Against a Universal Trading Strategy: No-Arbitrage, No-Free-Lunch, and Adversarial Cantor Diagonalization

2026-04-14

AI Summary

This study investigates whether a universally profitable trading strategy exists across all market trajectories. By integrating measure theory, combinatorics, and computability theory—alongside the no-arbitrage principle, the no-free-lunch theorem, and Turing-style diagonalization—it constructs an adversarial market model and establishes an analogy between financial martingales and thermodynamic detailed balance. Employing tools such as equivalent martingale measures, combinatorial averaging, and Cantor diagonalization, the paper demonstrates that any practically effective trading strategy must rely on specific assumptions about market states, and its automated execution systematically amplifies tail risk. The work thereby theoretically refutes the feasibility of universal trading strategies in competitive markets and reveals fundamental limits to their generalizability.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Adversarial Search
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

We investigate the impossibility of universally winning trading strategies -- those generating strict profit across all market trajectories -- through three distinct mathematical paradigms. Fundamentally, under standard admissibility constraints, the existence of such a strategy is a strict subset of strong arbitrage, which is mathematically precluded in competitive markets admitting an equivalent martingale measure. Beyond this rigorous measure-theoretic foundation, we explore analogous limitations in two alternative modeling regimes. Combinatorially, the No-Free-Lunch theorem demonstrates that outperformance requires exploitation of non-uniform market structure, as uniform averaging precludes universal dominance. Computationally, a Turing diagonalization argument constructs an adversarial environment that defeats any computable trading algorithm, shifting the impossibility from exogenous price paths to adaptive adversaries. These mathematical limits are framed by a time-reversal heuristic that establishes a formal analogy between financial martingale measures and thermodynamic detailed balance, resolving the Maxwell's Demon analogy for markets without relying on physically irrelevant Landauer erasure costs. Using the Wheel Options Strategy as a case study, we demonstrate that strategies succeeding ``for all practical purposes'' (FAPP) inherently depend on transient regime assumptions, meaning their automated execution systematically amplifies tail risks.

Problem

• universal trading strategy
• no-arbitrage
• No-Free-Lunch
• adversarial environment
• martingale measure

Innovation

• No-Arbitrage
• No-Free-Lunch
• Adversarial Diagonalization
• Martingale Measure
• Computable Trading Strategy