Geodesic
Optimal inventory management and order book modeling
Nicolas Baradel1 ; Bruno Bouchard2 ; David Evangelista3 ; Othmane Mounjid4
1Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris and ENSAE-ParisTech, CREST
2Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris
3King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900. Saudi Arabia
4CMAP, École Polytechnique
ESAIM. Proceedings, Tome 65 (2019), pp. 145-181
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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.
DOI : 10.1051/proc/201965145

Nicolas Baradel  1   ; Bruno Bouchard  2   ; David Evangelista  3   ; Othmane Mounjid  4

1 Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris and ENSAE-ParisTech, CREST
2 Université Paris-Dauphine, PSL University, CNRS, CEREMADE, Paris
3 King Abdullah University of Science and Technology (KAUST), CEMSE Division, Thuwal 23955-6900. Saudi Arabia
4 CMAP, École Polytechnique 
@article{EP_2019_65_a7,
     author = {Nicolas Baradel and Bruno Bouchard and David Evangelista and Othmane Mounjid},
     title = {Optimal inventory management and order book modeling},
     journal = {ESAIM. Proceedings},
     pages = {145--181},
     year = {2019},
     volume = {65},
     doi = {10.1051/proc/201965145},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201965145/}
}
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Nicolas Baradel; Bruno Bouchard; David Evangelista; Othmane Mounjid. Optimal inventory management and order book modeling. ESAIM. Proceedings, Tome 65 (2019), pp. 145-181. doi: 10.1051/proc/201965145

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