Optimal placement in a limit order book: an analytical approach

This paper proposes and studies an optimal placement problem in a limit order book. Under a correlated random walk model with mean-reversion for the best ask/bid price, optimal placement strategies for both static and dynamic cases are derived. In the static case, the optimal strategy involves only the market order, the best bid, and the second best bid; the optimal strategy for the dynamic case is shown to be of a threshold type depending on the remaining trading time, the market momentum, and the price mean-reversion factor. Critical to the analysis is a generalized reflection principle for correlated random walks, which enables a significant dimension reduction.