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Abstract
We consider the problem of how to close a large asset position in an illiquid market in such a way that very high liquidation costs are unlikely. To this end we introduce a discrete-time model that provides a simple device for designing and controlling the distribution of the revenues/costs from unwinding the position. By appealing to dynamic programming we derive semi-explicit formulas for the optimal execution strategies. We then present a numerical algorithm for approximating optimal execution rates as functions of the price. We provide error bounds and prove convergence. Finally, examples for the liquidation of forward positions in illiquid energy markets illustrate the efficiency of the algorithm.
Acknowledgements
We would like to thank Azzouz Dermoune and Sebastian Ebert for helpful discussions. Moreover, we thank two anonymous referees for suggestions that improved the paper considerably. Financial support from the German Research Foundation (DFG) through the Hausdorff Center for Mathematics, in particular the Bonn International Graduate School of Mathematics, is gratefully acknowledged.