正倒向随机微分方程最优控制

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