Paper: arXiv 2501.12591

Abstract

This study explores the design of an efficient rebate policy in auction markets, focusing on a continuous-time setting with competition among market participants. In this model, a stock exchange collects transaction fees from auction investors executing block trades to buy or sell a risky asset, then redistributes these fees as rebates to competing market makers submitting limit orders. Market makers influence both the price at which the asset trades and their arrival intensity in the auction. We frame this problem as a principal-multi-agent problem and provide necessary and sufficient conditions to characterize the Nash equilibrium among market makers. The exchange’s optimization problem is formulated as a high-dimensional Hamilton-Jacobi-Bellman equation with Poisson jump processes, which is solved using a verification result. To numerically compute the optimal rebate and transaction fee policies, we apply the Deep BSDE method. Our results show that optimal transaction fees and rebate structures improve market efficiency by narrowing the spread between the auction clearing price and the asset’s fundamental value, while ensuring a minimal gain for both market makers indexed on the price of the asset on a coexisting limit order book.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper employs highly advanced mathematical frameworks including high-dimensional Hamilton-Jacobi-Bellman equations with Poisson jumps and Deep BSDE methods for numerical solution, indicating very high math complexity. However, the empirical rigor is low as it presents theoretical models and conceptual results without any backtesting, real-world data analysis, or implementation details for trading systems.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Design Optimal Rebate Policy<br>to Maximize Market Efficiency"] --> B["Model Setup<br>Principal-Agent Framework<br>Competition among Market Makers"]
  B --> C["Formulation<br>High-dimensional HJB-PDE<br>with Poisson Jumps"]
  C --> D{"Solution Method"}
  D --> E["Analytical<br>Verification Result"]
  D --> F["Computational<br>Deep BSDE Method"]
  E & F --> G["Key Findings<br>Optimal Fee/Rebate Policy<br>Narrows Bid-Ask Spread<br>Preserves Market Maker Profit"]
  G --> H["Outcome<br>Improved Market Efficiency"]

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5 of 72 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.