  We solve the problem of optimal liquidation with volume weighted average
price (VWAP) benchmark when the market impact is linear and transient. Our
setting is indeed more general as it considers the case when the trading
interval is not necessarily coincident with the benchmark interval:
Implementation Shortfall and Target Close execution are shown to be particular
cases of our setting. We find explicit solutions in continuous and discrete
time considering risk averse investors having a CARA utility function. Finally,
we show that, contrary to what is observed for Implementation Shortfall, the
optimal VWAP solution contains both buy and sell trades also when the decay
kernel is convex.
