Abstract

The paper is an extended version of lecture notes from a mini-course given by the author in the workshop Optimal Control and PDE in Tohoku University in 2017. The main objective of the lecture notes is to give a short but rigorous introduction to the dynamic programming approach to stochastic optimal control problems. The manuscript discusses, among other things, the classical necessary and sufficient conditions for optimality, properties of the value function, and it contains a proof of the dynamic programming principle, and a proof that the value function is a unique viscosity solution of the associated Hamilton-Jacobi-Bellman equation.

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