Non-Markovian optimal stopping time problems

In this talk, we present a discretization scheme to solve continuous-time optimal stopping problems based on fully non-Markovian continuous processes adapted to the Brownian motion filtration. The approximations satisfy suitable variational inequalities which allow us to construct near optimal stopping times and optimal values in full generality. Explicit rates of convergence are presented for optimal values based on reward functionals of path-dependent SDEs driven by fractional Brownian motion. If time permits, we also discuss precise error estimates for the associate Monte Carlo approximation.