Dual Attainment in Multi-Period Multi-Asset Martingale Optimal Transport and Its Computation

Battle Count: 56

Highly relevant to quantitative trading and structured products desks. The paper provides rigorous theoretical foundations for model-independent pricing and hedging of complex multi-asset derivatives (autocallables, worst-of options, baskets) that are actively traded in equity-linked markets. The dual attainment result directly justifies the existence of optimal hedging strategies. The numerical methodology using PDLP demonstrates practical solvability of large-scale MOT problems. However, the paper is primarily theoretical, and the numerical component is illustrative rather than a production-ready trading system.

High implementation complexity. Requires deep understanding of martingale optimal transport theory, convex order, irreducibility conditions, and infinite-dimensional linear programming. The numerical implementation requires GPU-accelerated LP solvers (NVIDIA cuOpt with PDLP), careful discretization of the MOT problem, construction of marginal distributions from market data via Breeden-Litzenberger formula, and handling of relaxed martingale constraints. The theoretical proofs involve advanced functional analysis techniques (Komlos lemma, local L1 bounds, convex envelopes).

The paper provides detailed mathematical proofs (Section 7) and describes the numerical methodology (PDLP in NVIDIA cuOpt). However, the specific market data (option prices as of December 5, 2025) is proprietary and not publicly available. The PDLP algorithm is publicly available, but reproducing the exact numerical results requires access to the same market data and GPU hardware. The theoretical results are fully self-contained with complete proofs.