Optimal Asset Liquidation with Multiplicative Transient Price Impact

Article

Abstract

We study a multiplicative transient price impact model for an illiquid financial market, where trading causes price impact which is multiplicative in relation to the current price, transient over time with finite rate of resilience, and non-linear in the order size. We construct explicit solutions for the optimal control and the value function of singular optimal control problems to maximize expected discounted proceeds from liquidating a given asset position. A free boundary problem, describing the optimal control, is solved for two variants of the problem where admissible controls are monotone or of bounded variation.

Keywords

Singular control Finite-fuel problem Free boundary Variational inequality Illiquidity Multiplicative price impact Limit order book 

Mathematics Subject Classification

35R35 49J40 49L20 60H30 93E20 91G80 

Notes

Acknowledgements

Dirk Becherer: We thank Peter Bank for fruitful discussions on an early version of the control problem. Todor Bilarev: Support by German Science foundation DFG via Berlin Mathematical School BMS and research training group RTG1845 StoA is gratefully acknowledged.

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of MathematicsHumboldt-Universität zu BerlinBerlinGermany

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