  We study the problem of optimal execution of a trading order under Volume
Weighted Average Price (VWAP) benchmark, from the point of view of a
risk-averse broker. The problem consists in minimizing mean-variance of the
slippage, with quadratic transaction costs. We devise multiple ways to solve
it, in particular we study how to incorporate the information coming from the
market during the schedule. Most related works in the literature eschew the
issue of imperfect knowledge of the total market volume. We instead incorporate
it in our model. We validate our method with extensive simulation of order
execution on real NYSE market data. Our proposed solution, using a simple model
for market volumes, reduces by 10% the VWAP deviation RMSE of the standard
"static" solution (and can simultaneously reduce transaction costs).
