Conservation of Short-term Flows: Signed Optimal Transport

Battle Count: 82

The paper is primarily a theoretical contribution to optimal transport and mathematical economics. Its relevance to quantitative trading is indirect: it provides a rigorous framework for analyzing interbank liquidity flows, systemic risk contagion, and network structural changes. The signed transport formulation naturally captures net flows (assets minus liabilities) in financial networks. However, it does not propose trading strategies, alpha signals, or direct market microstructure models. The framework could inform risk management and network-based trading signal construction but requires substantial additional work for practical trading applications.

Extremely high complexity. Requires deep expertise in: (1) functional analysis and spectral theory of unbounded operators, (2) harmonic analysis on locally compact abelian groups, (3) variational calculus in infinite-dimensional spaces, (4) optimal transport theory, (5) operator theory (closed range theorem, duality). The algorithm (Algorithm 1) involves computing spectral multipliers, Green's operators, and block matrix inversions in function spaces. Practical implementation would require significant numerical analysis expertise and careful handling of discretization on group structures.

Purely theoretical paper with complete mathematical proofs but no code, no empirical experiments in the main text, and no publicly available implementation. The empirical analysis framework is deferred to an Online Appendix. Reproduction requires deep expertise in functional analysis, harmonic analysis on groups, and variational methods.