Optimal Placement in a Limit Order Book

Abstract

This paper proposes and studies an optimal placement problem in a limit order book. Two simple models are proposed: one with price impact and one without price impact. For the first model, optimal placement strategies for both single-period and multi-period cases are derived. For the second model, it is shown that the optimal strategy never mixes market orders and (best) limit orders; in particular, with special choices of parameters, the optimal strategy reduces to the VWAP type of Bertsimas and Lo (1998) for the optimal execution problem.