A Simple Strategy to Deal with Toxic Flow

ArXiv ID: 2503.18005 “View on arXiv”

Authors: Unknown

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.

Keywords: Stochastic control, Adverse selection, Market making, Broker dealing strategy, Liquidity provision, Multi-asset (Execution)

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: 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.

  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"]