An Infinite-Dimensional Insider Trading Game

Battle Count: 70

Highly relevant to quantitative trading in derivatives markets. The paper provides a rigorous theoretical foundation for understanding how informed traders construct option portfolios (straddles, spreads, risk reversals) based on private information about volatility, skewness, and tail risk. The cross-market price impact characterization (Corollary 4.3, 7.5) directly informs execution strategy and market impact modeling. The information efficiency results speak to how quickly prices incorporate information. However, the paper is purely theoretical with no direct algorithmic implementation or backtesting.

Extremely high mathematical complexity. Requires expertise in infinite-dimensional functional analysis, rough paths theory, reproducing kernel Hilbert spaces, Bayesian game theory, and stochastic calculus. The canonical reduction and scalar fixed-point characterization are elegant but the underlying machinery (pathwise Young integrals, Gâteaux derivatives on function spaces, Bochner integrals, logistic-normal posteriors) is advanced. Practical implementation would require significant numerical approximation of the infinite-dimensional objects.

The paper is a fully self-contained theoretical work with complete mathematical proofs. All assumptions are explicitly stated (Assumption 1), all theorems are proved rigorously, and the equilibrium construction is fully specified. The binary-signal example (Example 6.3) provides a concrete finite-dimensional illustration. No code or data is needed for verification—only mathematical reasoning.