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

Alejandro Rodriguez Dominguez

Papers from arXiv.org

Abstract: This version corrects and supersedes an earlier preprint (arXiv:2601.12541) whose central impossibility theorem was incorrect; the nature of the error and its correction are stated explicitly in Section 1.1. We retain the parts that are valid - the local reduction of pricing to the natural price filtration and its stability properties - and we replace the erroneous global non-existence claim with the statement that is actually true. Two facts are established. First, when the information structure is treated as an admissible (immersion-preserving) enlargement, local martingale pricing reduces to the natural price filtration, and this reduction is stable under restriction and under aggregation when a common pricing measure exists. Second, non-anticipativity of information does not aggregate: there exist signals, each individually and pairwise non-anticipative with respect to the reference Brownian filtration, whose joint observation reveals a function of a future increment; the failure first occurs at order three and is invisible to every lower-order test. We show that this aggregation failure requires dependence among the signals (a masking relation), not independence, and that it is an obstruction at the level of information admissibility (immersion), not at the level of no-arbitrage: the enlarged market continues to admit a local martingale deflator. We situate the results relative to the filtration-reduction program of Grigorian and Jarrow and relate the admissibility notion to predictive (Granger) and interventionist (Pearl) causality.

Date: 2026-01, Revised 2026-06
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