An Introduction to Optimal Control of FBSDE with Incomplete Information (SpringerBriefs in Mathematics)

This book focuses on maximum principle and verification theorem for incomplete information forward-backward stochastic differential equations (FBSDEs) and their applications in linear-quadratic optimal controls and mathematical finance. ​Lots of interesting phenomena arising from the area of mathematical finance can be described by FBSDEs. Optimal control problems of FBSDEs are theoretically important and practically relevant. A standard assumption in the literature is that the stochastic noises in the model are completely observed. However, this is rarely the case in real world situations. The optimal control problems under complete information are studied extensively. Nevertheless, very little is known about these problems when the information is not complete. The aim of this book is to fill this gap. This book is written in a style suitable for graduate students and researchers in mathematics and engineering with basic knowledge of stochastic process, optimal control and mathematical finance. Front Matter ....Pages i-xi Introduction (Guangchen Wang, Zhen Wu, Jie Xiong)....Pages 1-25 Filtering of BSDE and FBSDE (Guangchen Wang, Zhen Wu, Jie Xiong)....Pages 27-40 Optimal Control of Fully Coupled FBSDE with Partial Information (Guangchen Wang, Zhen Wu, Jie Xiong)....Pages 41-58 Optimal Control of FBSDE with Partially Observable Information (Guangchen Wang, Zhen Wu, Jie Xiong)....Pages 59-74 LQ Optimal Control Models with Incomplete Information (Guangchen Wang, Zhen Wu, Jie Xiong)....Pages 75-96 Back Matter ....Pages 97-116