Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret with Infinite Variance

Researcher Hangyi Zhao has published a significant theoretical paper titled 'Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret with Infinite Variance' that addresses a critical challenge in AI-driven trading systems. The work tackles the problem of designing optimal trading algorithms when market valuations exhibit heavy-tailed distributions with potentially infinite variance—a realistic scenario in volatile financial markets where extreme price movements are common. Zhao extends previous theoretical results from bounded to real-valued valuations, proving that the expected regret of any pricing strategy satisfies specific mathematical bounds under minimal assumptions.

The paper's key contribution is establishing exact minimax rates for this problem class. Zhao proves that an epoch-based algorithm achieves regret bounds of Õ(T^{1-2β(p-1)/(βp+d(p-1))}) when the noise has finite p-th moment for p∈(1,2) and the market value function is β-Hölder continuous. This result interpolates between classical nonparametric rates when p=2 and trivial linear rates as p approaches 1 from above. The work also provides matching lower bounds via Assouad's method with a smoothed moment-matching construction, completing the theoretical characterization.

This research provides crucial theoretical foundations for AI agents operating in financial markets, particularly algorithmic trading systems and automated market makers. By establishing provable performance guarantees even when market data exhibits extreme volatility and infinite variance, the work enables more robust deployment of AI in real-world trading environments where traditional assumptions about normally distributed returns often fail dramatically.