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

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.