A Parametric Contextual Online Learning Theory of Brokerage

ArXiv ID: 2407.01566 “View on arXiv”

Authors: Unknown

Abstract

We study the role of contextual information in the online learning problem of brokerage between traders. In this sequential problem, at each time step, two traders arrive with secret valuations about an asset they wish to trade. The learner (a broker) suggests a trading (or brokerage) price based on contextual data about the asset and the market conditions. Then, the traders reveal their willingness to buy or sell based on whether their valuations are higher or lower than the brokerage price. A trade occurs if one of the two traders decides to buy and the other to sell, i.e., if the broker’s proposed price falls between the smallest and the largest of their two valuations. We design algorithms for this problem and prove optimal theoretical regret guarantees under various standard assumptions.

Keywords: online learning, brokerage, contextual information, regret guarantees, sequential problem, General Asset Trading

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper presents a highly theoretical framework with advanced mathematical proofs for regret bounds and structural lemmas, but lacks any empirical validation, backtesting, or implementation details, focusing solely on theoretical guarantees.

  flowchart TD
    A["Research Goal: Design optimal brokerage<br>algorithms using contextual information"] --> B["Key Methodology: Online Learning Framework<br>with sequential trader arrivals"]
    B --> C["Data/Inputs: Asset context, market conditions,<br>trader valuations v1, v2"]
    C --> D["Computational Process: Broker proposes price p(t)<br>based on context and past regret"]
    D --> E{"Trade occurs?"}
    E -- Yes<br>p(t) between v1 and v2 --> F["Update Model & Algorithm<br>Zero Regret/No Update"]
    E -- No<br>Trade Fails --> G["Update Model & Algorithm<br>Incur Regret"]
    F & G --> H["Key Outcomes: Optimal regret guarantees,<br>Parametric contextual trading algorithms"]
    style A fill:#f9f,stroke:#333,stroke-width:2px
    style H fill:#ccf,stroke:#333,stroke-width:2px
    style D fill:#9cf,stroke:#333,stroke-width:1px
    style C fill:#9f9,stroke:#333,stroke-width:1px