Optimal inventory management and order book modeling

Nicolas Baradel (), Bruno Bouchard (), David Evangelista and Othmane Mounjid ()
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Nicolas Baradel: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, ENSAE - Ecole Nationale de la Statistique et de l'Analyse Economique - Ecole Nationale de la Statistique et de l'Analyse Economique
Bruno Bouchard: CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique, PSL - Université Paris Sciences et Lettres
David Evangelista: KAUST - King Abdullah University of Science and Technology [Saudi Arabia]
Othmane Mounjid: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: 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 [14, 20, 21], 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.

Keywords: Optimal control; Optimal trading; market impact (search for similar items in EconPapers)
Date: 2019
New Economics Papers: this item is included in nep-mst
Note: View the original document on HAL open archive server: https://hal.science/hal-01710301v2
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Citations: View citations in EconPapers (1)

Published in ESAIM: Proceedings and Surveys, 2019, 65, pp.145-181

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01710301

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