  In this paper, we study the long time behavior of an optimal liquidation
problem with semimartingale strategies and external flows. To investigate the
limit rigorously, we study the convergence of three BSDEs characterizing the
value function and the optimal strategy, from finite horizon to infinite
horizon. We find that in the long time limit the player may not necessarily
liquidate her assets at all due to the existence of external flows, even if in
any given finite time horizon, the player is forced to liquidate all assets.
Moreover, when the intensity of the external flow is damped, the player will
liquidate her assets in the long run.
