随机控制 英文2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

随机控制 英文PDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Chapter 1．Basic Stochastic Calculus1

1．Probability1

1.1．Probability spaces1

1.2．Random variables4

1.3．Conditional expectation8

1.4．Convergence of probabilities13

2．Stochastic Processes15

2.1．General considerations15

2.2．Brownian motions21

3．Stopping Times23

4．Martingales27

5．It？'s Integral30

5.1．Nondifferentiability of Brownian motion30

5.2．Definition of It？'s integral and basic properties32

5.3．It？'s formula36

5.4．Martingale representation theorems38

6．Stochastic Differential Equations40

6.1．Strong solutions41

6.2．Weak solutions44

6.3．Linear SDEs47

6.4．Other types of SDEs48

Chapter 2．Stochastic Optimal Control Problems51

1．Introduction51

2．Deterministic Cases Revisited52

3．Examples of Stochastic Control Problems55

3.1．Production planning55

3.2．Investment vs.consumption56

3.3．Reinsurance and dividend management58

3.4．Technology diffusion59

3.5．Queueing systems in heavy traffic60

4．Formulations of Stochastic Optimal Control Problems62

4.1．Strong formulation62

4.2．Weak formulation64

5．Existence of Optimal Controls65

5.1．A deterministic result65

5.2．Existence under strong formulation67

5.3．Existence under weak formulation69

6．Reachable Sets of Stochastic Control Systems75

6.1．Nonconvexity of the reachable sets76

6.2．Noncloseness of the reachable sets81

7．Other Stochastic Control Models85

7.1．Random duration85

7.2．Optimal stopping86

7.3．Singular and impulse controls86

7.4．Risk-sensitive controls88

7.5．Ergodic controls89

7.6．Partially observable systems89

8．Historical Remarks92

Chapter 3．Maximum Principle and Stochastic Hamiltonian Systems101

1．Introduction101

2．The Deterministic Case Revisited102

3．Statement of the Stochastic Maximum Principle113

3.1．Adjoint equations115

3.2．The maximum principle and stochastic Hamiltonian systems117

3.3．A worked-out example120

4．A Proof of the Maximum Principle123

4.1．A moment estimate124

4.2．Taylor expansions126

4.3．Duality analysis and completion of the proof134

5．Sufficient Conditions of Optimality137

6．Problems with Statc Constraints141

6.1．Formulation of the problem and the maximum principle141

6.2．Some preliminary lemmas145

6.3．A proof of Theorem 6.1149

7．Historical Remarks153

Chapter 4．Dynamic Programming and HJB Equations157

1．Introduction157

2．The Detcrministic Case Revisited158

3．The Stochastic Principle of Optimality and the HJB Equation175

3.1．A stochastic framework for dynamic programming175

3.2．Principle of optimality180

3.3．The HJB equation182

4．Other Properties of the Value Function184

4.1．Continuous dependence on parameters184

4.2．Semiconcavity186

5．Viscosity Solutions189

5.1．Definitions189

5.2．Some properties196

6．Uniqueness of Viscosity Solutions198

6.1．A uniqueness theorem198

6.2．Proofs of Lemmas 6.6 and 6.7208

7．Historical Remarks212

Chapter 5．The Relationship Between the Maximum Principle and Dynamic Programming217

1．Introduction217

2．Classical Hamilton-Jacobi Thcory219

3．Relationship for Deterministic Systems227

3.1．Adjoint variable and value function:Smooth case229

3.2．Economic interpretation231

3.3．Methods of characteristics and the Feynman-Kac formula232

3.4．Adjoint variable and value function:Nonsmooth case235

3.5．Vcrification theorems241

4．Relationship for Stochastic Systems247

4.1．Smooth case250

4.2．Nonsmooth case:Differentials in the spatial variable255

4.3．Nonsmooth case:Differentials in the time variable263

5．Stochastic Vcrification Theorems268

5.1．Smooth case268

5.2．Nonsmooth case269

6．Optimal Feedback Controls275

7．Historical Remarks278

Chapter 6．Linear Quadratic Optimal Control Problems281

1．Introduction281

2．The Deterministic LQ Problems Revisited284

2.1．Formulation284

2.2．A minimization problem of a quadratic functional286

2.3．A linear Hamiltonian system289

2.4．The Riccati equation and feedback optimal control293

3．Formulation of Stochastic LQ Problems300

3.1．Statement of the problems300

3.2．Examples301

4．Finiteness and Solvability304

5．A Necessary Condition and a Hamiltonian System308

6．Stochastic Riccati Equations313

7．Global Solvability of Stochastic Riccati Equations319

7.1．Existence:The standard case320

7.2．Existence:The case C=0，S=0，and Q,G≥0324

7.3．Existence:The one-dimensional case329

8．A Mean-variance Portfolio Selection Problem335

9．Historical Rcmarks342

Chapter 7．Backward Stochastic Differential Equations345

1．Introduction345

2．Linear Backward Stochastic Diffrential Equations347

3．Nonlinear Backward Stochastic Differential Equations354

3.1．BSDEs in finite deterministic durations:Method of contraction mapping354

3.2．BSDEs in random durations:Method of continuation360

4．Feynman-Kac-Type Formulae372

4.1．Representation via SDEs372

4.2．Representation via BSDEs377

5．Forward-Backward Stochastic Differential Equations381

5.1．General formulation and nonsolvability382

5.2．The four-step scheme,a heuristie dcrivation383

5.3．Several solvablc classes of FBSDEs387

6．Option Pricing Problems392

6.1．European call options and the Black-Scholes formula392

6.2．Other options396

7．Historical Remarks398

References401

Index433