Paper: arXiv 2407.17393

Authors: Robert Boyce, Martin Herdegen, Leandro Sánchez-Betancourt

Abstract

We study liquidity provision in the presence of exogenous competition. We consider a reference market maker' who monitors her inventory and the aggregated inventory of the competing market makers. We assume that the competing market makers use a rule of thumb’ to determine their posted depths, depending linearly on their inventory. By contrast, the reference market maker optimises over her posted depths, and we assume that her fill probability depends on the difference between her posted depths and the competition’s depths in an exponential way. For a linear-quadratic goal functional, we show that this model admits an approximate closed-form solution. We illustrate the features of our model and compare against alternative ways of solving the problem either via an Euler scheme or state-of-the-art reinforcement learning techniques.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a strong theoretical contribution by extending the classic Avellaneda-Stoikov market making framework to account for exogenous competition via stochastic control and HJB equations. However, it relies predominantly on synthetic illustrations and approximate closed-form/RL comparisons rather than rigorous empirical validation on real limit order book data.

Research Flowchart

  flowchart TD
    A[Research Goal: Optimal Market Making<br/>with Exogenous Competition] --> B[Inputs: Reference Inventory,<br/>Competitor Inventory & Rule-of-Thumb Depths]
    B --> C[Model Formulation: Stochastic Control<br/>with Exponential Fill Probabilities]
    C --> D[Solution Method: Approximate<br/>Closed-Form Linear-Quadratic Solution]
    C --> E[Benchmarking: Compare vs.<br/>Euler Scheme & Reinforcement Learning]
    D --> F[Key Outcomes: Efficient Closed-Form<br/>Policy for Inventory Management]
    E --> F

Cited References (26)

  1. Automated Market Makers Designs Beyond Constant Functions (2023)
  2. Algorithmic and High-Frequency Trading (2015)
  3. The Financial Mathematics of Market Liquidity: From Optimal Execution to Market Making (2016) — link
  4. Adaptive Optimal Market Making Strategies with Inventory Liquidation Cost — → 2405.11444
  5. High-frequency trading in a limit order book (2008)
  6. The dynamics of dealer markets under competition (1983)
  7. Market making with alpha signals (2020)
  8. Optimal market making with persistent order flow (2021)
and 18 more
  1. Algorithmic market making in foreign exchange cash markets: a new model for active market makers (2021) — link
  2. Liquidity provision with adverse selection and inventory costs (2023)
  3. Market Making via Reinforcement Learning (2018) — link
  4. Latency and liquidity risk (2021)
  5. Order-book modeling and market making strategies (2018)
  6. Algorithmic trading with model uncertainty (2017)
  7. Optimal high-frequency trading with limit and market orders (2013)
  8. Optimal liquidity provision (2015)
  9. Closed-form approximations in multi-asset market making (2021)
  10. Mbt-gym: Reinforcement learning for model-based limit order book trading (2023)
  11. The Financial Mathematics of Market Liquidity: From optimal execution to market making (2016)
  12. Proximal policy optimization algorithms (2017) — link
  13. Dynamics of Market Making Algorithms in Dealer Markets: Learning and Tacit Collusion (2024)
  14. Brokers and Informed Traders: dealing with toxic flow and extracting trading signals (2022)
  15. Unwinding Stochastic Order Flow: When to Warehouse Trades (2023) — link
  16. Optimal execution with limit and market orders (2015)
  17. Proximal policy optimization algorithms (2017) — link
  18. Order imbalance, liquidity, and market returns (2002)

1 of 26 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.