Solving non-Markovian stochastic control problems driven by Wiener functionals.

In this talk, we present a numerical scheme for computing near-optimal controls associated with controlled Wiener functionals via a finite-dimensional approximation procedure. Explicit rates of convergence are provided under rather weak conditions for distinct types of non-Markovian and non-semimartingale states.The theory is applied to stochastic control problems based on path-dependent SDEs and rough stochastic volatility models, where both drift and possibly degenerated diffusion components are controlled. Optimal control of drifts for nonlinear path-dependent SDEs driven by fractional Brownian motion with exponent H \in (0, 1) is also discussed. If time permits, we also discuss, in the simplest case of optimal stopping, the Monte Carlo scheme and overall error estimates in terms of concrete approximation spaces with finite Vapnik-Chervonenkis dimension