Randomized controlled(Chinese Edition) by YONG JIONG MIN

paperback. New. Ship out in 2 business day, And Fast shipping, Free Tracking number will be provided after the shipment.Pub Date: 2012 09 Pages: 438 in Publisher: World Publishing Company randomized controlled called tentative control. is the most original control mode. is the basis of all other control methods. Random control is fully established on the basis of the opportunities in the occasional. Try thinking embodied in the control activities. Stochastic Control success. it is often accompanied by failure. Greater risk of this control method. this control method stakes activity. generally should not be used. The randomized control (Yong Hyung Min) on the introduction of the randomized controlled English textbook. Contents: PrefaceNotationAssumption IndexProblem IndexChapter 1. Basic Stochastic Calculus 1. Probability 1.1. Probability spaces 1.2. Random variables 1.3. Conditional expectation 1.4. Convcrgence of probabilities 2. Stochastic Processes 2.1. General considerations 2.2. Ownian motions 3. Stopping Times 4. Martingales 5 . ItS's Integral 5.1. Nondifferentiability of ownian motion 5.2. Definition of Ites integral and basic properties 5.3. ItS's formula 5.4. Martingale representation theorems 6. Stochastic Differential Equations 6.1. Strong solutions 6.2. Weak solutions 6.3. Linear SDEs 6.4. Other types of SDEsChapter 2. Stochastic Optimal Control Problems 1. Introduction 2. Deterministic Cases Revisited 3. Examples of Stochastic Control Problems 3. 1. Production planning 3.2. Investment vs. consumption 3.3. Reinsurance and dividend management 3.4. Technology diffusion 3.5. Queueing systems in heavy traffic 4. Formulations of Stochastic Optimal Control Problems 4.1. Strong formulation 4.2. Weak formulation 5. Existence of Optimal Controls 5.1. A deterministic result 5.2. Existence under strong formulation 5.3. Existence under weak formulation 6. Reachable Sets of Stochastic Control Systems 6.1. Nonconvexity of the reachable sets 6.2. Nonclnseness of the reachable sets 7. Other Stochastic Control Models 7.1. Random duration 7.2. Optimal stopping 7.3. Singular and impulse controls 7.4. Risk-sensitive controls 7.5. Ergodic controls 7.6. Partially observable systems 8. Historical RemarksChapter 3. Maximum Principle and Stochastic Hamiitonian Systems 1. Introduction 2. The Deterministic Case Rcvisited 3. Statement of the Stochastic Maximum Principle 3.1. Adjoint equations 3.2. The maximum principle and stochastic Hamiltonian systems 3.3. A worked-out example 4. A Proof of the Maximum Principle 4.1. A moment estimate 4.2. Taylor expansions 4.3. Duality analysis and complction of thc proof 5. Sufficient Conditions of Optimality 6. Problems with Statc Constraints 6.1. Formulation of the problem and the maximum principle 6.2. Some preliminary lemmas 6.3. A proof of Theorem 6.1 7. Historical RemarksChapter 4. Dynamic Programming and HJB Equations 1. Introduction 2. The Deterministic Casc Revisited 3. The Stochastic Principle of Optimality and the HJB Equation 3.1. A stochastic framework for dynamic programming 3.2. Principlc of optimality 3.3 . The HJB cquation 4. Other Properties of the Value Function 4.1. Continuous dependence on parameters 4.2. Semiconcavity 5. Viseo ~ ity Solutions 5.1. Definitions 5.2. Some properties 6. Uniqueness of Viscosity Solutions 6.1. A uniqueness theorem 6.2. Proofs of Lemmas 6.6 and 6.7 7. Historical RcmarksChapter 5. The Relationship Between the Maximum Principle and Dynamic Programming 1. Introduction 2. Classical Hamilton-Jacobi Theory 3. Relationship for Deterministic Systems 3.1. Adjoint variable and value function: Smooth case 3.2. Economic interpretation 3.3. Methods of characteristics and the Fcynman Kac formula 3.4. Adjoint variable and value function: Nonsmooth case 3.5. Vcrification theorems 4. Relationship for Stochastic Systems 4.1. Smooth case 4.2. Nonsmooth case: Differentials in the spatial variable 4.3. Nonsmooth case: Differentials in the time variable 5. Stochastic Vcrification Theorems 5.1. Smooth case 5.2. Nonsmooth case 6. Optimal Fccdback Controls 7. Historical RemarksChapter 6. Linear Quadratic Optimal Control Problems 1. Introduction 2. The Deterministic LQ Problems Revisited 2.1. Formulation 2.2. A minimization problem of a quadratic functional 2.3. A linear Hamiltonian system 2.4. The Riccati equation and feedback optimal control 3. FormuLation of Stochastic LQ Problems 3.1. Statement of the problems 3.2. Examples 4. Finiteness and Solvability 5. A Necessary Condition and a Hamiltonian System 6. Stochastic Riceati Equations 7. GLobal Solvability of Stochastic Riccati EQuations 7.1. Existence: Thc standard case 7.2. Existence: The case C = 0. S = 0. and QG _ 0 7.3. Existence: The one-dimensional case 8. A Mean- variance Portfolio Selection Problem 9. Historical RemarksChapter 7. Backward Stochastic Differential Equations 1. Introduction 2. Linear Backward Stochastic Differential EQuations 3. Nonlinear Backward Stochastic Differential Equations 3.1. BSDEs in finite deterministic durations: Method of contraction mapping 3.2. BSDEs in random durations: Method of continuation 4. Feynman-Kac-Type Formulae 4.1. Representation via SDEs 4.2. Representation via BSDEs 5. Forward-Backward Stochastic Differential Equations 5.1. General formulation and nonsolvability 5.2. The four-step scheme. a heuristic derivation 5.3. Several solvable classes of FBSDEs 6. Option Pricing Problems 6.1. European call options and the Black-Scholes formula 6.2. Other options 7. Historical RemarksReferencesIndex Satisfaction guaranteed,or money back.