We consider a liquidation problem in which a risk-averse trader tries to liquidate a fixed quantity of an asset in the presence of market impact and random price fluctuations. When deciding the liquidation strategy, the trader encounters a trade-off between the transaction costs incurred due to...

In modern equity markets, participants have a choice of many exchanges at which to trade. Exchanges typically operate as electronic limit order books operating under a “price-time” priority rule and, in turn, can be modeled as multi-class FIFO queueing systems. A market with multiple...

We model an electronic limit order book as a multi-class queueing system under fluid dynamics, and formulate and solve a problem of limit and market order placement to optimally buy a block of shares over a short, predetermined time horizon. Using the structure of the optimal execution policy,...

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...