My research activity lies in the intersection of stochastic calculus and the theory of partial differential equations, including:
- Stochastic calculus for jump processes (in particular, stochastic calculus for discontinuous Weak Dirichlet processes via the regularization approach);
- Stochastic optimal control (in particular, optimal control of discontinuous processes driven by random measures, Weak Dirichlet processes and the regularization approach);
- Hamilton-Jacobi-Bellman equations (in particular, integro-differential HJB equations, and their classical and viscosity solutions);
- Backward Stochastic Differential Equations (in particular, non-linear Feynman-Kac formulae, the randomization of the control method, and BSDEs driven by general random measures).