  In a fixed time horizon, appropriately executing a large amount of a
particular asset -- meaning a considerable portion of the volume traded within
this frame -- is challenging. Especially for illiquid or even highly liquid but
also highly volatile ones, the role of "market quality" is quite relevant in
properly designing execution strategies. Here, we model it by considering
uncertain volatility and liquidity; hence, moments of high or low price impact
and risk vary randomly throughout the trading period. We work under the central
assumption: although there are these uncertain variations, we assume they occur
in a fast mean-reverting fashion. We thus employ singular perturbation
arguments to study approximations to the optimal strategies in this framework.
By using high-frequency data, we provide estimation methods for our model in
face of microstructure noise, as well as numerically assess all of our results.
