Paper: arXiv 2503.18005

Abstract

We model the trading activity between a broker and her clients (informed and uninformed traders) as an infinite-horizon stochastic control problem. We derive the broker’s optimal dealing strategy in closed form and use this to introduce an algorithm that bypasses the need to calibrate individual parameters, so the dealing strategy can be executed in real-world trading environments. Finally, we characterise the discount in the price of liquidity a broker offers clients. The discount strikes the optimal balance between maximising the order flow from the broker’s clients and minimising adverse selection losses to the informed traders.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly complex mathematical model using infinite-horizon stochastic control, HJB equations, and closed-form derivations, placing it firmly in the high math complexity quadrant. However, it lacks backtesting, empirical data, or implementation details, focusing instead on theoretical derivations and a conceptual algorithm.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimal Broker Dealing Strategy<br>in Adverse Selection Setting"] --> B["Methodology<br>Infinite-Horizon Stochastic Control"]
  B --> C["Data & Inputs<br>Client Flow Dynamics &<br>Market Price Process"]
  C --> D["Computational Process<br>Solve HJB Equation for<br>Closed-Form Optimal Control"]
  D --> E["Key Findings & Outcomes<br>1. Closed-Form Dealing Strategy<br>2. Parameter-Free Algorithm<br>3. Optimal Liquidity Discount"]

Cited References (40)

  1. Lectures on BSDEs, stochastic control, and stochastic differential games with financial applications (2016)
  2. Internalisation by electronic FX spot dealers (2019)
  3. Algorithmic market making in dealer markets with hedging and market impact (2023)
  4. A mean-field game of market-making against strategic traders (2022) — link
  5. Optimal signal-adaptive trading with temporary and transient price impact (2022)
  6. Optimal trading: The importance of being adaptive (2021)
  7. Trading algorithms with learning in latent alpha models (2019)
  8. Merton’s Optimal Investment Problem with Jump Signals (2022) — link
and 32 more
  1. On the impossibility of informationally efficient markets (1980)
  2. Continuous auctions and insider trading (1985)
  3. Informed speculation with imperfect competition (1989)
  4. Market microstructure theory (1998)
  5. Enhancing trading strategies with order book signals (2018)
  6. Option Volume Imbalance as a predictor for equity market returns (2022) — link
  7. Double-Execution Strategies Using Path Signatures (2022)
  8. Fast and Slow Optimal Trading with Exogenous Information (2022) — link
  9. Optimal execution with stochastic delay (2023)
  10. Liquidation in target zone models (2018)
  11. Closed-loop Nash competition for liquidity (2023)
  12. Investing for the long run when returns are predictable (2000)
  13. Algorithmic trading with model uncertainty (2017)
  14. Continuous-time stochastic control and optimization with financial applications (2009)
  15. Incorporating signals into optimal trading (2019)
  16. Incorporating order-flow into optimal execution (2016)
  17. Algorithmic and high-frequency trading (2015)
  18. The relevance of broker networks for information diffusion in the stock market (2019)
  19. Brokers and informed traders: dealing with toxic flow and extracting trading signals (2022)
  20. A Mean Field Game between Informed Traders and a Broker — → 2401.05257
  21. Detecting toxic flow — → 2312.05827
  22. Liquidity provision with adverse selection and inventory costs (2023)
  23. Liquidity Competition Between Brokers and an Informed Trader — → 2503.08287
  24. Strategic Learning and Trading in Broker-Mediated Markets — → 2412.20847
  25. Nash Equilibrium between Brokers and Traders — → 2407.10561
  26. The dynamics of dealer markets under competition (1983)
  27. Optimal Execution under Incomplete Information — → 2411.04616
  28. Broker-Trader Partial Information N ash Equilibria — → 2412.17712
  29. Brokers and order flow leakage: Evidence from fire sales (2019)
  30. Buy Low, Sell High: A High Frequency Trading Perspective (2014) — link
  31. Unwinding toxic flow with partial information — → 2407.04510
  32. Market making with alpha signals (2020)

8 of 40 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.