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Conference Paper

Online and Offline Selling in Limit Order Markets

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Chang,  Kevin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

Chang, K. (2008). Online and Offline Selling in Limit Order Markets. In C. Papadimitriou, & S. Shang (Eds.), Internet and Network Economics (pp. 41-52). Berlin: Springer.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-1C73-B
Abstract
Completely automated electronic securities exchanges and algorithms for trading in these exchanges have become very important for modern finance. In \cite{kkmo04}, Kakade \etal 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 selling securities in limit order markets in order to maximize the total revenue realized from the sale. We first prove that the standard reservation price algorithm has an optimal competitive ratio for this problem. Since this is not constant, we turn to offline optimization in order to compute improved solutions. We show that the offline optimization problem is \textbf{NP}-hard, even for very restricted instances, by reducing from \knapsack. We complement the hardness result by presenting an approximation scheme that runs in polynomial time for a wide class of instances.