Optimal stopping for diffusions, both one-dimensional and multi-dimensional. Representation of the solution by the Green kernel of the process. I am also interested in optimal stopping problems for jump-processes, and in finite-horizon problems.
Fourier methods for option pricing and its error analysis. These methods, in the case of Levy process, usually require the computation of a discrete Fourier transform. I am interested in the optimal choose of the discretization, to minimize the error.
Markov control processes and stochastic games. Algorithms to find optimal strategies for Markov decision processes and competitive Markov decision processes. Algorithms to learn optimal strategies.
