Admissible Information Structures, Immersion, and the Order of Non-Anticipative Aggregation

Battle Count: 62

The paper addresses foundational questions about information structures in asset pricing that underpin quantitative trading. The key insight that non-anticipativity fails to aggregate at order three (with masking dependence) has implications for multi-signal trading strategies: combining individually valid information sources can create hidden anticipativity. The distinction between information-admissibility failure (immersion) and no-arbitrage failure (NUPBR/ELMM) is practically relevant for understanding when enlarged information sets remain tradeable. However, the paper is purely theoretical with no direct algorithmic or implementation guidance, limiting its immediate practical applicability.

The paper requires deep expertise in stochastic calculus, filtration theory, martingale theory, and measure-theoretic probability. Understanding the masking construction, immersion preservation, and the Girsanov-type measure changes requires graduate-level mathematical finance knowledge. There is no computational implementation to reproduce; the 'complexity' lies entirely in the mathematical sophistication of the proofs and concepts. The correction of the earlier version adds a layer of subtlety requiring careful reading of both versions.

The paper is a pure theoretical mathematics paper with complete proofs for all stated theorems and propositions. All mathematical arguments are self-contained within the paper. Reproducibility depends on the reader's ability to verify stochastic calculus proofs. The correction of the earlier version (arXiv:2601.12541v1) is explicitly documented. No computational experiments or code are involved. The key constructions (masking relation with Rademacher variables, independent driver setup) are fully specified.