  We study the optimal placement problem of a stock trader who wishes to clear
his/her inventory by a predetermined time horizon t, by using a limit order or
a market order. For a diffusive market, we characterize the optimal limit order
placement policy and analyze its behavior under different market conditions. In
particular, we show that, in the presence of a negative drift, there exists a
critical time t0>0 such that, for any time horizon t>t0, there exists an
optimal placement, which, contrary to earlier work, is different from one that
is placed "infinitesimally" close to the best ask, such as the best bid and
second best bid. We also propose a simple method to approximate the critical
time t0 and the optimal order placement.
