Forward-Backward Stochastic Differential Equations and their Applications

1. Front Matter

   Pages i-xiii

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2. Introduction

   Pages 1-24

3. Linear Equations

   Pages 25-50

4. Method of Optimal Control

   Pages 51-79

5. Four Step Scheme

   Pages 80-102

6. Linear, Degenerate Backward Stochastic Partial Di erential Equations

   Pages 103-136

7. The Method of Continuation

   Pages 137-168

8. FBSDEs with Reflections

   Pages 169-192

9. Applications of FBSDEs

   Pages 193-234

10. Numerical Methods for FBSDEs

    Pages 235-256

11. Back Matter

    Pages 257-274

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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.

• Backward Stochastic Partial Differential Equations
• Black's Consol Rate Conjecture
• Boundary value problem
• Forward-Backward Stochastic Differential Equations
• Four Step Scheme
• Nodal Solutions
• partial differential equation
• quantitative finance

• Department of Mathematics, Purdue University, 47906-1395, West Lafayette, USA

  Jin Ma

• Department of Mathematics, Fudan University, Shanghai, People's Republic of China

  Jiongmin Yong

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