Forward-Backward Stochastic Differential Equations and their Applications

Jin Ma, Jiongmin Yong (auth.)3540659609, 9783540659600

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the “Four Step Scheme”, and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

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Table of contents :
Front Matter….Pages i-xiii
Introduction….Pages 1-24
Linear Equations….Pages 25-50
Method of Optimal Control….Pages 51-79
Four Step Scheme….Pages 80-102
Linear, Degenerate Backward Stochastic Partial Di erential Equations….Pages 103-136
The Method of Continuation….Pages 137-168
FBSDEs with Reflections….Pages 169-192
Applications of FBSDEs….Pages 193-234
Numerical Methods for FBSDEs….Pages 235-256
Back Matter….Pages 257-274