The maximum principle and dynamic programming are the two most commonly used approaches in solving optimal control problems. These approaches have been developed independently. The theme of this book is to unify these two approaches, and to demonstrate that the viscosity solution theory provides the framework to unify them.
From the reviews: SIAM REVIEW "The presentation of this book is systematic and self-contained!Summing up, this book is a very good addition to the control literature, with original features not found in other reference books. Certain parts could be used as basic material for a graduate (or postgraduate) course!This book is highly recommended to anyone who wishes to study the relationship between Pontryagin's maximum principle and Bellman's dynamic programming principle applied to diffusion processes." MATHEMATICS REVIEW This is an authoratative book which should be of interest to researchers in stochastic control, mathematical finance, probability theory, and applied mathematics. Material out of this book could also be used in graduate courses on stochastic control and dynamic optimization in mathematics, engineering, and finance curricula. Tamer Basar, Math. Review