  We consider the problem of portfolio optimization in the presence of market
impact, and derive optimal liquidation strategies. We discuss in detail the
problem of finding the optimal portfolio under Expected Shortfall (ES) in the
case of linear market impact. We show that, once market impact is taken into
account, a regularized version of the usual optimization problem naturally
emerges. We characterize the typical behavior of the optimal liquidation
strategies, in the limit of large portfolio sizes, and show how the market
impact removes the instability of ES in this context.
