Optimal liquidation with dynamic parameter updating: A forward approach

Abstract

We propose a forward approach to study the performance of liquidation strategies under sequential model parameter updates. The forward liquidation program consists of pasting forward in time and in a time-consistent fashion a series of optimal liquidation problems. They are triggered at the parameter shift instances, thus entirely eliminating model error, and last at most till the next parameter update. However, due to the nature of the model dynamics, solutions may cease to exist in finite time, even before the subsequent parameter update. Furthermore, forward liquidation strategies may never lead to full liquidation, even though they maximize the average utility of revenue and always preserve time-consistency. In juxtaposition, the traditional approach delivers full liquidation at the sought horizon but encounters considerable model error, generates value erosion, and is time-inconsistent.

Keywords

Optimal liquidation / Dynamic parameter updating / Forward approach / Full liquidation / Time consistency / Backward approach / Expected utility model

Acknowledgements

Thaleia Zariphopoulou would like to thank the University of Chicago for its hospitality during the Spring 2023 longterm program, during which most of this work was completed.

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