Neural networks can detect model-free static arbitrage strategies

ArXiv ID: 2306.16422 “View on arXiv”

Authors: Unknown

Abstract

In this paper we demonstrate both theoretically as well as numerically that neural networks can detect model-free static arbitrage opportunities whenever the market admits some. Due to the use of neural networks, our method can be applied to financial markets with a high number of traded securities and ensures almost immediate execution of the corresponding trading strategies. To demonstrate its tractability, effectiveness, and robustness we provide examples using real financial data. From a technical point of view, we prove that a single neural network can approximately solve a class of convex semi-infinite programs, which is the key result in order to derive our theoretical results that neural networks can detect model-free static arbitrage strategies whenever the financial market admits such opportunities.

Keywords: Neural Networks, Model-Free Static Arbitrage, Convex Semi-Infinite Programming, High-Dimensional Markets, Multi-Asset (Derivatives)

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail
  • Why: The paper relies heavily on advanced mathematics, including convex semi-infinite programming and neural network approximation theory, to prove theoretical guarantees. It complements this with numerical experiments on real financial data, demonstrating practical implementation and backtest-readiness.
  flowchart TD
    A["Research Goal: Can NN detect<br>model-free static arbitrage<br>in high-dimensional markets?"] --> B["Key Methodology"]
    
    B --> C["Theoretical Proof<br>Convex Semi-Infinite Programming<br>approximation via NN"]
    B --> D["Computational Process<br>Single Neural Network<br>optimizes 1st-order conditions"]
    
    C --> E["Data Input<br>Real Financial Data<br>Multi-Asset Markets"]
    D --> E
    
    E --> F["Key Findings:<br>1. NN detects arbitrage if market admits it<br>2. Model-free approach<br>3. Handles high dimensions<br>4. Fast execution"]