  We study the optimal execution of market and limit orders with permanent and
temporary price impacts as well as uncertainty in the filling of limit orders.
Our continuous-time model incorporates a trade speed limiter and a trader
director to provide better control on the trading rates. We formulate a
stochastic control problem to determine the optimal dynamic strategy for trade
execution, with a quadratic terminal penalty to ensure complete liquidation. In
addition, we identify conditions on the model parameters to ensure optimality
of the controls and finiteness of the associated value functions. For
comparison, we also solve the schedule-following optimal execution problem that
penalizes deviations from an order schedule. Numerical results are provided to
illustrate the optimal market and limit orders over time.

Mathematical Finance;Trading and Market Microstructure