Rough Path Theory Reveals Market Limitations.

Rough Path Theory Reveals Market Limitations. A new mathematical framework challenges the boundaries of modern financial modeling. Researchers establish a "Rough Kreps-Yan" theorem demonstrating that continuous frictionless markets based on rough path theory inevitably collapse back to classical semimartingale models. The study analyzes unbiased rough integrators across different portfolio strategies, showing that as trading strategies become more sophisticated, from Markovian to signature-based approaches, the admissible market models narrow dramatically. This finding clarifies fundamental constraints in extending beyond traditional stochastic calculus for asset pricing. The research suggests rough path theory, while theoretically elegant, cannot escape the classical paradigm for arbitrage-free markets without friction.