The formulation of optimal control problems involving realistic models typically involves constraints on control and state variables, to take account of a target to be reached, mechanical or thermal constraints, obstacles, etc. When constraints are present and when, as is often the case, rather severe controllability conditions are not satisfied, it is known that the value function may be discontinuous and these discontinuities pose some well-known issue in the characterization of the value function as unique viscosity solution of a suitable Hmilton-Jacobi equation. Aim of my research is to provide a rigorous mathematical formalism that leads to a computation of the value function (or an other object of interest) also in absence of controllability assumption. Main topics of interest: First and second order Hamilton-Jacobi-Bellman equations, stochastic optimal control, viscosity solutions, numerical methods for partial differential equations.

TP for the course "Numerical methods for partial differential equations in finance".