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Dynamic optimal execution in a mixed-market-impact Hawkes price model

Authors
  • Alfonsi, Aurélien1
  • Blanc, Pierre1
  • 1 Université Paris-Est, CERMICS, Projet MATHRISK ENPC-INRIA-UMLV, 6 et 8 avenue Blaise Pascal, Marne La Vallée, Cedex 2, 77455, France , Marne La Vallée, Cedex 2 (France)
Type
Published Article
Journal
Finance and Stochastics
Publisher
Springer Berlin Heidelberg
Publication Date
Nov 06, 2015
Volume
20
Issue
1
Pages
183–218
Identifiers
DOI: 10.1007/s00780-015-0282-y
Source
Springer Nature
Keywords
License
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Abstract

We study a linear price impact model, including other liquidity takers, whose flow of orders is driven by a Hawkes process. The optimal execution problem is solved explicitly in this context, and the closed-form optimal strategy describes in particular how one should react to the orders of other traders. This result enables us to discuss the viability of the market. It is shown that Poissonian arrivals of orders lead to quite robust price manipulation strategies in the sense of Huberman and Stanzl (Econometrica, 72:1247–1275, 2004). Instead, a particular set of conditions on the Hawkes model balances the self-excitation of the order flow with the resilience of the price, excludes price manipulation strategies, and gives some market stability.

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