Optimal Trade Execution with Coherent Dynamic Risk Measures

We study the problem of optimal trade execution in an illiquid market by minimizing the coherent dynamic risk of the implementation shortfall. The prices of the assets are modeled as a discrete-time Markov process perturbed by both temporal and permanent impacts related to the trading volume. A closed-form optimal strategy is obtained for liquidating a single asset. In the case of multiple assets, we show that the optimal execution problem is equivalent to a saddle-point problem, for which efficient first-order methods are utilized to compute the optimal strategy numerically