Author | Yong, Jiongmin. author |
---|---|
Title | Stochastic Controls [electronic resource] : Hamiltonian Systems and HJB Equations / by Jiongmin Yong, Xun Yu Zhou |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1466-3 |
Descript | XXII, 439 p. online resource |
1. Basic Stochastic Calculus -- 1. Probability -- 2. Stochastic Processes -- 3. Stopping Times -- 4. Martingales -- 5. Itรดโs Integral -- 6. Stochastic Differential Equations -- 2. Stochastic Optimal Control Problems -- 1. Introduction -- 2. Deterministic Cases Revisited -- 3. Examples of Stochastic Control Problems -- 4. Formulations of Stochastic Optimal Control Problems -- 5. Existence of Optimal Controls -- 6. Reachable Sets of Stochastic Control Systems -- 7. Other Stochastic Control Models -- 8. Historical Remarks -- 3. Maximum Principle and Stochastic Hamiltonian Systems -- 1. Introduction -- 2. The Deterministic Case Revisited -- 3. Statement of the Stochastic Maximum Principle -- 4. A Proof of the Maximum Principle -- 5. Sufficient Conditions of Optimality -- 6. Problems with State Constraints -- 7. Historical Remarks -- 4. Dynamic Programming and HJB Equations -- 1. Introduction -- 2. The Deterministic Case Revisited -- 3. The Stochastic Principle of Optimality and the HJB Equation -- 4. Other Properties of the Value Function -- 5. Viscosity Solutions -- 6. Uniqueness of Viscosity Solutions -- 7. Historical Remarks -- 5. The Relationship Between the Maximum Principle and Dynamic Programming -- 1. Introduction -- 2. Classical Hamilton-Jacobi Theory -- 3. Relationship for Deterministic Systems -- 4. Relationship for Stochastic Systems -- 5. Stochastic Verification Theorems -- 6. Optimal Feedback Controls -- 7. Historical Remarks -- 6. Linear Quadratic Optimal Control Problems -- 1. Introduction -- 2. The Deterministic LQ Problems Revisited -- 3. Formulation of Stochastic LQ Problems -- 4. Finiteness and Solvability -- 5. A Necessary Condition and a Hamiltonian System -- 6. Stochastic Riccati Equations -- 7. Global Solvability of Stochastic Riccati Equations -- 8. A Mean-variance Portfolio Selection Problem -- 9. Historical Remarks -- 7. Backward Stochastic Differential Equations -- 1. Introduction -- 2. Linear Backward Stochastic Differential Equations -- 3. Nonlinear Backward Stochastic Differential Equations -- 4. FeynmanโKac-Type Formulae -- 5. ForwardโBackward Stochastic Differential Equations -- 6. Option Pricing Problems -- 7. Historical Remarks -- References