Deciding between the use of market orders and limit orders is an important question in practical optimal trading problems. A key ingredient in making this decision is understanding the uncertainty of the execution of a limit order, that is, the fill probability or the probability that an order...

We consider a broad class of dynamic portfolio optimization problems that allow for complex models of return predictability, transaction costs, trading constraints, and risk considerations. Determining an optimal policy in this general setting is almost always intractable. We propose a class of...