Online and offline selling in limit order markets

Abstract

Completely automated electronic securities exchanges and algorithms for trading in these exchanges have become very important for modern finance. In [4], Kakade et al. introduced the limit order market model, which is a prevalent paradigm in electronic markets. In this paper, we consider both online and offline algorithms for maximizing revenue when selling in limit order markets. We first prove that the standard reservation price algorithm has an optimal competitive ratio for this problem. This ratio is not constant, and so we consider computing solutions offline. We show that the offline optimization problem is NP-hard, even for very restricted instances. We complement the hardness result by presenting an approximation scheme that runs in polynomial time for a wide class of instances. © 2008 Springer Berlin Heidelberg.