Trade execution and market making are two central problems in algorithmic trading that have largely been studied in separate literatures. In this talk, I present a unified approach that addresses both problems simultaneously in three steps.

We introduce a macroscopic market making model à la Avellaneda-Stoikov, using continuous processes for orders instead of discrete point processes. Since the impact of a single market maker on price is typically negligible, we then develop the corresponding game formulation. Finally, we can connect traders with market makers.

Subsequently, we present our mathematical contributions. The goal is to derive the global well‑posedness of the optimal control/Nash equilibrium. The discussion addresses topics in game theory, non‑smooth analysis, FBSDEs, and Riccati equations.

References:
Ivan Guo, Shijia Jin, and Kihun Nam, Macroscopic Market Making. Forthcoming in Finance & Stochastics. Preprint: arXiv:2307.14129.
Ivan Guo and Shijia Jin, Macroscopic Market Making Games. Forthcoming in Mathematical Finance. DOI: 10.1111/mafi.70010.
Ivan Guo and Shijia Jin, Optimal Execution and Macroscopic Market Making. Working paper. Preprint: arXiv:2504.06717.