Dynamic Characterization of Barycentric Optimal Transport Problems and Their Martingale Relaxation

Battle Count: 94

While optimal transport and martingale transport have deep connections to model-independent finance (e.g., bounds on option prices, robust hedging), this paper is purely theoretical mathematics. The results on barycentric transport and martingale relaxation could theoretically inform model-independent pricing frameworks, but no direct trading applications, numerical methods, or empirical results are presented. The connection to quantitative trading is indirect through the broader literature on martingale optimal transport in finance.

This is a pure mathematics paper requiring advanced knowledge of stochastic calculus, optimal transport theory, convex analysis, and measure theory. There is no code or algorithm to implement. Understanding the proofs requires expertise in: (1) Benamou-Brenier dynamic formulations, (2) martingale representation theorem, (3) disintegration of measures, (4) convex order theory, (5) stretched Brownian motions and Bass martingales. The mathematical sophistication is very high.

Pure mathematics paper with complete self-contained proofs. All theorems (Theorem 1, Theorem 2) are proven rigorously within the paper. Key auxiliary results (Propositions 3, 4, 5) are cited from existing literature with precise references. No computational experiments or data are involved, making the results fully verifiable by mathematical reasoning.