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Preface
Chapter 1 Preliminaries
1£®1 Probability and Random Variables
1£®1£®1 Probability Spaces
1£®1£®2 Convergence of Probabilities
1£®2 Stochastic Processes
1£®2£®1 Continuous Time Martingales
1£®2£®2 Stochastic Integration
1£®3 The Basic Theory of FBSDEs
1£®3£®1 A Black-Scholes Formula in Finance
1£®3£®2 Formulations of Stochastic Optimal Control Problems
Bibliography

Chapter 2 Singular Optimal Controls of Stochastic Recursive Systems and H-J-B Inequality
2£®1 Introduction
2£®2 Formulation of the Problem
2£®3 Dynamic Programming Principle
2£®4 Example
2£®5 Appendix
Bibliography

Chapter 3 Stochastic Verification Theorem of Forward-Backward Controlled Systems for Viscosity Solutions
3£®1 Introduction
3£®2 Super-differentials£¬ Sub-differentials£¬ and Viscosity Solutions
3£®3 Stochastic Verification Theorem for Forward-Backward Controlled Systems£®£®£®
3£®4 Optimal Feedback Controls
Bibliography

Chapter 4 Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications
4£®1 Introduction
4£®2 Statement of the Problem
4£®3 Variational Equations and Variational Inequalities
4£®4 The Maximum Principle in Global Form
4£®5 Applications to Optimal Control Problems of Stochastic PDEs
4£®6 Linear Quadratic Nonzero Sum Doubly Stochastic Differential Games
Bibliography

Chapter 5 Stochastic Maximum Principle for Near-Optimal Control of FBSDEs
5£®1 Introduction
5£®2 Formulation of the Optimal Control Problem and Basic Assumptions
5£®3 Main Results
5£®3£®1 Necessary Condition of Near-Optimality
5£®3£®2 Sufficient Condition of Near-Optimality
5£®4 Examples
5£®5 Concluding Remarks
5£®6 Appendix
Bibliography

Chapter 6 Near Optimal Control of Stochastic Recursive Systems via Viscosity Solution
6£®1 Introduction
6£®2 Preliminaries and Notations
6£®3 Main Results
6£®4 Conclusions
Bibliography

Chapter 7 Asymptotic Properties of Coupled Forward-Backward Stochastic Differential Equations
7£®1 Introduction
7£®2 Preliminaries
7£®3 Regularity of the solution of FBSDEs
7£®4 Main Results
7£®4£®1 Convergence of distributions
7£®4£®2 Large deviation principle
Bibliography