My research activity includes:
- Stochastic calculus for jump processes (in particular, stochastic calculus for discontinuous Weak Dirichlet processes via the regularization approach, and applications to the hedging problem).
- Stochastic optimal control with financial applications (in particular, optimal control of discontinuous processes driven by random measures).
- Stochastic filtering, stochastic optimal control with partial observations, enlargement of filtrations, with applications to mathematical finance.
- 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).
