Adapted Wasserstein distance between the laws of SDEs
We consider an adapted optimal transport problem between the laws of Markovian stochastic differential equations (SDEs) and establish optimality of the so-called synchronous coupling between the given laws. The proof of this result is based on time-discretisation methods and reveals an interesting connection between the synchronous coupling and the celebrated discrete-time Knothe–Rosenblatt rear- rangement. We also provide a related result on equality of various topologies when restricted to certain laws of continuous-time stochastic processes. The result is of relevance for the study of stability with respect to model specification in mathematical finance.
The talk is based on joint work with Julio Backhoff-Veraguas and Ben Robinson.