Non-cooperative Stochastic Differential Game Theory of Generalized Markov Jump Linear Systems - Zhang, Cheng-ke.; Zhou, Hai-ying.; Zhu, Huai-nian.; Bin, Ning.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2017)
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.
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.
Keywords: Control engineering; Operations research; Electronics; Control and Systems Theory; Operations Research and Decision Theory; Electronics and Microelectronics, Instrumentation