  The paper addresses the problem of meta order execution from a
broker-dealer's point of view in Almgren-Chriss model under order fill
uncertainty. A broker-dealer agency is authorized to execute an order of
trading on client's behalf. The strategies that the agent is allowed to deploy
is subject to a benchmark, referred to as the reservation strategy, regulated
by the client. We formulate the broker's problem as a utility maximization
problem in which the broker seeks to maximize his utility of excess
profit-and-loss at the execution horizon. Optimal strategy in feedback form is
obtained in closed form. In the absence of execution risk, the optimal
strategies subject to reservation strategies are deterministic. We establish an
affine structure among the trading trajectories under optimal strategies
subject to general reservation strategies using implementation shortfall and
target close orders as basis. We conclude the paper with numerical experiments
illustrating the trading trajectories as well as histograms of terminal wealth
and utility at investment horizon under optimal strategies versus those under
TWAP strategies.
