Paper: arXiv 2404.14252

Abstract

This paper establishes that conditioning the probability of execution of new orders on the self-generated historical trading information (HTI) of a trading strategy is a necessary condition for a statistical trading edge. It is shown, in particular, that, given any trading strategy S that does not use its own HTI, it is always possible to construct a new strategy S* that yields a systematically increasing improvement over S in terms of profit and loss (PnL) by using the self-generated HTI. This holds true under rather general conditions that are frequently met in practice, and it is proven through a decision mechanism specifically designed to formally prove this idea. Simulations and real-world trading evidence are included for validation and illustration, respectively.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a formal proof using measure-theoretic probability and stochastic processes, involving dense LaTeX notation and intricate mathematical constructs like order matching and PnL decomposition. While it mentions simulations and real-world evidence, the excerpt focuses on theoretical construction and lacks specific backtesting metrics, code, or detailed empirical datasets, indicating a strong theoretical foundation with moderate validation.

Research Flowchart

  flowchart TD
  A["Research Goal:<br/>Conditioning on Historical Trading Information<br/>is necessary for a statistical edge"] --> B["Methodology:<br/>Theoretical Proof & Decision Mechanism"]
  A --> C["Data/Inputs:<br/>Self-Generated Historical Trading Information<br/>- Order Execution Logs<br/>- Trade Outcomes"]
  B --> D["Computational Process:<br/>Construct S* from S<br/>Apply HTI Conditioning<br/>Compare PnL Metrics"]
  C --> D
  D --> E["Key Finding:<br/>S* systematically outperforms S<br/>Proof holds under general market conditions"]
  E --> F["Validation:<br/>Simulations &<br/>Real-World Trading Evidence"]