Aharonov–Bohm Type Arbitrage and Homological Obstructions in Financial Markets

Battle Count: 72

The paper provides a novel theoretical perspective on arbitrage as a global (holonomy) phenomenon rather than a local price inconsistency. While intellectually stimulating and potentially foundational, it is highly abstract and does not provide directly implementable trading algorithms. The framework could inform the design of global market consistency checks and exotic arbitrage detection systems, but practical implementation would require significant additional work in discretization, computational methods, and empirical validation. The self-financing strategy construction (Section 6) is the most directly relevant component, but it remains theoretical.

Extremely high complexity. Requires deep expertise in category theory (functors, natural transformations, nerves of categories), algebraic topology (simplicial homology, holonomy), measure-theoretic probability (conditional expectation, Radon-Nikodym derivatives), and stochastic analysis. The recursive simplicial distortion operator involves nested transported multiplicative accumulation that is non-trivial to compute. No code or algorithms are provided. Practical implementation would require constructing the time category, defining the filtration functor, computing conditional expectations in L1 spaces, and verifying admissibility conditions—all non-trivial computational tasks.

The paper is a theoretical mathematics paper with complete proofs and two finite illustrative examples (Sections 7.1 and 7.2) that can be independently verified. However, the framework is highly abstract and requires deep expertise in category theory, simplicial homology, and measure-theoretic probability. No computational code or empirical data is provided. The mathematical constructions are self-contained and verifiable by experts in the field.