Optimal inventory management and order book modeling
Nicolas Baradel (CEREMADE, ENSAE), Bruno Bouchard (CEREMADE, PSL),, David Evangelista (KAUST), Othmane Mounjid (CMAP)

TL;DR
This paper models the interactions of market makers, high-frequency traders, and institutional brokers in a limit order book, deriving PDEs for their strategies and simulating their dynamic interactions.
Contribution
It introduces a multi-agent model with optimal control strategies for different market participants in a limit order book setting.
Findings
Derived variational PDEs for agent value functions
Demonstrated near-optimal control strategies
Simulated interactions among agents in order book dynamics
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…
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