributions to the subject of multicriteria decision making and differential games, all of which are based wholly or in part on papers that have appeared in the Journal of Optimization Theory and Applications. The authors take this opportunity to revise, update, or enlarge upon their earlier publications. The theory of multicriteria decision making and differential games is concerned with situations in which a single decision maker is faced with a multiplicity of usually incompatible criteria, performance indices or payoffs, or in which a number of decision makers, or players, must take into account criteria each of which depends on the decisions of all the decision makers. The first six chapters are devoted to situations involving a single decision maker, or a number of decision makers in complete collaboration and thus being in effect a single decision maker. Chapters I -IV treat various topics in the theory of domination structures and nondominated decisions. Chapter V presents a discussion of efficient, or Pareto-optimal, decisions. The approach to multicriteria decision making via preference relations is explored in Chapter VI. When there is more than one decision maker, cooperation, as well as noncooperation, is possible. Chapters VII and VIII deal with the topic of coalitions in a dynamic setting, while Chapters IX and X address the situation of two unequal decision makers, a leader and a follower.