|
In stock, usually dispatched within 24 hours
|
Rate this book...
Rating: 0.0/5 (0 votes cast)
|
|
|
|
|
Description of Forward-Backward Stochastic Differential Equations and Their Applications |
This book 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 book is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. The book can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
|
Contents of Forward-Backward Stochastic Differential Equations and Their Applications |
Preface
1. Introduction
1. Some Examples
1.1. A first glance
1.2. A stochastic optimal control problem
1.3. Stochastic differential utility
1.4. Option pricing and contingent claim valuation
2. Definitions and Notations
3. Some Nonsolvable FBSDEs
4. Well-posedness of BSDEs
5. Solvability of FBSDEs in Small Time Durations
6. Comparison Theorems for BSDEs and FBSDEs
2. Linear Equations
1. Compatible Conditions for Solvability
2. Some Reductions
3. Solvability of Linear FBSDEs
3.1. Necessary conditions
3.2. Criteria for solvability
4. A Riccati Type Equation
5. Some Extensions
3. Method of Optimal Control
1. Solvability and the Associated Optimal Control Problem
1.1. An optimal control problem
1.2. Approximate Solvability
2. Dynamic Programming Method and the HJB Equation
3. The Value Function
3.1. Continuity and semi-concavity
3.2. Approximation of the value function
4. A Class of Approximately Solvable FBSDEs
5. Construction of Approximate Adapted Solutions
4. Four Step Scheme
1. A Heuristic Derivation of Four Step Scheme
2. Non-Degenerate Case-Several Solvable Classes
2.1. A general case
2.2. The case when h has linear growth in z
2.3. The case when m = 1
3. Infinite Horizon Case
3.1. The nodal solution
3.2. Uniqueness of nodal solutions
3.3. The limit of finite duration problems
5. Linear, Degenerate Backward Stochastic Partial Differential Equations
1. Formulation of the Problem
2. Well-posedness of Linear BSPDEs
3. Uniqueness of Adapted Solutions
3.1. Uniqueness of adapted weak solutions
3.2. An Itô formula
4. Existence of Adapted Solutions
5. A Proof of the Fundamental Lemma
6. Comparison Theorems
6. The Method of Continuation
1. The Bridge
2. Method of Continuation
2.1. The solvability of FBSDEs linked by bridges
2.2. A priori estimate
3. Some Solvable FBSDEs
3.1. A trivial FBSDE
3.2. Decoupled FBSDEs
3.3. FBSDEs with monotonicity conditions
4. Properties of Bridges
5. Construction of Bridges
5.1. A general consideration
5.2. A one dimensional case
7. FBSDEs with Reflections
1. Forward SDEs with Reflections
2. Backward SDEs with Reflections
3. Reflected Forward-Backward SDEs
3.1 A priori estimates
3.2 Existence and uniqueness of the adapted solutions
3.3 A continuous dependence result
8. Applications of FBSDEs
1. An Integral Representation Formula
2. A Nonlinear Feynman-Kac Formula
3. Black's Consol Rate Conjecture
4. Hedging Options for a Large Investor
4.1. Hedging without constraint
4.2. Hedging with constraint
5. A Stochastic Black-Scholes Formula
5.1. Stochastic Black-Scholes formula
5.2. The convexity of the European contingent claims
5.3. The robustness of Black-Scholes formula
6. An American Game Option
9. Numerical Methods for FBSDEs
1. Formulation of the Problem
2. Numerical Approximation of the Quasilinear PDEs
2.1 A special case
2.1.1. Numerical scheme
2.1.2. Error analysis
2.1.3. The approximating solutions {u^(n)}^infinity_n=1
2.2 General case
2.2.1. Numerical scheme
2.2.2. Error analysis
3. Numerical Approximation of the Forward SDE
Comments and Remarks
References
Index 269
|
Bulk buying
| If you need bulk copies of Forward-Backward Stochastic Differential Equations and Their Applications, or are interested in opening a corporate account, please contact us. |
|
Shopping basket