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Optimal execution with liquidity risk in a diffusive order book market

Hyoeun Lee

Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL, USA

E-mail Address: hyoeun@illinois.edu

Corresponding author.

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Kiseop Lee

Department of Statistics, Purdue University, West Lafayette, IN, USA

E-mail Address: kiseop@purdue.edu

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https://doi.org/10.1142/S2424786323500184Cited by:0 (Source: Crossref)

Abstract

We study the optimal order placement strategy with the presence of a liquidity cost. In this problem, a stock trader wishes to clear her large inventory by a predetermined time horizon T. A trader uses both limit and market orders, and a large market order faces an adverse price movement caused by the liquidity risk. First, we study a single period model where the trader places a limit order and/or a market order at the beginning. We show the behavior of optimal amount of market order, $m^{*}$ $m^{*}$ , and optimal placement of limit order, $y^{*}$ $y^{*}$ , under different market conditions. Next, we extend it to a multi-period model, where the trader makes sequential decisions of limit and market orders at multiple time points.

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