Convergence of Sinkhorn’s Algorithm for Entropic Martingale Optimal Transport Problem
研究了熵正则化鞅最优运输问题的对偶形式，证明了Sinkhorn算法在温和条件下指数收敛，为求解该问题提供了理论基础，对随机波动率模型校准有用。
In this paper, we study the entropic martingale optimal transport (EMOT) problem on [Formula: see text]. The investigation of the EMOT problem arises in the calibration problem of the stochastic volatility models, where martingale constraints reflect no-arbitrage pricing conditions under the risk-neutral measure, as originally proposed by Henry-Labordère. We first establish the dual formulation of the EMOT problem and prove that Sinkhorn’s algorithm achieves an exponential convergence rate under mild conditions. Notably, our analysis does not presuppose the existence of optimal potentials and rigorously confirms the absence of a primal-dual gap. These results provide a theoretical foundation for solving EMOT via Sinkhorn’s method and constructing the optimal distribution from dual coefficients. Funding: Z. Ren’s research was supported by EXCELLENCES/SPRINGBOARD - UP SACLAY - Soutien recherche et attractivité France 2030 [Grant ANR-21-EXES-0003], PEPR PDE-AI project, and the Finance for Energy Market Research Centre.