In this talk, we will present a general methodology for stochastic control problems driven by the Brownian motion filtration including non-Markovian and non-semimartingale state processes controlled by mutually singular measures. The general convergence of the method is established under rather weak conditions for distinct types of non-Markovian and non-semimartingale states. Explicit rates of con- vergence are provided in case the control acts only on the drift component of the controlled system. Near-closed/open-loop optimal controls are fully characterized by a dynamic programming algorithm and they are classified according to the strength of the possibly underlying non-Markovian memory. 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 ∈ (0, 1/2) is also discussed.
Solving non-Markovian stochastic control problems driven by Wiener functionals
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