From the reviews:
"This book provides a comprehensive introduction to stochastic control. … The treatment is at the level of a first course, with several examples and exercises. The book can be used by undergraduate students, but also by graduate students, engineers and others who study control, systems and related areas or want to extend their knowledge in these topics." (Krzysztof Szajowski, Mathematical Reviews, Issue 2009 j)
This book provides a comprehensive introduction to stochastic control problems in discrete and continuous time. The material is presented logically, beginning with the discrete-time case before proceeding to the stochastic continuous-time models. Central themes are dynamic programming in discrete time and HJB-equations in continuous time. Topics covered include stochastic maximum principles for discrete time and continuous time, even for problems with terminal conditions. Numerous illustrative examples and exercises, with solutions at the end of the book, are included to enhance the understanding of the reader. By interlinking many fields in stochastic control, the material gives the student the opportunity to see the connections between different fields and the underlying ideas that unify them.
This text will benefit students in applied mathematics, economics, engineering, and related fields. Prerequisites include a course in calculus and elementary probability theory. No knowledge of measure theory is assumed.