Stochastic Controls

Hamiltonian Systems and HJB Equations

Jiongmin Yong, Xun Yu Zhou

438 pages, parution le 01/07/1999

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Résumé

This book gives a self-contained and systematic exposition of the major optimal control theory for continuous-time stochastic diffusion processes, including the Pontryagin type maximum principle (MP) featuring second-order adjoint equations, the Bellman dynamic programming (DP) method via viscosity solution theory, and the Kalman linear-quadratic (LQ) models with indefinite cost functionals. A major feature of the controlled systems under consideration is that the controls enter into both the drifts and the diffusions, making it fundamentally different from the deterministic systems. The main theme of the book is on establishing relations between MP and DP, or essentially those between Hamiltonian systems and Hamilton-Jacobi-Bellman (HJB) equations.

This book can be used as a textbook for graduate students majoring in stochastic controls and applications. Some knowledge in measure theory and real analysis will be helpful. It can also serve as a reference for researchers in applied probability, control theory, operations research, physics, economics, and finance.

Contents

Preface
Notation
Assumption Index
Problem Index

Ch. 1 Basic Stochastic Calculus 1
Ch. 2 Stochastic Optimal Control Problems 51
Ch. 3 Maximum Principle and Stochastic Hamiltonian Systems 101
Ch. 4 Dynamic Programming and HJB Equations 157
Ch. 5 The Relationship Between the Maximum Principle and Dynamic Programming 217
Ch. 6 Linear Quadratic Optimal Control Problems 281
Ch. 7 Backward Stochastic Differential Equations 345

References 401
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Jiongmin Yong, Xun Yu Zhou
Parution	01/07/1999
Nb. de pages	438
Format	16 x 24
Couverture	Relié
Poids	756g
Intérieur	Noir et Blanc
EAN13	9780387987231
ISBN13	978-0-387-98723-1