Paper: arXiv 2601.12541

Authors: Alejandro Rodriguez Dominguez

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 2.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly rigorous mathematical analysis challenging a foundational assumption in asset pricing by treating filtrations as endogenous objects. While it lacks empirical validation using real-world market data, it offers strong theoretical novelty and formal proofs regarding global martingale pricing and dynamic completeness.

Research Flowchart

  flowchart TD
    A[Research Goal: Does a single admissible global filtration exist to jointly price all assets?] --> B[Input: Finite asset collection driven by 1-3 unspanned finite-variation processes]
    B --> C[Method: Endogenous Filtration Analysis & Minimal Asset-Generated Filtrations]
    C --> D[Computation: Discrete-time Doob-Meyer Decompositions & Predictability Diagnostics]
    D --> E[Outcome 1: Local pricing-sufficient filtrations are unique and stable]
    D --> F[Outcome 2: Global pricing fails with 3 drivers due to lost dynamic completeness]