Admissible Information Structures and the Non-Existence of Global Martingale Pricing

2026-01-18

AI Summary

This study addresses the existence of a unified admissible information structure under which all assets simultaneously become martingales in multi-asset pricing when economic drivers are not fully spanned by traded assets. Treating the information flow as endogenously determined by admissibility and temporal ordering, the paper integrates an endogenous filtering framework with Doob–Meyer decomposition and discrete-time martingale theory to uncover a fundamental obstruction to globally extending locally admissible martingale measures: the presence of just three independent, unspanned finite-variation drivers suffices to preclude the existence of a global martingale measure, and this condition is sharp. The work further establishes that global martingale pricing generally fails under admissible information structures and demonstrates numerically how admissibility suppresses predictable components, whereas inadmissible filters induce systematic predictability.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Adversarial Agents
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• Security and Privacy: Large-scale security measurements

Abstract

No-arbitrage asset pricing characterizes valuation through the existence of equivalent martingale measures relative to a filtration and a class of admissible trading strategies. In practice, pricing is performed across multiple asset classes driven by economic variables that are only partially spanned by traded instruments, raising a structural question: does there exist a single admissible information structure under which all traded assets can be jointly priced as martingales?. We treat the filtration as an endogenous object constrained by admissibility and time-ordering, rather than as an exogenous primitive. For any finite collection of assets, whenever martingale pricing is feasible under some admissible filtration, it is already feasible under a canonical minimal filtration generated by the asset prices themselves; these pricing-sufficient filtrations are unique up to null sets and stable under restriction and aggregation when a common pricing measure exists. Our main result shows that this local compatibility does not extend globally: with three independent unspanned finite-variation drivers, there need not exist any admissible filtration and equivalent measure under which all assets are jointly martingales. The obstruction is sharp (absent with one driver and compatible pairwise with two) and equivalent to failure of admissible dynamic completeness. We complement the theory with numerical diagnostics based on discrete-time Doob--Meyer decompositions, illustrating how admissible information structures suppress predictable components, while inadmissible filtrations generate systematic predictability.

Problem

• martingale pricing
• admissible information structures
• unspanned drivers
• filtration
• no-arbitrage

Innovation

• admissible information structures
• martingale pricing
• filtration endogeneity
• dynamic completeness
• Doob–Meyer decomposition