Stability of weak supermartingale optimal transport problems

Battle Count: 78

The paper is primarily a pure mathematics contribution to optimal transport theory. However, martingale and supermartingale optimal transport have direct connections to model-independent pricing and hedging in mathematical finance. The supermartingale constraint (conditional barycentre ≤ x) corresponds to no-arbitrage conditions for certain derivative pricing problems. The stability results ensure that small perturbations in marginal distributions (e.g., from market data estimation) lead to small changes in optimal transport values, which is practically relevant. The monotonicity principle could inform the structure of optimal hedging strategies. However, the paper does not directly propose trading strategies or computational methods.

This is a highly theoretical paper with no computational implementation. The proofs involve sophisticated techniques: irreducible decomposition of supermartingale couplings, adapted Wasserstein topology, put function characterizations, barycentre corrections, and Strassen-type theorems. The mathematical machinery is advanced and requires deep expertise in optimal transport, stochastic orders, and measure theory. Even if one wanted to implement related numerical schemes, the paper provides no algorithmic guidance.

The paper is a pure mathematics paper with complete proofs provided. All definitions, lemmas, and theorems are stated precisely with full proofs in Sections 3 and 4, plus Appendix A. No computational experiments are needed. Reproducibility depends on the reader's ability to verify the mathematical arguments. The paper builds on well-established prior work (Beiglböck, Jourdain, Margheriti, Pammer [12,13]; Nutz-Stebegg [32]) with clear references.