Macroscopic Market Making

TL;DR

This paper introduces a macroscopic market making model that uses continuous order processes to better understand the relationship between market making and optimal execution, analyzing various noise and intensity scenarios.

Contribution

It develops a novel continuous-process-based market making model with rigorous mathematical guarantees for optimal control existence and uniqueness.

Findings

Model bridges market making and optimal execution.

Mathematically guarantees well-posedness of the control problem.

Applicable to price impact and execution strategies.

Abstract

We propose a macroscopic market making model \`a la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. The model intends to bridge the gap between market making and optimal execution problems, while shedding light on the influence of order flows on the optimal strategies. We demonstrate our model through three problems. The study provides a comprehensive analysis from Markovian to non-Markovian noises and from linear to non-linear intensity functions, encompassing both bounded and unbounded coefficients. Mathematically, the contribution lies in the existence and uniqueness of the optimal control, guaranteed by the well-posedness of the strong solution to the Hamilton-Jacobi-Bellman equation and the (non-)Lipschitz forward-backward stochastic differential equation. Finally, the model's applications to price impact and optimal execution are discussed.