Macroscopic Market Making and Optimal Execution

This thesis bridges optimal execution and market making by integrating their frameworks. We introduce the macroscopic market making, a model in which trading activity is modelled by continuous rates rather than discrete order events. We establish existence and uniqueness of optimal strategies in both Markovian and non-Markovian settings, and then study the price competition among market makers via stochastic differential games. Finally, we connect the optimal execution with the macroscopic market-making framework. Mathematically, we contribute results in nonsmooth analysis, the well-posedness of stochastic equations, the analysis of Riccati equations, etc.