Paper: arXiv 2504.06717

Abstract

We propose a stochastic game modelling the strategic interaction between market makers and traders of optimal execution type. For traders, the permanent price impact commonly attributed to them is replaced by quoting strategies implemented by market makers. For market makers, order flows become endogenous, driven by tactical traders rather than assumed exogenously. Using the forward-backward stochastic differential equation (FBSDE) characterization of Nash equilibria, we establish a local well-posedness result for the general game. In the specific Almgren-Chriss-Avellaneda-Stoikov model, a decoupling approach guarantees the global well-posedness of the FBSDE system via the well-posedness of an associated backward stochastic Riccati equation. Finally, by introducing small diffusion terms into the inventory processes, global well-posedness is achieved for the approximation game.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is dense with advanced mathematics, including stochastic games, forward-backward SDEs, and matrix Riccati equations, but lacks empirical data, backtests, or implementation details, focusing entirely on theoretical well-posedness.

Research Flowchart

  flowchart TD
  A["Research Goal: Analyze strategic interaction<br>between market makers and traders"] --> B["Model Setup: Stochastic Game Formulation"]
  B --> C{"Key Methodology: FBSDE Characterization<br>of Nash Equilibria"}
  C --> D["Specific Model: Almgren-Chriss-Avellaneda-Stoikov"]
  D --> E{"Computational Approach:<br>Decoupling & Riccati Equation"}
  E --> F["Approximation: Small Diffusion Terms"]
  F --> G["Outcomes: Local & Global Well-Posedness<br>of FBSDE System"]