  We study the optimal order placement strategy with the presence of a
liquidity cost. In this problem, a stock trader wishes to clear her large
inventory by a predetermined time horizon $T$. A trader uses both limit and
market orders, and a large market order faces an adverse price movement caused
by the liquidity risk. First, we study a single period model where the trader
places a limit order and/or a market order at the beginning. We show the
behavior of optimal amount of market order, $m^*$, and optimal placement of
limit order, $y^*$, under different market conditions. Next, we extend it to a
multi-period model, where the trader makes sequential decisions of limit and
market orders at multiple time points.

Computational Finance;Trading and Market Microstructure