Markets are Efficient if and Only if P = NP

ArXiv ID: ssrn-1773169 “View on arXiv”

Authors: Unknown

Abstract

I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational p

Keywords: Market Efficiency Hypothesis, Computational Complexity, Algorithmic Trading, P vs NP Problem, Informational Efficiency, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.0/10
• Quadrant: Lab Rats
• Why: The paper presents a formal theoretical proof linking market efficiency to computational complexity classes (P vs NP), requiring advanced mathematical reasoning and abstract computer science concepts. However, it contains no actual data, backtests, or implementation details; the empirical part is a brief illustrative example rather than rigorous analysis.

  flowchart TD
    A["Research Goal: Are Markets Efficient?"]
    B["Key Methodology: Complexity Theoretic Proof"]
    C["Input: Historical Price Data & Market Efficiency Assumption"]
    D["Computational Process: Reducing Market Arbitrage to NP-Hard Problem"]
    E["Key Finding: Market Efficiency Implies P = NP"]
    F["Implication: If P ≠ NP, Markets are Not Fully Efficient"]
    
    A --> B
    B --> C
    C --> D
    D --> E
    E --> F