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Optimal inventory management and order book modeling

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1802.08135v2-1.pdf (3.020Mb)
Date
2019
Link to item file
https://arxiv.org/abs/1802.08135v2
Dewey
Probabilités et mathématiques appliquées
Sujet
Optimal trading; market impact; optimal control
Journal issue
ESAIM: Proceedings and Surveys
Volume
65
Publication date
2019
Article pages
145-181
Publisher
EDP Sciences
DOI
http://dx.doi.org/10.1051/proc/201965145
URI
https://basepub.dauphine.fr/handle/123456789/18733
Collections
  • CEREMADE : Publications
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Author
Baradel, Nicolas
Bouchard, Bruno
Evangelista, David
Mounjid, Othmane
Type
Article accepté pour publication ou publié
Abstract (EN)
We model the behavior of three agent classes acting dynamically in a limit order book of a financial asset. Namely, we consider market makers (MM), high-frequency trading (HFT) firms, and institutional brokers (IB). Given a prior dynamic of the order book, similar to the one considered in the Queue-Reactive models [12, 18, 19], the MM and the HFT define their trading strategy by optimizing the expected utility of terminal wealth, while the IB has a prescheduled task to sell or buy many shares of the considered asset. We derive the variational partial differential equations that characterize the value functions of the MM and HFT and explain how almost optimal control can be deduced from them. We then provide a first illustration of the interactions that can take place between these different market participants by simulating the dynamic of an order book in which each of them plays his own (optimal) strategy.

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