Stochastic Optimal Control

We start this lecture by introducing some classical stochastic control problems, including optimal portfolio allocation, Merton utility maximization problem, real option, and contract theory. This introduction motivates us to study, after a short recall on stochastic calculus, some ways to solve stochastic control problems as well as optimal stopping problem. This leads us on a journey through the dynamic programming principle, the Hamilton Jacobi Bellman (HJB) equations, the notion of viscosity solution, up to the theory of BSDEs.