Paper: arXiv 2604.13334

Authors: Karl Svozil

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly sophisticated theoretical framework combining measure theory, computability theory (Turing diagonalization), and thermodynamic heuristics to formalize limits on universal trading strategies. However, it lacks quantitative backtesting or empirical validation, grounding its practical case study primarily in conceptual analysis of option tail risks.

Research Flowchart

  flowchart TD
    A["Research Goal: Prove Impossibility of Universal Winning Trading Strategies"] --> B["Three Theoretical Paradigms & Case Study"]
    
    B --> C["Measure Theory: No-Arbitrage & Martingale Measures"]
    B --> D["Combinatorics & Computation: No-Free-Lunch & Turing Diagonalization"]
    B --> E["Empirical Case Study: Wheel Options Strategy"]
    
    C --> F["Analogy: Detailed Balance & Time Reversal"]
    D --> F
    
    E --> G["Key Finding: Strategies FAPP Amplifying Tail Risks & Subject to Adversarial Limits"]
    F --> G