Biblioteca CRAI Dulce Chacón - Universidad Europea de Madrid

CRAI Library - Madrid
Your cart is empty.
My folder ( items) | My account
Image from Google Jackets

Non-cooperative stochastic differential game theory of generalized Markov jump linear systems / Cheng-ke Zhang, Huai-nian Zhu, Hai-ying Zhou, Ning Bin

By: Ning, B.(Bin), autor
Contributor(s): Zhang, Cheng-ke, autor | Zhou, Hai-ying, autor | Zhu, Huai-nian, autor
Material type: materialTypeLabelE-bookSeries: (Studies in systems, decision and control, 2198-4182 ; volume 67).Publisher: Switzerland : Springer, [2017]Copyright date: 2017Description: 1 recurso en línea (xv, 187 páginas) : ilustraciones.ISBN: 331940587X; 9783319405872.Subject: Teoría de juegosOnline resources: Acceso a este recurso digital (usuarios Universidad Europea de Madrid)Digital Resources
Contents:
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.
Abstract: 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.
Tags from this library: No tags from this library for this title. Log in to add tags.
Star ratings
    Average rating: 0.0 (0 votes)
Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
LIBRO-E NO PRÉSTAMO LIBRO-E NO PRÉSTAMO Madrid Digital Acceso Electrónico (UEM) Ciencias e Ingeniería QA272.5 2017 EB (Browse shelf(Opens below)) Acceso electrónico eBook.20022166
Total holds: 0

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.

Online resource; title from PDF title page (SpringerLink, viewed September 12, 2016).

There are no comments on this title.

to post a comment.
Share