Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems

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.

Investigating systematically both the theory and methods, and their applications Introduces the developments and research status of the theory for singular Markov jump linear systems, deterministic and stochastic differential games, non-cooperative stochastic differential game theory of discrete-time, continuous-time and singular Markov jump linear systems as well as an approach to its robust control Presents applications of the game theoretic approach to finance and insurance under Markovian regime-switching models Serves as learning reference materials for researchers in applied and management science, engineering, operations research, systems science, and applied mathematics Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- Deterministic and Stochastic Differential Games.- Stochastic Differential Games of Continuous-time Markov Jump Linear Systems.- Stochastic Differential Game of Discrete-time Markov Jump Linear System.- Stochastic Differential Game of Stochastic Markov Jump Singular Systems.- Game Theory Approach to Stochastic H2/H Control of Markov Jump Linear Singular Systems.- Applications of Stochastic Differential Game Theory for Linear Markov Jump Systems to Finance and Insurance.