The main purpose of the book is to give a rigorous introduction to the most important and
useful solution methods of various types of stochastic control problems for jump diffusions and
their applications. Both the dynamic programming method and the stochastic maximum principle
method are discussed as well as the relation between them. Corresponding verification theorems
involving the Hamilton-Jacobi-Bellman equation and or (quasi-)variational inequalities are
formulated. The text emphasises applications mostly to finance. All the main results are
illustrated by examples and exercises appear at the end of each chapter with complete
solutions. This will help the reader understand the theory and see how to apply it. The book
assumes some basic knowledge of stochastic analysis measure theory and partial differential
equations.The 3rd edition is an expanded and updated version of the 2nd edition containing
recent developments within stochastic control and its applications. Specifically there is a
new chapter devoted to a comprehensive presentation of financial markets modelled by jump
diffusions and one on backward stochastic differential equations and convex risk measures.
Moreover the authors have expanded the optimal stopping and the stochastic control chapters to
include optimal control of mean-field systems and stochastic differential games.
