Convergence of Sinkhorn's Algorithm for Entropic Martingale Optimal Transport Problem

Abstract: In this paper, we study the Entropic Martingale Optimal Transport (EMOT) problem on R. We begin by introducing the dual formulation and prove the exponential convergence of Sinkhorn's algorithm on the dual potential coefficients. Our analysis does not require prior knowledge of the optimal potential and confirms that there is no primal-dual gap. Our findings provide a theoretical guarantee for solving the EMOT problem using Sinkhorn's algorithm. In applications, our result provides insight into the calibration of stochastic volatility models, as proposed by Henry-Labordere.