Optimal execution strategy of liquidation

Liquidity risks arise from the presence of time lags on execution of market orders in trading securities and "quantity" effect (liquidation discount) on security price. In this paper, we consider an investor who is holding a portfolio of stock and cash (in the form of market money account) with the objective to unwind his position on the risky asset so that the expected value of cash at the end of a fixed time horizon is maximized. Assuming that the executive time lags and liquidation discount are deterministic, we construct the numerical algorithms for computing the optimal trading strategy that maximizes the expected terminal value of cash position in the portfolio. We also investigate the probability of meeting the target cash level under different liquidation discount function