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      Optimal Asset Liquidation with Multiplicative Transient Price Impact

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          Abstract

          We study a limit order book 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.

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          Author and article information

          Journal
          2015-01-08
          2016-03-17
          1501.01892

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          35R35, 49J40, 49L20, 60H30, 93E20, 91G80
          This version concentrates on and improves the results in Sections 1-5 of version 1. The results from later Sections 6 and 7 from version 1 have been significantly extended and will be developed into a separate paper
          math.OC math.PR q-fin.TR

          Numerical methods, Probability, Trading & Market microstructure

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