Aharanov-Bohm Type Arbitrage and Homological Obstructions in Financial Markets

2026-04-12

AI Summary

This work proposes a novel notion of arbitrage rooted in global loop effects within filtered market systems, addressing the limitation of classical arbitrage theory, which focuses solely on local price discrepancies and fails to capture opportunities arising from the market’s global structure. By modeling market filtration as a contravariant functor and incorporating a multiplicative distortion induced by conditional expectations, the authors define the holonomy of loops in a temporal category, interpreting nontrivial holonomy as a manifestation of global inconsistency. Drawing an analogy to the Aharonov–Bohm effect—introduced here for the first time in finance—they establish a link between homological obstructions and economically realizable arbitrage. Under suitable admissibility conditions, the framework yields a predictable, self-financing trading strategy, thereby demonstrating the economic viability of this global loop-based arbitrage.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

We introduce a new notion of arbitrage based on global loop effects in filtered market systems. Given a filtration modeled as a contravariant functor $F : \mathcal{T}^{op} \to \mathrm{Prob}$, we consider the associated conditional expectation functor $\mathcal{E} \circ F$ and show that it induces a canonical multiplicative distortion $dF(i) := (\mathcal{E} \circ F)(i)(1)$, which measures the failure of constant functions to be preserved under non-measure-preserving transitions. We define the holonomy of $dF$ along loops in $\mathcal{T}$ and interpret non-trivial holonomy as a global inconsistency that is invisible at the level of individual transitions. This leads to a notion of Aharonov--Bohm (AB) arbitrage, in which arbitrage arises from loop effects rather than local price discrepancies. We further show that, under suitable admissibility conditions, non-trivial holonomy can be converted into a predictable self-financing trading strategy. This provides a conceptual link between cohomological structures and economically realizable arbitrage opportunities.

Problem

• arbitrage
• Aharonov-Bohm effect
• holonomy
• filtered market systems
• global inconsistency

Innovation

• Aharonov-Bohm arbitrage
• holonomy
• filtered market systems
• cohomological obstructions
• self-financing strategy