Non-cooperative stochastic differential game theory of generalized Markov jump linear systems
Ning, B.
Non-cooperative stochastic differential game theory of generalized Markov jump linear systems Cheng-ke Zhang, Huai-nian Zhu, Hai-ying Zhou, Ning Bin - 1 recurso en línea (xv, 187 páginas) ilustraciones - Studies in systems, decision and control volume 67 2198-4182 .
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Incluye referencias bibliográficas
Preface; Contents; Representation of Symbol; Content Introduction; 1 Introduction; 1.1 Research and Development Status of Generalized Markov Jump Linear System Theory; 1.1.1 Basic Model of Generalized Markov Jump Linear Systems; 1.1.2 Research Status of Generalized Markov Jump Systems; 1.2 Differential Games for the Generalized Markov Jump Linear Systems; 1.3 Contents of This Book; References; 2 Deterministic and Stochastic Differential Games; 2.1 Dynamic Optimization Techniques; 2.1.1 Dynamic Programming; 2.1.2 Optimal Control; 2.1.3 Stochastic Control. 2.2 Differential Games and Their Solution Concepts2.2.1 Open-Loop Nash Equilibria; 2.2.2 Closed-Loop Nash Equilibria; 2.2.3 Feedback Nash Equilibria; 2.3 Stochastic Differential Games and Their Solutions; 2.3.1 The Model of Stochastic Differential Game; 2.3.2 The Solutions of Stochastic Differential Game; 3 Stochastic Differential Games of Continuous-Time Markov Jump Linear Systems; 3.1 Stochastic LQ Problem-Differential Game with One Player; 3.1.1 Finite-Time Horizon Case; 3.1.1.1 Problem Formulation; 3.1.1.2 Main Results; 3.1.2 Infinite-Time Horizon Case; 3.1.2.1 Problem Formulation. 3.1.2.2 Main Results3.2 Stochastic Nash Differential Games with Two Player; 3.2.1 Finite-Time Horizon Case; 3.2.1.1 Problem Formulation; 3.2.1.2 Main Results; 3.2.2 Infinite-Time Horizon Case; 3.2.2.1 Problem Formulation; 3.2.2.2 Main Results; 3.2.3 Two Person Zero-Sum Stochastic Differential Game; 3.2.3.1 Finite-Time Horizon Case; 3.2.3.2 Infinite-Time Horizon Case; 3.2.4 Numerical Example; 3.3 Stochastic Stackelberg Differential Game with Two Person; 3.3.1 Problem Formulation; 3.3.2 Main Results; 3.4 Summary; References. 4 Stochastic Differential Game of Discrete-Time Markov Jump Linear Systems4.1 Stochastic LQ Problem-Differential Game with One Person; 4.1.1 Finite-Time Horizon; 4.1.1.1 Problem Formulation; 4.1.1.2 Main Results; 4.1.2 Infinite-Time Horizon; 4.2 Stochastic Nash Differential Games with Two Person; 4.2.1 Finite-Time Horizon; 4.2.1.1 Problem Formulation; 4.2.1.2 Main Result; 4.2.2 Infinite-Time Horizon; 4.2.2.1 Problem Formulation; 4.2.2.2 Main Result; 4.2.3 Two Person Zero-Sum Stochastic Differential Games; 4.2.3.1 Finite Time Horizon; 4.2.3.2 Infinite-Time Horizon. 4.3 Stackelberg Differential Games with Two Person4.3.1 Finite-Time Horizon; 4.3.1.1 Problem Formulation; 4.3.1.2 Main Result; 4.3.2 Infinite-Time Horizon; 4.4 Summary; References; 5 Stochastic Differential Game of Stochastic Markov Jump Singular Systems; 5.1 Stochastic LQ Problems-Differential Games of One Player; 5.1.1 Preliminaries; 5.1.1.1 Stability of the Stochastic Markov Jump Singular Systems; 5.1.2 LQ Problem of Stochastic Markov Jump Singular Systems; 5.1.2.1 Finite-Time Horizon LQ Problem; 5.1.2.2 Infinite-Time Horizon LQ Problem; 5.2 Two Person Zero-Sum Differential Games.
This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.
331940587X 9783319405872
Teoría de juegos
QA272.5 / 2017 EB
Non-cooperative stochastic differential game theory of generalized Markov jump linear systems Cheng-ke Zhang, Huai-nian Zhu, Hai-ying Zhou, Ning Bin - 1 recurso en línea (xv, 187 páginas) ilustraciones - Studies in systems, decision and control volume 67 2198-4182 .
SpringerLink
Incluye referencias bibliográficas
Preface; Contents; Representation of Symbol; Content Introduction; 1 Introduction; 1.1 Research and Development Status of Generalized Markov Jump Linear System Theory; 1.1.1 Basic Model of Generalized Markov Jump Linear Systems; 1.1.2 Research Status of Generalized Markov Jump Systems; 1.2 Differential Games for the Generalized Markov Jump Linear Systems; 1.3 Contents of This Book; References; 2 Deterministic and Stochastic Differential Games; 2.1 Dynamic Optimization Techniques; 2.1.1 Dynamic Programming; 2.1.2 Optimal Control; 2.1.3 Stochastic Control. 2.2 Differential Games and Their Solution Concepts2.2.1 Open-Loop Nash Equilibria; 2.2.2 Closed-Loop Nash Equilibria; 2.2.3 Feedback Nash Equilibria; 2.3 Stochastic Differential Games and Their Solutions; 2.3.1 The Model of Stochastic Differential Game; 2.3.2 The Solutions of Stochastic Differential Game; 3 Stochastic Differential Games of Continuous-Time Markov Jump Linear Systems; 3.1 Stochastic LQ Problem-Differential Game with One Player; 3.1.1 Finite-Time Horizon Case; 3.1.1.1 Problem Formulation; 3.1.1.2 Main Results; 3.1.2 Infinite-Time Horizon Case; 3.1.2.1 Problem Formulation. 3.1.2.2 Main Results3.2 Stochastic Nash Differential Games with Two Player; 3.2.1 Finite-Time Horizon Case; 3.2.1.1 Problem Formulation; 3.2.1.2 Main Results; 3.2.2 Infinite-Time Horizon Case; 3.2.2.1 Problem Formulation; 3.2.2.2 Main Results; 3.2.3 Two Person Zero-Sum Stochastic Differential Game; 3.2.3.1 Finite-Time Horizon Case; 3.2.3.2 Infinite-Time Horizon Case; 3.2.4 Numerical Example; 3.3 Stochastic Stackelberg Differential Game with Two Person; 3.3.1 Problem Formulation; 3.3.2 Main Results; 3.4 Summary; References. 4 Stochastic Differential Game of Discrete-Time Markov Jump Linear Systems4.1 Stochastic LQ Problem-Differential Game with One Person; 4.1.1 Finite-Time Horizon; 4.1.1.1 Problem Formulation; 4.1.1.2 Main Results; 4.1.2 Infinite-Time Horizon; 4.2 Stochastic Nash Differential Games with Two Person; 4.2.1 Finite-Time Horizon; 4.2.1.1 Problem Formulation; 4.2.1.2 Main Result; 4.2.2 Infinite-Time Horizon; 4.2.2.1 Problem Formulation; 4.2.2.2 Main Result; 4.2.3 Two Person Zero-Sum Stochastic Differential Games; 4.2.3.1 Finite Time Horizon; 4.2.3.2 Infinite-Time Horizon. 4.3 Stackelberg Differential Games with Two Person4.3.1 Finite-Time Horizon; 4.3.1.1 Problem Formulation; 4.3.1.2 Main Result; 4.3.2 Infinite-Time Horizon; 4.4 Summary; References; 5 Stochastic Differential Game of Stochastic Markov Jump Singular Systems; 5.1 Stochastic LQ Problems-Differential Games of One Player; 5.1.1 Preliminaries; 5.1.1.1 Stability of the Stochastic Markov Jump Singular Systems; 5.1.2 LQ Problem of Stochastic Markov Jump Singular Systems; 5.1.2.1 Finite-Time Horizon LQ Problem; 5.1.2.2 Infinite-Time Horizon LQ Problem; 5.2 Two Person Zero-Sum Differential Games.
This book systematically studies the stochastic non-cooperative differential game theory of generalized linear Markov jump systems and its application in the field of finance and insurance. The book is an in-depth research book of the continuous time and discrete time linear quadratic stochastic differential game, in order to establish a relatively complete framework of dynamic non-cooperative differential game theory. It uses the method of dynamic programming principle and Riccati equation, and derives it into all kinds of existence conditions and calculating method of the equilibrium strategies of dynamic non-cooperative differential game. Based on the game theory method, this book studies the corresponding robust control problem, especially the existence condition and design method of the optimal robust control strategy. The book discusses the theoretical results and its applications in the risk control, option pricing, and the optimal investment problem in the field of finance and insurance, enriching the achievements of differential game research. This book can be used as a reference book for non-cooperative differential game study, for graduate students majored in economic management, science and engineering of institutions of higher learning.
331940587X 9783319405872
Teoría de juegos
QA272.5 / 2017 EB