Macroscopic Market Making

ArXiv ID: 2307.14129 “View on arXiv”

Authors: Unknown

Abstract

We propose a macroscopic market making model à 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.

Keywords: Market Making, Optimal Execution, Hamilton-Jacobi-Bellman, Stochastic Differential Equations, Price Impact, Equities

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats
  • Why: The paper employs highly advanced mathematics, including non-Lipschitz forward-backward stochastic differential equations (FBSDEs), Hamilton-Jacobi-Bellman equations, and the stochastic maximum principle, but presents no backtests, datasets, or implementation details, focusing instead on theoretical existence and uniqueness proofs.
  flowchart TD
    A["Research Goal<br>Bridge Market Making & Optimal Execution<br>using Continuous Order Processes"] --> B["Methodology<br>Macroscopic Market Making Model<br>à la Avellaneda-Stoikov"]

    B --> C["Model Formulation<br>HJB & FBSDE Framework"]
    
    C --> D["Computational Analysis<br>Stochastic Analysis &<br>Numerical Methods"]

    D --> E1["Markovian &<br>Non-Markovian Noises"]
    D --> E2["Linear &<br>Non-linear Intensities"]
    D --> E3["Bounded &<br>Unbounded Coefficients"]

    E1 --> F{"Outcomes"}
    E2 --> F
    E3 --> F

    F --> G1["Existence & Uniqueness<br>of Optimal Control"]
    F --> G2["Well-posed Strong Solution<br>to HJB Equation"]
    F --> G3["Applications:<br>Price Impact & Optimal Execution"]