Tutorial for Viscosity Solutions in Optimal Control of Diffusions

This tutorial is an introduction to the theory of viscosity solutions of Hamilton-Jacobi-Bellman equations/inequalities in the realm of stochastic control problems. It is an easy to use reference for application-oriented users of this theory. The presentation is based mainly on the book Pham (2009) "Continuous-time Stochastic Control and Optimization with Financial Applications", but borrows from many other references as well. What sets it apart from existing publications is the devotion to details and avoidance of "hand-waving". In particular, all assumptions are clearly stated and proofs are presented in a complete form